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Book of abstracts
Book of Abstracts
The Eleventh International School on Theoretical Physics
Symmetry and Structural Properties of Condensed Matter
(SSPCM 2014)
Rzeszów, Poland
Rzeszów University of Technology
September 1-6, 2014
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Detailed program of the conference
Monday, September 1, 2014
7:30 - 8:30
7:30 - 8:30
9:00 - 10:30
10:30 - 11:15
11:15 - 11:45
11:45 - 13:15
13:15 - 14:30
14:30 - 16:00
16:00 - 16:20
16:20 - 16:40
16:40 - 17:00
17:00 - 17:20
Registration
Opening
Session I
Boris Altshuler, Columbia University, New York, USA
Anderson localization
Jamal Berakdar, Martin-Luther University, Halle, Germany
Multiferroic dynamics
coffee break
Efim Kats, Landau Institute for Theoretical Physics, Moscow, Russia
Landau theory of week crystallization and its application
lunch
Session II
Patrick Bruno, European Synchrotron Radiation Facility, Grenoble, France
Geometric phase in quantum magnets
coffee break
Miguel Araujo, Universidade de Évora, Portugal
Effect of Majorana fermions on Andreev spectroscopy of multiband topological superconductors
Paweł Zi˛eba, University of Rzeszów, Poland
Relaxation and luminescence of cavity polaritons in an external magnetic field
Ireneusz Weymann, Adam Mickiewicz University, Poznań, Poland
Transport properties of quantum dots coupled to ferromagnetic and superconducting leads
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Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Tuesday, September 2, 2014
9:00 - 10:30
10:30 - 11:15
11:15 - 11:45
11:45 - 12:30
12:30 - 13:15
13:15 - 14:30
14:30 - 15:15
15:15 - 16:00
16:00 - 16:20
16:20 - 17:20
17:20 - 17:40
17:40 - 18:00
Session III
Apostolos Vourdas, University of Bradford, UK
Dempster-Shafer probabilities in d-dimensional quantum systems and the large d limit
Tadeusz Lulek, Adam Mickiewicz University, Poznań, Poland
Rigged string configurations, Bethe Ansatz qubits, and conservation of parity
coffee break
Karol I. Wysokiński, Maria Curie - Skłodowska University, Lublin, Poland
Quantum transport in hybrid nanostructures
Elżbieta Zipper, University of Silesia, Katowice, Poland
Complex nanostructures as single electron transistors and current rectifiers
lunch
Session IV
Arkadiusz Wójs, Wrocław University of Technology, Poland
Composite fermions and topological quantum liquids
Marek Szopa, University of Silesia, Katowice, Poland
Entanglement in quantum game theory
coffee break
Karol Penson, Sorbonne Universités, Paris, France
t. b. a.
Magdalena Margańska, University of Regensburg, Germany
Valley-mixed states and energy splitting as a finite size effect in chiral carbon nanotubes
Marian Kuźma, University of Rzeszów, Rzeszów, Poland
Symmetry- induced hybridization in hexagonal and zinc-blende CrTe crystals
SSPCM-iv
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Wednesday, September 3, 2014
9:00 - 10:30
10:30 - 11:15
11:15 - 11:45
11:45 - 13:15
13:15 - 14:30
14:30 - 16:00
16:00 - 16:20
16:20 - 18:00
18:30 - 19:30
Session V
Claudine Lacroix, Institut Neel, CNRS, Grenoble, France
Fermi surface instabilities in Kondo alloys and Kondo lattice
Jakub Tworzydło, University of Warsaw, Poland
Quantum phase transitions of a disordered antiferromagnetic topological insulator
coffee break
Józef Spałek, Jagiellonian University, Kraków, Poland
Real space pairing in high-Tc and heavy-fermion systems and comparison to experiment
lunch
Session VI
Włodzimierz Zawadzki, Institute of Physics PAS, Warsaw, Poland
Reservoir model for two-dimensional electron gases in quantizing magnetic fields
coffee break
POSTER SESSION
concert
Thursday, September 4, 2014
9:00 - 10:30
10:30 - 11:15
11:15 - 11:45
11:45 - 13:15
13:15 - 14:30
14:30 - 16:00
16:00 - 16:20
18:00 -
Session VII
Jaroslav Fabian, Universität Regensburg, Germany
Spin phenomena in graphene
Józef Barnaś, Adam Mickiewicz University, Poznań, Poland
Molecular spintronics
coffee break
Alexei Tsvelik, Brookhaven National Laboratory, USA
Topological Kondo effect
lunch
Session VIII
Feo Kusmartsev, Loughborough University, UK
Topological insulators and Majorana fermions
coffee break
excursion/banquet
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Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Friday, September 5, 2014
9:00 - 10:30
10:30 - 11:15
11:15 - 11:45
11:45 - 13:15
13:15 - 14:30
14:30 - 16:00
16:00 - 16:20
16:20 - 17:50
Session IX
Mikhail Katsnelson, Radboud University, Nijmegen, The Netherlands
Effective electron-electron interaction and many-body effects in graphene
Małgorzata Śliwińska-Bartkowiak, Adam Mickiewicz University, Poznań, Poland
t. b. a.
coffee break
Evgeny Sherman, Universidad del Pais Vasco, Bilbao, Spain
Spin relaxation in solids: from nuclear magnetic resonance to gauge field theory
lunch
Session X
Alexander Khaetskii, University at Buffalo, New York, USA
Spin-orbit interaction and related transport phenomena in 2D electron and hole system
coffee break
Arthur Ernst, Max-Planck- Institut für Mikrostrukturphysik, Halle, Germany
First principles material design
Saturday, September 6, 2014
9:00 - 10:30
10:30 - 11:00
11:00 - 12:30
12:30 - 13:00
13:00 - 14:00
Session XI
Jairo Sinova, Texas A&M University, College Station, USA
Joining spin-dependent transport phenomena and magnetization dynamics for future MRAM technology
coffee break
Vitor Vieira, Instituto Superior Tecnico, Lisbon, Portugal
Non-Markovian effects in the Lindblad master equation approach to electronic transport
Closing
lunch
SSPCM-vi
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
List of abstracts
Oral abstracts
1 Effect of Majorana fermions on Andreev spectroscopy of multiband topological superconductors
A. C. Silva, M. A. N. Araujo, P. D. Sacramento
2 Multiferroic dynamics
A. Sukhov, L. Chotorlishvili, R. Khomeriki, P. Horley, C.L. Jia, S. Ru Ffo, J. Berakdar
3 First principles material design
A. Ernst
4 Spin physics in graphene
J. Fabian
5 An algorithm for the determination of tensor symmetries superposed by noise
B. Fiedler
6 Landau weak crystallization theory and its applications
E. Kats
7 Spin-orbit interaction and related transport phenomena in 2D electron and hole system
A. Khaetskii
8 Stabilization of cubic crystal structure in CrTe compounds
M. Kuźma
9 Influence of doping on threshold performance of mid-IR QCL -a NEGF based picture
G. Hałdaś ,A. Kolek
10 Kondo effect: from magnetic impurities, to Kondo lattice
C. Lacroix
11 Rigged string configurations, Bethe Ansatz qubits, and conversion of parity
T. Lulek
12 Valley-mixed states and energy splitting as a finite size effect in chiral carbon nanotubes
M. Margańska, P. Chudziński, M. Grifoni
13 Spin relaxation in solids: from nuclear magnetic resonance to gauge field theory
E. Ya. Sherman
14 Entanglement in quantum game theory
M. Szopa
15 Undulator-like radiation and cooperative phenomena in semiconductor microstructures with grating
I. Tralle, P. Zi˛eba
16 Non-Markovian effects in the Lindblad master equation approach to electronic transport
P. Ribeiro, V. Vieira
17 Dempster-Shafer probabilities in d-dimensional quantum systems and the large d limit
A. Vourdas
18 Composite fermions and topological quantum liquids
A. Wójs
19 Transport properties of quantum dots coupled to ferromagnetic and superconducting leads
I. Weymann, K. P. Wójcik, P. Trocha
20 Quantum transport in hybrid nanostructures
K. I. Wysokiński
21 Reservoir model for two-dimensional electron gases in quantizing magnetic fields
W. Zawadzki
22 Relaxation and luminescence of cavity polaritons in an external magnetic field
P. Zi˛eba, B. Pi˛etka, I. Tralle, J. Łusakowski
SSPCM-vii
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
23 Complex nanostructure as a single electron transistor and current rectifier.
E. Zipper, A. Gorczyca-Goraj, I. Janus-Zygmunt, B. Kedzierska, M. Kurpas, M. M. Maśka
Poster Session
24 Local Kondo temperatures in atomic chains
R. Agundez, J. Salfi, S. Rogge, M. Blaauboer
25 Photon-assisted thermoelectric effects in ferromagnet-quantum dot-ferromagnet system with additional superconducting lead
K. Bocian, W. Rudziński
26 Interaction effects in low-buckled graphene-like crystals
E. Castro
27 Dynamics of Localized Modes in a Composite Multiferroic Chain
L. Chotorlishvili, R. Khomeriki, A. Sukhov, S. Ruffo, J. Berakdar
28 Ultrasonic methods of the cells separation in human blood
H. Czyż, A. Włoch, T. Jasiński
29 Bound Magnetic Polaron in 2D System with the Strong Spin-Orbit Interaction
K. Denisov, N.S. Averkiev
30 Current induced spin polarization in magnetized graphene with Rashba spin-orbit interaction
A. Dyrdał, J. Barnaś, V. K. Dugaev
31 Size and Impurities Effects on Resistivity of Ultra-Thin Metallic Layer
A. Działo, A. Paja
32 Electrical properties of aluminium oxide-ethylene glycol (Al2 O3 − EG) nanofluids
J. Fal, G. Żyła, M. Cholewa
33 Thermodynamics of the exactly solvable spin-electron tetrahedral chain
L. Gálisová
34 Simulations of Guided Vortex Motion in Type II Superconductors with Asymmetric Corrugated Channels and
Oscillating Vortex Radii
R. Glavey
35 Spin pumping and charge-spin current injection in graphene with Rashba spin-orbit interaction
M. Inglot, V. Dugaev, E. Ya. Sherman, J. Barnaś
36 Some exact results in the one-dimensional attractive Hubbard model
D. Jakubczyk
37 A partial classification of bipartite entanglement in multipartite systems
P. Jakubczyk, Y. Kravets
38 Quantum entanglement of two dipolar particles within a Harmonic Trap
P. Kościk
39 Scanning gate microscopy simulations of the quantum Hall electron interferometer
K. Kolasiński, Bartłomiej Szafran
40 Two-electron resonances in quasi-one dimensional quantum dots with Gaussian confinement
A. Kuroś
41 Spin-orbit coupling in pure and hydrogenated carbon nanotubes in a transverse electric field
M. Kurpas, M. Gmitra, J. Fabian
42 Crystallographic interpretation of Galois symmetries for magnetic pentagonal ring
J. Milewski, T. Lulek, M. Łabuz
43 New approach to the design of tunable THz-detector
I. Tralle, G. Hałdaś, K. Majchrowski A. Kolek
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Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
44 A method for measuring thermal conductivity of liquid by using a laser beam
J. Mamczur, A. Wasilewski, T. Wi˛ecek
45 Self-energy electronic structure renormalization effects in first-principles calculations of solids
A. Marmodoro, P. Trevisanutto, L. Sandratskii, A. Ernst
46 Semi-Classical Phase Space dynamics for the Quantum Toffoli Gate
B. M. S. Mera, P. Mateus, N. Paunkovic, R. Loura, V. R. Vieira
47 Imaging localization of resonant states in antidots defined within a finite graphene flake
A. Mreńca, K. Kolasiński, B. Szafran
48 Spin polarization without magnetic field in a spin-orbit-coupled quantum point contact
M. P. Nowak, B. Szafran
49 Simulations of spin-valley transitions in single and double quantum dots defined in carbon nanotube
E. N. Osika, A. Mreńca, B. Szafran
50 Majorana Fermions in Disordered Multichannel Wires
B. Pekerten, Ö. Bozat, A. Teker, M. Wimmer, İ. Adagideli
51 Transport properties of twisted bilayer nanoribbon systems
M. Z. Pelc, L. Chico, E. Suárez Morell, M. Pacheco and L. Brey
52 Spin dynamics in asymmetric and macroscopically symmetric (110)-grown quantum wells
A. Poshakinskiy, S.A. Tarasenko
53 Focussing of electrons in graphene by n-p and n-p-n junctions
K. Reijnders, M. Katsnelson
54 Supercapacity of soft-expanded graphite in Li-intercalational electric current generation
R. Ya. Shvets, I. I. Grygorchak, A. S. Kurepa, N. T. Pokladok, Yu. I. Sementsov, G. I. Dovbeshko, Ye. Sheregii, B.
Seredyuk
55 An influence of dephasing processes on the ’2kF ‘ scattering mechanism of conduction electrons in the threedimensional structurally disordered systems
B. Spisak, M. Wołoszyn
56 Combinatorics of Lax objects in Bethe Ansatz
R. Stagraczyński
57 Strain designed magnetic properties in III-V semiconductors
S. Stagraczyński, C. Jasiukiewicz, V. K. Dugaev, J. Berakdar
58 Theoretical study of ferromagnetic resonance in thin composite multiferroic structures
A. Sukhov, P.P. Horley, C.-L. Jia, L. Chotorlishvili, D. Sander, J. Berakdar
59 Resonant tunneling in a semiconductor structure
T. Szczepański, V. K. Dugaev
60 Spin-transport dependence on spin-orbit interaction in MTJs
M. Titova, A. V. Vedyaev, N. V. Ryzhanova, M. Ye. Zhuravlev, N. V. Strelkov, E. Y. Tsymbal, B. Dieny
61 Interference of mobits in Quantum Cognition Models
S. Topolewicz
62 Density of electron states and relaxation time of intercalated layer crystals
N. Tovstyuk
63 Three-component gyrotropic metamaterial
I. Tralle, P. Zi˛eba, W. Paśko
64 Measuring System for Observation of Electric Parameters of Graphene in Presence of Temperature Gradient
M. Trybus, B. Woś, T. Ciuk, M. Inglot
65 Magnetic band Brillouin zone of an electron in a periodic potential and quantized magnetic field
A. Wal
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Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
66 Electric and thermoelectric properties of T-shaped double quantum dots coupled to ferromagnetic leads
K. P. Wójcik, I. Weymann
67 An investigation of the dynamic Young’s modulus for twisted fibers
A. Wasilewski, T. Wi˛ecek
68 Spin and charge transport through the Fe/MgO/GaAs heterostructure
S. Wolski, V. K. Dugaev, J. Barnaś, T. Slobodskyy, W. Hansen
69 Density functional theory simulation of an electrostatic defined graphene quantum dot
D. Żebrowski, B. Szafran
70 Changes of nanoparticles agglomerates sizes during rotation measurement of rheological properties of MgAl2 O4 diethylene glycol nanofluids
G. Żyła, M. Cholewa
72
Index of Authors
SSPCM-x
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Effect of Majorana fermions on Andreev spectroscopy of multiband topological
superconductors
A NA C. S ILVA1 , M IGUEL A. N. A RA ÚJO1,2 , AND P EDRO D. S ACRAMENTO1
1
CFIF, Instituto Superior Técnico, Universidade de Lisboa,
Av. Rovisco Pais, 1049-001 Lisboa, Portugal
[email protected]
2
Departamento de Fı́sica, Universidade de Évora, P-7000-671, Évora, Portugal
ABSTRACT
We consider models for multiband topological superconductors with two orbitals per lattice site. The
bands’ topological numbers can be varied as function of hopping parameters. The appropriate wave function matching conditions for an interface with a normal metal were previously derived in the framework
of a quantum waveguide theory [1]. This theory predicts the Andreev bound states’ dipersion successfully. Concentrating on the Andreev reflection problem, we obtain the differential conductance, dI/dV, as
a function of bias voltage, which displays the contribution of Majorana fermions. Interface disorder is
also considered. By varying band structure parameters, topological transitions can be induced, whereby
the number of Majorana modes varies. We observe the effect of such transitions on the dI/dV curves.
References
[1]
Araújo M. A. N. and Sacramento P. D. Quantum waveguide theory of Andreev spectroscopy in multiband superconductors: the case
of iron pnictides, Physical Review B 79, 174529 (2009)
SSPCM-1
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Multiferroic dynamic
A. S UKHOV1 , L. C HOTORLISHVILI1 , R. K HOMERIKI1,2 , P. H ORLEY3 , C.L. J IA4 , S. RU F FO5 , AND J. B ERAKDAR1
1
Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, 06099 Halle/Saale, Germany
[email protected]
2
Physics Department, Tbilisi State University, 0128 Tbilisi, Georgia
3
Centro de Investigacion en Materiales Avanzados, Chihuahua/Monterrey, Mexico
4
Key Laboratory for Magnetism and Magnetic Materials of the Ministry of Education, Lanzhou, China
5
Dipartimento di Fisica e Astronomia and CSDC, Universita di Firenze, CNISM and INFN, Italy
ABSTRACT
Multiferroics (MF) are materials that exhibit coupled ferroic (magnetic, electric, or elastic) ordering
[1-3]. They can be in a single phase or synthesized, e.g., as composite ferroelectric- (FE)/ ferromagnetic (FM) nano- and multilayer structures. The latter show a substantially larger multiferroic coupling
strength as compared to bulk matter. MFs are useful for addressing fundamental questions regarding the
interplay between electronic correlation, symmetry, magnetism, and polarization. In addition, MFs allow for qualitatively new device concepts for steering magnetism (ferroelectricity) by electric (magnetic)
fields by virtue of the magnetoelectric coupling. Key issues of research concern the origin of the underlying multiferroic coupling mechanisms and how to handle efficiently the coupled magnetic/ferroelectric
excitations. This talk will be focused on the physics of FM/FE composites. Based on quantum as well
as classical and semiclassical models a possible MF coupling mechanism will be discussed as well the
dynamics of conversion of magnetic excitations and solitons into ferroelectric signals [4].
References
[1] Eerenstein W. et al. , Nature (London) 442, 759 (2006).
[2] Tokura Y. and Seki S., Adv. Mater. 22, 1554 (2010).
[3] Vaz C. A. F. et al. Adv. Mater. 22, 2900 (2010).
[4] Sukhov A. et al. J. Phys. D: Appl. Phys. 47, 155302 (2014), Horely P. et al. Phys. Rev. B 85, 054401 (2012); Chotorlishvili L. et al.
Phys. Rev. Lett. 111, 117202 (2013) , Jia C.L. et al. Phys.Rev. B (at press).
SSPCM-2
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
First-principles material design
A RTHUR E RNST1
1
Max-Planck-Institut für Mikrostrukturphysik, Halle, Germany
[email protected]
ABSTRACT
Development and engineering of new magnetic materials is one of the main goals in modern condensed matter physics. Thereby, first-principles simulations play a significant role in the design of new
materials. Nowadays ab-initio methods based on the density functional theory can provide very accurate
information about magnetic properties of realistic systems and has become a major supplement and alternative to the experiment. In my talk I present a general overview of the first-principles approach, which
is adapted for parameter-free calculations in the condensed matter physics. Starting from the many body
Hamiltonian I’ll systematically derive basic equations of modern first-principles methods and illustrate
the efficiency of them with various examples from my own research experience.
SSPCM-3
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Spin physics in graphene
JAROLAV FABIAN1
1
Institute for Theoretical Physics, University of Regensburg, Regensburg, Germany
[email protected]
ABSTRACT
Intrinsic spin-orbit coupling in graphene is relatively weak, some tens of micro eVs. On one hand,
this is good, as the projected intrinsic spin relaxation is also slow, on the order of microseconds. On the
other hand, a greater value for the spin-orbit interaction is desired for spin manipulation and spin-orbit
induced phenomena, such as the spin Hall effect. In this lecture I will review the basics of the spin-orbit
physics in graphene and show how to effectively increase the value of the spin-orbit interaction (to meVs)
by adding adatoms [1]. I will also discuss the spin relaxation problem in graphene: experiments get the
spin relaxation times of 100 ps, while theory predicts microseconds. The cause appears to be extrinsic,
due to impurities. I will argue that the mechanism is resonant scattering by a small concentration of
magnetic moments (wherever they come from) [2].
References
[1] M. Gmitra, D. Kochan, and J. Fabian, Spin-orbit coupling in hydrogenated graphene, Phys. Rev. Lett. 110, 246602 (2013).
[2] D. Kochan, M. Gmitra, and J. Fabian, Spin relaxation mechanism in graphene: resonant scattering by magnetic impurities, Phys. Rev.
Lett. 112, 116602 (2014).
SSPCM-4
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
An algorithm for the determination of tensor symmetries superposed by noise
B ERND F IEDLER1
1
Hochschule für Technik, Wirtschaft und Kultur Leipzig, Fakultät Maschinenbau und Energietechnik, Postfach 30 11 66, D-04251 Leipzig,
Germany
[email protected]
ABSTRACT
We consider tensors or other multilinear functions which have no symmetries in an exact sense but only
symmetries up to small errors (small deviations, noise). Such symmetries can not be found by algorithms
which search for exact symmetries.
We present an algorithm which can determine ”non-exact” symmetries. The algorithm uses discrete
Fourier transforms [1] and procedures from our algorithm [2].
References
[1]
Clausen, M. and Baum, U. 1993 Fast Fourier Transforms (Mannheim, Leipzig, Wien, Zürich: BI Wissenschaftsverlag)
[2]
Fiedler, B. 2001 Ideal decomposition and computation of tensor normal forms Seminare Lotharingien de Combinatoire B45g 16
pages (http://www.mat.univie.ac.at/ slc/ )
SSPCM-5
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Landau weak crystallization theory and its applications
E.I.K ATS1
1
Landau Institute for Theoretical Physics, RAS, 142432, Chernogolovka, Moscow region, Russia, and,
Moscow Institute of Physics and Technology, 141700, Dolgoprudny, Moscow region, Russia
ABSTRACT
Aim of this lecture is to explain main features and ingredients of weak first order phase transitions between liquid-like (uniform in space) and solid-like (non-uniform with characteristic wave vector q0 )
states. We illustrate how this theory (traditionally termed as Landau weak crystallization theory) works.
We consider two examples describing universal temperature dependence of shear viscosity in liquids,
and so-called main phase transition in membranes. Our results are in a good qualitative agreement with
experimental data, offering a deeper understanding of this kind of phase transitions. We discuss also why
and where predicted universal effects can be masked.
PACS: 64.60.A-, 64.70.D-, 64.70.qj
SSPCM-6
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Spin-orbit interaction and related transport phenomena in 2D electron and hole system
A LEXANDER K HAETSKII1
1
Department of Physics, University at Buffalo, SUNY, Buffalo, NY
[email protected]
ABSTRACT
Spin-orbit interaction is responsible for many physical phenomena which are under intensive study
currently. Here we discuss several of them.
The first phenomenon is the edge spin accumulation, which appears due to spin-orbit interaction in 2D
mesoscopic structures in the presence of a charge current. We consider the case of a strong spin-orbitrelated splitting of the electron spectrum, i.e. a spin precession length is small compared to the mean
free path l. The structure can be either in a ballistic regime (when the mean free path is the largest scale
in the problem) or quasi-ballistic regime (when l is much smaller than the sample size). We show how
physics of edge spin accumulation in different situations should be understood from the point of view
of unitarity of boundary scattering. Using transparent method of scattering states, we are able to explain
some previous puzzling theoretical results. In particular, we clarify the important role of the form of the
spin-orbit Hamiltonian, the role of the boundary conditions, etc., and reveal the wrong results obtained
in the field by other researchers. The relation between the edge spin density and the bulk spin current in
different regimes is discussed. The detailed comparison with the existing theoretical works is presented.
Besides, we consider several new transport phenomena which appear in the presence of spin-orbit interaction, for example, magnetotransport phenomena in an external classical magnetic field. In particular,
new mechanism of negative magnetoresistance appears which is due to destruction of spin fluxes by the
magnetic field, and which can be really pronounced in 2D systems with strong scatterers.
SSPCM-7
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Symmetry- induced hybridization in hexagonal and zinc-blende CrTe crystals
M ARIAN K U ŹMA1
1
Faculty of Mathematics and Natural Sciences, University of Rzeszów, Pigonia 1, 35-959 Rzeszów, Poland
[email protected]
ABSTRACT
Transition metal chalcogenides with zinc-blende structure are predicted theoretically to be half metallic and therefore, they are interesting for spintronic applications. However, the ground state of these
compounds is hexagonal of NiAs type. Here we investigate the stabilization of both phases . The hybridization in octahedral and tetrahedral lattice is studied for Cr Te and Cr2 Te3 crystals. The influence of
Cd impurities on stabilization of zinc- blende structure of Cr2 Te3 is addressed.
SSPCM-8
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Influence of doping on threshold performance of mid-IR QCL -a NEGF based picture
G RZEGORZ H AŁDA Ś1
1
AND
A NDRZEJ KOLEK1
Department of Electronics Fundamentals, Rzeszów University of Technology, Al. Powstańców Warszawy 12, 35-959 Rzeszów, Poland
[email protected]
ABSTRACT
Although not exclusively, most experiments on quantum cascade lasers (QCLs) emitting at midwavelength infrared (mid-IR) show monotonic increase of the threshold current with the doping of the
active layers localized in the injector. Such dependence was observed e.g. for InGaAs/AlInAs devices
lasing at 9µm and was attributed to the ”increased free carrier absorption in the core region” [1]. This
statement mirrors the current state of art of understanding this phenomenon. Numerical simulations
of the device like this in Ref. [1] performed with our nonequilibrium Greens function (NEGF) solver
[2][3] reveal, however, that apart from ISB (which moreover appears only in devices with improperly
design injector) the threshold current increases due to the thermal backfilling of lower laser subband
what destroys optical gain. We have been able to quantitatively describe this dependence with the scaling
relation binding threshold current density Jth and threshold voltage Uth . Namely,
Jth τ4 = a + ebns exp(−CeUth /kT )
where e is electronic charge, a, b, C are numerical coefficients, τ4 is the upper state lifetime and ns is the
sheet doping density of the active wells. This relation has been tested with the simulation data: threshold
I-V values for different doping and temperatures after appropriate rescaling collapse onto a single straight
line. Such test has been passed by m-IR QCL devices with properly designed injector e.g. like these in
Refs. [4][5]. We conclude that Eq. (1) becomes a general test that QCLs should pass in the case when
thermal backfilling of lower laser state is the major deteriorating process.
References
[1] T. Aellen, M. Beck, N. Hoyler, M. Giovannini, J. Faist, and E. Gini, ”Doping in quantum cascade lasers. I. InAlAs-InGaAs/InP
midinfrared devices”, J. Appl. Phys., 100, 043101 - 4p., 2006.
[2] A. Kolek, G Hałdaś, and M. Bugajski ”Nonthermal carrier distributions in the subbands of 2-phonon resonance mid-infrared quantum
cascade laser” Appl. Phys. Lett., 101, 061110 - 4p., 2012.
[3] G. Hałdaś, A. Kolek, and I. Tralle, ”Modeling of Mid-Infrared Quantum Cascade Laser by Means of Nonequilibrium Green’s Functions”, IEEE J. Quantum Electron., 47, pp. 878-885, 2011.
[4] A. Wittmann Y. Bonetti, J. Faist, E. Gini, and M. Giovannini, ”Intersubband linewidths in quantum cascade laser designs”, Appl.
Phys. Lett., 93, 141103-4p., 2008.
[5] A. Evans, S. R. Darvish, S. Slivken, J. Nguyen, Y. Bai, and M. Razeghi, ”Buried heterostructure quantum cascade lasers with high
continuous-wave wall plug efficiency”, Appl. Phys. Lett., 91, 071101-4p., 2007.
SSPCM-9
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Kondo effect: from magnetic impurities, to Kondo lattice
C LAUDINE L ACROIX1
1
Institut Néel, CNRS & Université de Grenoble, France
[email protected]
ABSTRACT
The Kondo effect was discovered more than 50 years ago and it is still an active field of research. It
was first observed in metals containing magnetic impurities; then similar effect was observed in quantum
dots. A review will be presented. When concentration of magnetic impurities is increasing, interactions
between impurities play a crucial role. The phase diagram of the Kondo lattice will be discussed. We
emphasize the possibility of strong changes of the Fermi surface topology, not necessarily associated with
any order parameter.
SSPCM-10
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Rigged string configurations, Bethe Ansatz qubits,
and conservation of parity
TADEUSZ L ULEK1
1
Faculty of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland
[email protected]
ABSTRACT
We consider a two-dim subspace h ∼
= C2 of the 27 -dim space of all quantum states of the heptagonal
ring of N = 7 nodes with spin 1/2, within the r = 3 spin deviation sector, and zero total quasimomentum, i.e. the centre of the Brillouin zone [1]-[2]. The space h is an example of a well defined qubit,
distinguished by its arithmetic properties, stemming from the structure of the eigenproblem of the Heisenberg Hamiltonian. More specificly, it is the eigenspace of the Hamiltonian, with the eigenvalue E = −5.
We examine the validity of Bethe Ansatz solution [3] for this qubit, given by the string configurations
{21} (Fig. 1).
It results that (i) Bethe Ansatz is valid also in this degenerate case, but (ii) the eigenstates provided by
Bethe Ansatz yield a distinguished basis in h: non-trivial superpositions of them, which are admissible
by degeneracy, do not have the form of rigged string configurations, and (iii) rigging by quasimomenta,
proposed in paper [4], reveals the symmetry of parity, presented manifestly in Fig. 1.
Figure 1. a) Rigged string configurations for the arithmetic qubit h. The two-string and one-string entering a complex are rigged by maximal quasimomenta
from the Brillouin zone B = {0, ±1, ±2, ±3} of the heptagon, giving zero total qusimomentum k = 0 of each complex. b) The corresponding pyramid
picture of rigged string configurations.
References
[1] Milewski J., Lulek B., Lulek T., Łabuz M., Stagraczyński R., Physica B 434, 14, 2014.
[2] Milewski J., Banaszak G., Lulek T., Łabuz M., Stagraczyński R., OSID 19, 1250012, 2012.
[3] Bethe H., Z. Physik 71, 205, 1931 (in German; English translation in: D.C. Mattis, The Many-Body Problem, World Sci., Singapore
1993, pp. 689-716.).
[4] Lulek B., Lulek T., Labuz M., Stagraczynski R., Physica B 405, 2654, 2010.
SSPCM-11
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Valley-mixed states and energy splitting as a finite size effect in chiral carbon
nanotubes
M AGDALENA M ARGA ŃSKA1 , P IOTR C HUDZI ŃSKI1 ,
1
AND
M ILENA G RIFONI1
Institute for Theoretical Physics, University of Regensburg, 93 053 Regensburg, Germany
[email protected]
ABSTRACT
The two main degrees of freedom of an electron in a carbon nanotube (CNT) are valley and spin.
The electronic spectra obtained in transport experiments on CNT quantum dots in parallel magnetic
field often show an anticrossing of spectral lines assigned to the opposite valleys. One source of this
phenomenon could be the disorder, with impurity induced scattering. However, we show that this effect
can be reproduced also in ultraclean CNTs, where it is caused solely by the presence of the boundaries.
It is therefore a finite size effect, not an inherent property of the CNT. We identify the nanotube chirality
class which supports this phenomenon and analyze its dependence on the CNT parameters and on the
distance from the charge neutrality point.
SSPCM-12
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Spin relaxation in solids: from paramagnetic and nuclear magnetic resonance to gauge
field theory
E.YA . S HERMAN1
1
Department of Physical Chemistry, Universidad del Pa is Vasco UPV-EHU, 48080 Bilbao, Spain and IKERBASQUE Basque Foundation
for Science, Bilbao, Spain
ABSTRACT
Nonequilibrium spin dynamics, usually seen as exponential decay of magnetization with time, became a topic
of a great interest in the studies of magnetic resonance in solids. Here the macroscopic magnetization is transferred
to the host lattice via a random in time interaction of the spins of individual localized electrons and nuclei with the
host. A theory, based on the conventional density matrix approach, was developed and applied to the understanding
of the width of the paramagnetic electron and nuclear spin resonances. One of the most important features in this
understanding is the "motional narrowing", that is a slow spin relaxation and, correspondingly, a narrow resonance
line in the presence of "fast" interactions between nuclei or electron’s spins and the environment [1].
At the beginning of 70th , spin-related phenomena in semiconductors became a rapidly developing research field and
spin relaxation due to spin-orbit coupling, cubic in the electron momentum, lavished a lot of attention. At that time,
semiconductor samples were bulk and still rather dirty, and the spin precession induced by spin-orbit coupling was
slow compared to the momentum relaxation. Here, the application of the Boltzmann kinetic equation gives the famous
Dyakonov-Perel’ relaxation mechanism, corresponding to the expected in this regime motion narrowing. With the
fast development of semiconductor technologies, two-dimensional electron systems with the linear in the momentum
spin-orbit coupling in the Rashba and Dresselhaus forms became available. For these couplings the Dyakonov-Perel’
mechanism worked well and interesting dependences of spin dynamics on the relative strength of the Rashba and
Dresselhaus terms were predicted and observed [2]. Recently, novel high-quality semiconductor structures, where
spin dynamics is not in the motion narrowing regime anymore, have been produced and studied.
It is interesting that this linear in momentum coupling can be described in terms of non-Abelian and, at certain
conditions, Abelian gauge field. In this gauge field theory approach, the analysis of the spin dynamics can be done in
a very general and elegant form, which allows to map spin and the particle density evolutions [3] both for irreversible
and reversible processes. Very recently, it was shown that artificial spin-orbit coupling can be optically produced
in ensembles of cold atoms, both bosonic and fermionic [4]. Relative strength of this coupling is much stronger
than can be achieved in semiconductors. This opens a venue to new effects, not seen in solid-state spintronics of
semiconductors, and described with the gauge theory approach. Some of these effects will be discussed as illustration.
References
[1] Principles of Magnetic Resonance (Springer Series in Solid State Sciences) by C. P. Slichter (1996).
[2] Spin Physics in Semiconductors (Springer Series in Solid State Sciences) by M. I. Dyakonov (2008).
[3] I.V. Tokatly and E.Ya. Sherman, Annals of Physics 325, 1104 (2010).
[4] V. Galitski and I.B. Spielman, Nature 494, 49 (2013).
SSPCM-13
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Entanglement in quantum game theory
M AREK S ZOPA1
1
Institute of Physics, University of Silesia, Uniwersytecka 4, 40-007 Katowice
[email protected]
ABSTRACT
In this paper we define the notion of a quantum game, for which players’ strategies are parameterized
by 3D rotations. Meta-strategies of the quantum game are correlated through the mechanism of quantum
entanglement and the result of the game is obtained by the collapse of the wave function. They can be
realized by quantum computers and they are completely safe against eavesdropping. Classical games
are particular examples of quantum games. Quantum games have richer class of Nash equilibria then
classical games. In this paper we show examples of quantum games and their corresponding classical
counterparts and show how can one utilize the additional quantum meta-strategies.
SSPCM-14
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Undulator-like radiation and cooperative phenomena in semiconductor microstructures
with grating
I. T RALLE1
1
AND
1
P. Z I EBA
˛
Faculty of Mathematics and Natural Sciences, Theoretical Physics Department University of Rzesz/’ow 35-310 Rzesz’ow, Poland
ABSTRACT
2
In this work the cooperative N - effect is considered, that is the radiation whose power is N 2 , where
N is the number of emitters which in this case is equal to the number of nonlinear coupled oscillators
which model the electrons in a bunch. We consider two different models: in first case the predicted effect
is the result of combining two others, namely Gunn-effect in GaAs and undulator-like radiation which can
be produced by means of microstructure with grating (microundulator) [1]. In the second case, suggested
effect is in a sense similar to Dicke superradiance, however it is not the spontaneous phase coherence
arising in the ensemble of two-level atoms interacting via the emitted electromagnetic field, but rather,
the result of interplay of another two effects. The first one is the ’pumping wave’ acting on the electrons
and which is the result of undulator field, while the second is the backward effect of radiation which
is produced by electrons moving within such microundulator. As a result, the specific phase coherence
(’synchronization’) develops in the ensemble of emitters and they start to generate as a single oscillating
charge Ne, while the power of emitted radiation becomes N 2 [2]. It is very probable, that the effect
can be used for the developing of a new semiconductor-based room temperature sources of the GHz and
THz-radiation.
References
[1] I.Tralle and P. Zi˛eba. Undulator-like radiation and cooperative phenomenon in semiconductor microstructure with grating. Acta phys
polon A, vol. 121, pp. 520-524 (2012)
[2] I. Tralle , P. Zi˛eba. Induced N2-cooperative phenomenon in an ensemble of the nonlinear coupled oscillators. Phy Lett A, 378, pp.
1364-1368 (2014)
SSPCM-15
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Non-Markovian effects in the Lindblad master equation approach to electronic transport
P EDRO R IBEIRO1
AND
V ÍTOR ROCHA V IEIRA1
1
CFIF, Instituto Superior Técnico, Universidade de Lisboa,
Avenida Rovisco Pais, 1049-001 Lisboa, Portugal
[email protected]
ABSTRACT
Non-equilibrium processes in open quantum systems can be generically described within the framework of the Lindblad master equation i.e. without a memory kernel. This statement holds even for
processes where information can flow-back from the environment to the system. This rather contraintuitive fact lead to define a process as non-Markovian if, during the time evolution of two different
initial states of the system, their distinguishability increases, reflecting a back-flow of information from
the environment to the system. However, for non-Markovian dynamics, the set of conditions to ensure
the positivity of the density matrix for all times is not known, making difficult the explicit construction
of non-Markovian Lindblad operators.
Using the Keldysh non-equilibrium Green’s functions, we explicitly solve a generic quadratic model
of electrons coupled at t = 0 to a set of wide-band baths characterised by temperature and chemical
potential. We identify the equivalent Lindblad operator describing the evolution of the density matrix and
show that the resulting dynamical process is generically non-Markovian. We further discuss the cases in
which Markovian dynamics is recovered.
We apply our approach to a simple model for electronic transport thought a one dimensional wire coupled
at t = 0 to wide-band metallic leads.
SSPCM-16
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Dempster-Shafer probabilities in d-dimensional quantum systems and the large d limit
A. VOURDAS1
1
Department of Computing, University of Bradford, Bradford BD7 1Dp, UK
[email protected]
ABSTRACT
The talk consists of two parts:
• In the first part, quantum probabilities in a quantum system with variables in Z(d), are interpreted
as Dempster-Shafer probabilities[1, 2]. The ‘quantum logic’ relevant to these systems is discussed.
• In the second part, inverse and direct limits are used to show that for large d we get a system with
b
positions in Q/Z (rational numbers on a circle) and momenta in the profinite group Z(for
a review
see [3]).
References
[1]
A. Vourdas, J. Phys. A, to appear
[2]
A. Vourdas, preprint
[3]
A. Vourdas, J. Phys. A46, 043001 (2013)
SSPCM-17
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Composite fermions and topological quantum liquids
A RKADIUSZ W ÓJS1
1
Institute of Physics, Wrocław University of Technology, 50-370 Wrocław, Poland
[email protected]
ABSTRACT
Fractional quantum Hall effect (FQHE) involves condensation of two-dimensional electrons in a high
magnetic field B into various topological quantum liquids at different Landau level (LL) filling fractions.
The key concept in the FQHE theory is emergence of ”composite fermions” (CFs) - electrons binding
an even number (2p) of vortices of the many-body wave function. The CFs are collective, topological
particles which can loosely be viewed as charge-e fermions in a reduced magnetic field B ∗ . Most of
about 75 filling factors at which FQHE has been observed so far belong to the so-called Jain sequence
ν = n/(2pn ± 1) which can be understood in terms of essentially free CFs filling an integral number
n of effective Landau-like ”Λ levels” (ΛLs). But there are also a few others, like ν = 5/2 or 4/11,
crucially dependent on complex residual interaction among the CFs, and remaining the subject of intensive experimental and theoretical investigation. In this lecture, I will present the electron liquids of
FQHE in the broader context of topological states of matter, introduce the grand concept of CFs, apply
it to the puzzling states represented by ν = 5/2 and 4/11, and review our recent (numerical) studies
giving new insight into the microscopic origin of their incompressibility. In particular, the 5/2 state [1]
which conventionally has been viewed as a p-type superconductor of interacting CFs made of electrons
half-filling the second LL and subject to B ∗ = 0, will be pictured in an original ”multi-flavor” model, in
which the essentially free CFs with additional discrete freedom completely fill the lowest ΛL [2,3]. I will
discuss predictions of this picture that go beyond the conventional ”B ∗ = 0” model and agree well with
(otherwise unexplained) experimental and numerical observations. As another example, I will discuss
the 4/11 state [4], which in the CF picture corresponds to the ν ∗ = 1/3 filled second ΛL, and hence
was initially expected to realize a Laughlin 1/3 state of CFs (i.e., second-generation state of CFs made
of CFs made of electrons). I will present evidence to the contrary - that this state has distinct microscopic
origin and hence realizes a different type of condensation [5]. I will also briefly discuss computational
methods applicable to these (correlated) systems with particular emphasis on exact diagonalization of
finite systems on the Haldane sphere
References
[1] R. Willett et al., Phys. Rev. Lett. 59, 1776 (1987)
[2] G. J. Sreejith, C. Tőke, A. Wójs, J. K. Jain, Phys. Rev. Lett. 107, 086806 (2011)
[3] G. J. Sreejith, A. Wójs, J. K. Jain, Phys. Rev. Lett. 107, 136802 (2011)
[4] W. Pan et al., Phys. Rev. Lett. 90, 016801 (2003)
[5] S. Mukherjee, S. S. Mandal, Y.-H. Wu, A. Wójs, J. K. Jain, Phys. Rev. Lett. 112, 016801 (2014)
SSPCM-18
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Transport properties of quantum dots coupled to ferromagnetic and superconducting
leads
I. W EYMANN1 , K. P. W ÓJCIK1 , AND P. T ROCHA1
1
Faculty of Physics, Adam Mickiewicz University, Poznań, Poland
[email protected]
ABSTRACT
We study the transport properties of quantum dots coupled to ferromagnetic and superconducting
leads. In the nonlinear response regime, by means of the real-time diagrammatic technique, we analyze
the behavior of the Andreev current and differential conductance by including the first and second-order
tunneling processes in the coupling to ferromagnetic leads. We find a zero-bias anomaly of the Andreev
differential conductance in the parallel configuration of the device, which is associated with a nonequilibrium spin accumulation in the dot triggered by Andreev processes [1]. Moreover, we also analyze the
linear response transport properties in the case of strong coupling to ferromagnetic leads, when the Kondo
effect can emerge. Using the numerical renormalization group method, we show that the transmission
due to Andreev processes strongly depends on the magnitude of exchange field due to the presence of
ferromagnetic leads, and the coupling strength to the superconducting lead [2].
References
[1]
I. Weymann, P. Trocha, Phys. Rev. B 89, 115305 (2014).
[2]
K. P. Wójcik, I. Weymann, Phys. Rev. B 89, 165303 (2014).
SSPCM-19
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Quantum transport in hybrid nanostructures
K AROL I ZYDOR W YSOKI ŃSKI1
1
Institute of Physics, M. Curie-Skłodowska University, Radziszewskiego 10, Pl 20-031 Lublin, Poland
ABSTRACT
The study of transport in nanodevices is of theoretical and practical interest. The presence of normal
metallic, ferromagnetic and/or superconducting electrodes adds new functionalities to the studied devices
and at the same time allows the observation of the interplay between various many body effects like
e.g. Kondo effect and Andreev scattering. Here we shall consider nanosystems containing quantum
dot or a molecule coupled to three external leads and analyse local and non-local conductivities and
thermoelectric effects. One of the systems discussed here consists of a quantum dot attached to normal,
ferromagnetic and superconducting lead. The system allows the observation of the pure spin current in
one of the electrodes. In the system with quantum dot coupled to a superconducting lead the proximity
effect induces pairing correlations on the quantum dot. In the subgap region one observes the anomalous
tunneling via direct and crossed Andreev scattering, whereas the usual single particle electronic transfer
is suppressed. The interactions of electrons on the dot leading to such phenomena as the Coulomb
blockade and the Kondo effect severely modify the currents flowing in the system. Thermal effects like
thermopower and voltages induced in the floating electrodes will be are also discussed. (This work has
been partially supported by the NCN grant DEC-2011/01/B/ST3/04428)
References
[1] Karol I. Wysokinski, Thermoelectric transport in the three terminal quantum dot, J. Phys. Condensed Matter 24, 335303 (2012)
[2] Grzegorz Michalek, Bogdan R. Bulka, Tadeusz Domanski, and Karol I. Wysokinski Interplay between direct and crossed Andreev
reflections in hybrid nanostructures Phys. Rev. B 88, 155425 (2013).
SSPCM-20
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Reservoir model for two-dimensional electron gases in quantizing magnetic fields
W ŁODZIMIERZ Z AWADZKI1
1
Institute of Physics, Polish Academy of Sciences, 02-668, Warsaw, Poland
ABSTRACT
We review works which treat two-dimensional electron gases (2DEGs) in quantum wells (QWs,
mostly GaAs/ GaAlAs heterostructures) in the presence of quantizing magnetic fields as open systems
in contact with outside reservoirs. If a reservoir is sufficiently large, it pins the Fermi level to a certain
energy. As a result, in a varying external magnetic field, the thermodynamic equilibrium will force oscillations of the electron density in and out of the QW. This leads to a number of physical phenomena in
magneto-transport, interband and intraband magneto-optics, magnetization, magneto- plasma dispersion,
etc. In particular, as first proposed by Baraff and Tsui, the density oscillations in and out of QW lead
to plateaus in the integer quantum Hall effect (IQHE) at values observed in experiments. The gathered
evidence, especially from magneto-optical investigations, allows us to conclude that, indeed, in most
GaAs/GaAlAs hetrostructures one deals with open systems in which the electron density in QWs oscillates as the magnetic field varies. Relation of the density oscillations to other factors, such as electron
localization, and their combined influence on the quantum transport in 2DEGs, is discussed. In particular,
a validity of the classical formula for the Hall resistivity is considered. The density oscillations can not
be regarded as the only source of plateaus in IQHE. Still, the reservoir approach should be included in
various descriptions of 2DEGs in the presence of a magnetic field.
SSPCM-21
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Relaxation and luminescence of cavity polaritons in an external magnetic field
1
2
P. Z I EBA
˛
, B. P I ETKA
˛
, I. T RALLE1 ,
1
AND
J. Ł USAKOWSKI2
Theoretical physics Department, Faculty of Mathematics and Natural Sciences, University of Rzeszów, Pigonia 1, Rzeszów, Poland
[email protected], [email protected]
2
Institute of Experimental Physics, faculty of Physics, University of Warsaw, Hoża 69, Warsaw, Poland
[email protected], [email protected]
ABSTRACT
Modern semiconductor technology allows the realization of nanostructures where both electronic and photonic states undergo quantum confinement. Thus, the recent development of quantum microcavity (QMC) structures has resulted in a major boost to both experimental and theoretical investigations of exciton- polariton phenomena in semiconductors. These phenomena attracted worldwide interest
due to their potential in polariton based devices, a possibility to create Bose-Einstein condensate and a formation of a superfluid state with
zero viscosity as wells as many others. Cavity polaritons are mixed states of light and matter formed as a result of the strong coupling
of quantum-well excitons with the photonic mode in the microcavity which embraces the quantum well [1]. The strong coupling regime
of cavity quantum electrodynamics [2] is particularly interesting because it is in this regime that one can best take advantage of the
coherent energy transfer between emitter and cavity modes to favor emission into the cavity mode over the other transversely propagating
modes, leading to the possibility of an efficient light-emitting diode LED or very low threshold laser. In the present work we investigate
the strong coupling regime for a semiconductor microcavity under an applied magnetic field. The results of numerical simulations of
polariton kinetics and luminescence are presented in Figs. 1-4. Fig. 1 shows the polariton distribution in the lower polariton branch vs
the in-plane wave vector at two different detunings, negative as well as positive ones at zeroth magnetic field and at B = 14T. Figs. 2 and
3 present the polariton distribution in the lower polariton branch vs in-plane wave vector at different magnetic fields as well as different
pumping (the number of generated polaritons per unite time and unite surface area). Fig. 4 shows luminescence from the lower polariton
branch at different values of the magnetic field. This work was supported by the NCN grant 2011/01/D/ST7/04088.
fig. 1
fig. 2
fig. 3
fig. 4
References
[1]
A. V. Kavokin, J. J. Baumberg, G. Malpuech, and F. P. Laussy, Microcavities, Oxford University Press, Oxford, 2007.
[2]
Y. Yamamoto, T. Tassone, H. Cao, Semiconductor Cavity Quantum Electrodynamics, Springer Verlag, Berlin 2000.
SSPCM-22
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Complex nanostructure as a single electron transistor and current rectifier.
E L ŻBIETA Z IPPER 1 , A NNA G ORCZYCA -G ORAJ1 , I WONA JANUS -Z YGMUNT1 , BARBARA K EDZIERSKA1 , M ARCIN K URPAS1 ,
M ACIEJ M. M A ŚKA1
1
AND
Institute of Physics, University of Silesia, ul Uniwersytecka 4, 40-007 Katowice, Polska
[email protected]
ABSTRACT
Conducting properties of a quasi two-dimensional nanostructure in the form of a quantum dot (QD)
surrounded by a quantum ring (QR) are discussed. This complex system is a highly controllable object.
It was shown [1] that by changing the confinement potential, e.g., by the electrical gating one can change
the shape and distribution of the electron wave functions which determine many physical, measurable
quantities. Such structure which conserves the circular symmetry has been recently fabricated [2].
Conduction through dot-ring nanostructure depends crucially on the coupling strength of its states to the
leads, which are related to the spatial distribution of the electron’s wave functions: states localized in
the QD (QR) are weakly (strongly) coupled to the leads. We perform microscopic calculations of the
tunneling rates for a set of the confinement potentials modified by the electrical gating. We then calculate
the sequential tunneling currents in the Coulomb blockade regime from the steady state solutions of the
rate equations.
In particular, we show that one can adjust the confinement potential of the dot-ring nanostructure so that
it can be used as: a) single electron transistor b) electrical current rectifier
The results indicate an opportunity to tune the performance of nanostructures and to optimize their specific properties by means of sophisticated design.
References
[1] E. Zipper, M. Kurpas, and M. M. Maśka, New J.of Phys.14, (2012)093029; M. Kurpas, E. Zipper, and M. M. Maśka, ”Engineering
of Electron States and Spin Relaxation in Quantum Rings and Quantum Dot-Ring Nanostructures” in ”Physics of Quantum Rings”,
Vladimir M. Fomin (editor), Springer 2014, p. 455
[2] C. Somaschini, S. Bietti, N. Koguchi and S. Sanguinetti, Nanotechnology 22, 185602 (2011).
SSPCM-23
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Local Kondo temperatures in atomic chains
R. R. AGUNDEZ1 , J. S ALFI2 , S. ROGGE2 ,
1
AND
M. B LAAUBOER1
Klavi Institute of Nanoscience, Delft University of Technology
[email protected]
2
Centre for Quantum Computation and Communication Technology
ABSTRACT
We study the effect of disorder in strongly interacting small dopant chains. Using the KotliarRuckenstein slave-boson approach we diagonalize the Hamiltonian via scattering matrix theory. We
numerically solve the Kondo transmission and the slave-boson parameters that allow us to calculate the
Kondo temperature. We demonstrate that in the weak disorder regime, disorder in the energy levels of
the dopants induces a non-screened disorder in the coupling energy between dopants. We find that this
disorder in the couplings comes from a local distribution of Kondo temperatures along the chain. We
propose an experimental setup where these local Kondo temperatures can be observed.
SSPCM-24
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Photon-assisted thermoelectric effects in ferromagnet-quantum dot-ferromagnet
system with additional superconducting lead
K ACPER B OCIAN1
1
AND
W OJCIECH RUDZI ŃSKI1
Faculty of Physics, Adam Mickiewicz University, ul. Umultowska 85, 61-614 Poznań, Poland
ABSTRACT
Spin-polarized thermoelectric features in tunnelling through a single level quantum dot connected to
external ferromagnetic leads are investigated theoretically.
Using the equation of motion method within the nonequilibrium Green function technique we examined the influence of the harmonic ac field on the electric and thermal conductance, Seebeck coefficient
as well as proper figure of merit. Another goal is to discuss the role of attaching to the dot also the
third, superconducting lead. In particular it is shown that the photonic field may strongly modulate the
Seebeck coefficient resulting in multi-peaks structure of figure of merit. In turn, in situation when the
superconducting proximity effect occurs, a slight change of the position of the resonances
SSPCM-25
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Interaction effects in low-buckled graphene-like crystals
E DUARDO V. C ASTRO1
1
CFIF and Physics Department, Instituto Superior Ténico, Universidade de Lisboa, Avenida Rovisco Pais, 1049-001 Lisboa, Portugal
[email protected]
ABSTRACT
One of the first proposals for a two-dimensional (2D) topological insulator was made for graphene,
but the very low spin-orbit (SO) coupling makes this phase undetectable. A much stronger SO coupling
occurs for the 2D version of other group IV elements: silicene, germanene, and stanene. However, with
increasing atomic number, also the lattice constant gets bigger, which implies a reduced band width. In
this scenario, in addition to SO coupling also electron-electron interactions become important.
In this contribution the effect of short range interactions in the minimal model of low-buckled honeycomb
crystals is discussed. Interactions are very often associated with trivial ground states, but cases are,
in particular for the honeycomb lattice, where topological phases are established instead.[1, 2] On the
other hand, strong competition with trivial phases has been identified,[2, 3] which makes the problem
highly non-trivial. A key observation is related with the purely local Hubbard interaction, which affects
topological transitions in a stronger way than previously anticipated,[4] and has here the effect of critically
renormalize the spin-orbit coupling to lower values.[5] The physics behind this effect will be unveiled on
the light of the slave rotor approach.
References
[1]
E. V. Castro, A. G. Grushin, B. Valenzuela, M. A. H. Vozmediano, A. Cortijo, and F. de Juan, Topological Fermi liquids from
Coulomb interactions in the doped honeycomb lattice, Phys. Rev. Lett. 107, 106402 (2011).
[2]
A. G. Grushin, E. V. Castro, A. Cortijo, F. de Juan, M. A. H. Vozmediano, and B. Valenzuela, Charge instabilities and topological
phases in the extended Hubbard model on the honeycomb lattice with enlarged unit cell, Phys. Rev B 87, 085136 (2013).
[3]
N. A. Garcı́a-Martı́nez, A. G. Grushin, T. Neupert, B. Valenzuela, E. V. Castro, Interaction driven phases in the honeycomb lattice
from exact diagonalization, Phys. Rev B 88, 245123 (2013).
[4]
M. A. N. Araújo, E. V. Castro, P. D. Sacramento, Change of an insulator’s topological properties by a Hubbard interaction, Phys.
Rev. B 87, 085109 (2013).
[5]
E. V. Castro, M. A. N. Araújo, P. D. Sacramento, in preparation
SSPCM-26
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Dynamics of Localized Modes in a Composite Multiferroic Chain
L EVAN C HOTORLISHVILI1 , R AMAZ K HOMERIKI2 , A LEXANDER S UKHOV1 , S TEFANO RUFFO3 , AND JAMAL B ERAKDAR1
1
Institut fur Physik, Martin-Luther-Universitat Halle-Wittenberg, D-06120 Halle/Saale, Germany
2
Physics Department, Tbilisi State University, 0128 Tbilisi, Georgia
3
Dipartimento di Fisica e Astronomia and CSDC, Universita di Firenze, CNISM and INFN, via G. Sansone 1, 50019 Sesto Fiorentino,
Italy
ABSTRACT
In a coupled ferroelectric-ferromagnetic system, i.e., a composite multiferroic, the propagation of
magnetic or ferroelectric excitations across the whole structure is a key issue for applications. Of special interest is the dynamics of localized magnetic or ferroelectric modes (LM) across the ferroelectric
ferromagnetic interface, particularly when the LM’s carrier frequency is in the band of the ferroelectric
and in the band gap of the ferromagnet. For a proper choice of the system’s parameters, we find that
there is a threshold amplitude above which the interface becomes transparent and an in-band ferroelectric
LM penetrates the ferromagnetic array. Below that threshold, the LM is fully reflected. Slightly below this transmission threshold, the addition of noise may lead to energy transmission, provided that the
noise level is neither too low nor too high, an effect that resembles stochastic resonance. These findings
represent an important step towards the application of ferroelectric and/or ferromagnetic LM-based logic.
References
[1] L. Chotorlishvili, R. Khomeriki, A. Sukhov, S. Ruffo, and J. Berakdar Dynamics of Localized Modes in a Composite Multiferroic
Chain Phys. Rev. Lett. 111, 117202 (2013)
SSPCM-27
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Ultrasonic methods of the cells separation in human blood
H ENRYKA C ZY Ż1
1
AND
A NDRZEJ W ŁOCH1
Rzeszow University of Technology
[email protected]
ABSTRACT
The physical properties of ultrasound and their complex interactions with human tissues led to the
fact that they are an important tool in medicine [1]. In this work we explore physical and engineering
principles of acoustics and ultrasound as used for medical applications. This work deals with the problem
of ultrasound in the context of biomedical and clinical applications. The influence of ultrasonic waves
on the diffracting phase is interesting by itself as one of the fundamental physical effects of ultrasound.
Under the influence of ultrasonic waves cells included in the liquid experience a certain characteristic
displacement, referred to as drift [2]. This motion of cells in the ultrasonic field consists of monotonically
approaching to the stable equilibrium point or quasiperiodical vibration with amplitude damping. The
ultrasonic wave accelerates the transport of cells to the minimal zone of potential drift force. This kinetics
process depends: on ultrasonic field, liquid and cells parameters. Ultrasonic waves can be used for
the separation cells in human blood [3]. This work shows that only radiation pressure should be taken
into account as a mechanism of a motion of cells in an ultrasonic field. The ultrasonic agglomeration
mechanisms are complicated processes and their theoretical descriptions are not completely established.
It has been demonstrated that the growth of cells concentration around the points of stable equilibrium
is exponential. The theoretical consideration of the ultrasonic agglomeration of cells in the liquid have
become a new focus in the acoustic fundamental research. Some numerical examples will be presented
during the conference.
References
[1] Benes E., Gröschl M., Radel S., Hauser C., Böhm H., Nowotny H. New simple mathematical model for the separation performance
of ultrasonic cell filters, Proc. 2nd Congress of Alps-Adria Acoustics Association and 1st Congress of Acoustical Society of Croatia,
Croatia, pp. 23-24, 2005.
[2] Mitome H., Kozuka T., Tuziuti T., Gröschl M., Handl B., Benes E. Generation of acoustic streaming in an ultrasonic resonator for
particle separation, Proc. WCU 97 - World Congress on Ultrasonics, Yokohama, Japan, pp. 24-27, 1997.
[3] Trampler F., Schwartz D., Mayr W., Benes E. Purification of platelets in human blood by means of ultrasonics, Proc. WCU 97 World Congress on Ultrasonics, Yokohama, Japan, pp. 24-27, 1997.
SSPCM-28
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Bound Magnetic Polaron in 2D System with the Strong Spin-Orbit Interaction
KONSTANTIN S. D ENISOV1
1
AND
N.S. AVERKIEV1
Ioffe Physical-Technical Institute of the Russian Academy of Science, Street Politekhnicheskaya 26, St.Petersburg, Russia
[email protected]
ABSTRACT
The Diluted magnetic semiconductors (DMS), i.e. semiconductor compounds doped with magnetic
impurities (most often Mn-atoms) constitute an important branch of modern solid state physics. The
coupling of localized spins with carriers, originating from the exchange interaction between the latter
and the electrons of the d-shell of manganese impurities, leads to the broadband spectrum of specific
optical and transport effects, such as Giant Zeeman splitting, the red shift of photoluminescence, etc [1].
The heightened sensibility of mutual orientation of the carrier spin and the neighbour manganese momentums may provide the formation of collective state (bound magnetic polaron BMP) characterized by
correlated spin distribution with the lowest energy. At low temperatures, when fluctuations are muted,
this distribution is imposed on carrier exchange field Bex acting on localized spins and orienting them
along itself (with the energy shift Eex = −Bex M ). Researches of BMPs connected with hole-states
in bulk and low-dimensional semiconductor systems show that its complicated properties are due to the
complex structure of the valence band in such alloys [2,3]. In quantum well systems with the valuable
spin-orbital energy splitting of conductivity band states, originating from the presence of the structural
inversion asymmetry (SIA), or the bulk inversion asymmetry (BIA) of quantum well material, the nontrivial behaviour of BMP is expected. In present work the ground state of BMP formed by the bound
carrier on donor under the spin-orbit interaction (SIA or BIA) in QW is theoretically studied [4]. The
spin-dependant localization in 2D systems was investigated in [5]. In this work two orthogonal wave
functions ψ↑,↓ of the electron bound state are received in accordance with the method of zero-radius
potential. The internal structure of BMP is complex because of specific form of ψ↑,↓ originating from
two-dimensionality and spin-orbit interaction. The polaron ground state is twice degenerated. The external magnetic field removes the symmetric influence of these carrier states. The manganese spins are
aligned along the resulting field. It constrains the electron to choose the state with Bex , corresponding to
the lowest energy of spins system. A remarkable feature of the studied system is the dependence of such
an electron state on weak magnetic. It leads to reorganization of spin orientation, thus the dependence of
magnetization on the external field takes a jump, when electron state changes.
References
[1] J. Kossut, Jan A, Gaj, "Introduction to the physics of diluted magnetic semiconductors"
[2] Yu.F. Berkovskaya, E.M. Vahkabova, B.L.Gel’mont et al., Sov. Phys. JETP 67(4), pp. 750.
[3] K.V.Kavokin, I.A.Merkulov and D.R.Yakovlev, Phys. of Solid State 40(5), pp. 734.
[4] K.S.Denisov, N.S.Averkiev, JETP Lett. 99(7), pp. 467.
[5] L.I.Magarill, A.V.Chaplik, JETP Lett. 81(4), pp.198.
SSPCM-29
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Current induced spin polarization in magnetized graphene with Rashba spin-orbit
interaction
A. DYRDAŁ1 , J. BARNA Ś2 , AND V. K. D UGAEV3
1
Faculty of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland
[email protected]
2
Institute of Molecular Physics, Polish Academy of Sciences, ul. M. Smoluchowskiego 17, 60-179 Pozna n, Poland
3
Department of Physics, Rzeszów University of Technology, Powstańców Warszawy 6, 35-959 Rzeszów, Poland
ABSTRACT
Electric current flowing in a system with spin-orbit interaction can induce spin polarization of conduction electrons. Such a nonequilibrium spin polarization in magnetic structures can generate a spin-orbit
torque exerted on localized magnetic moments, and under certain circumstances can lead to magnetization switching in the system. We consider theoretically current-induced spin polarization in graphene
with Rashba spin-orbit interaction. To find the stationary nonequilibrium polarization in the linear response regime, we have used the Green’s function method and derived some analytical formulas for the
induced spin polarization [1]. This polarization is oriented in the graphene plane and is normal to the
current orientation. The sign of the spin polarization depends on the chemical potential µ and changes at
µ = 0. When graphene is deposited on a magnetic substrate, a nonzero equilibrium magnetization can
be induced due to the proximity effect. In such a case, the other components of the current-induced spin
polarization become nonzero, which in the lowest-order approximation depend linearly on the exchange
field. We have derived analytical formulas for all components of the spin polarization. The spin-orbit
torque exerted on the magnetization has also been determined.
References
[1] A. Dyrdał, J. Barnaś, and V. K. Dugaev, Phys. Rev. B 89, 075422 (2014).
SSPCM-30
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Size and Impurities Effects on Resistivity of Ultra-Thin Metallic Layer
A RTUR D ZIAŁO1
1
AND
A NTONI PAJA1
AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, Department of Solid State Physics,
al. A. Mickiewicza 30, 30-059 Krakow, Poland.
[email protected]
ABSTRACT
Our goal was to calculate the electrical resistivity of ultra-thin metallic layers with consideration of quantum size effects, electron-phonon interactions which gives temperature dependence and impurities scattering giving additional resistivity.
In our work we use standard variational formula for the electrical resistivity of metals due to electronphonon scattering proposed by Ziman. At first we considered a single mono-atomic metallic layer through
which a two-dimensional (2D) electron gas is moving. Charge carriers are scattered by thermal lattice
vibrations. Lattice vibrations coupled to the phonons are treated in the Born-Oppenheimer approximation and the fluctuation is the first order term of electron-ion potential energy expansion. Later expansion
of this work was a simple particle-in-a-box model in which independent electrons are confined by an
infinitely deep and smooth (perfect surfaces) confining potential. In this case the matrix element of
electron-phonon interactions is assumed to be proportional to the square of the ratio of electron concentration to the density of states at the Fermi energy level. Impurities scattering problem is treated in the
first Born approximation applied to the three-dimensional Lippmann-Schwinger integral equation. The
kernel function is found using eigenvalue exppansion. We also assume the dopant atoms to be nonmagnetic so there is no spin-spin scattering.
What we have found is that the resistivity weakly depends on the film thickness and at fixed temperature
only oscillates around its bulk value. The reason of this oscillations comes from the electronic density
of states which changes with the film thickness. We assume that the build-up in electrical resistivity observed in experiment is brought on by surface roughness and cracks that may occasionally appear in the
film. The results for impurity scattering show that the incident wave quickly returns to its unperturbed
state after scattering and the scattering cross-section depends on the momentum and spatial coordinate
unlike the cross-section in the spherically symmetrical 3D system
Acknowledgments: This work has been partly supported by the EU Human Capital Operation Program,
Polish Project No. POKL.04.0101-00-434/08-00. It was also partially supported by the Polish Ministry
of Science and Higher Education and its grants for Scientific Research.
SSPCM-31
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Electrical properties of aluminium oxide-ethylene glycol (Al2 O3 − EG) nanofluids
JACEK FAL1 , G AWEŁ Ż YŁA1 , AND M ARIAN C HOLEWA1
1
Department of Physics, Rzeszow University of Technology
[email protected]
ABSTRACT
Nanofluids are suspensions of particles with sizes up to 100 nm in a liquid base, which is usually water, oil or ethylene glycol. The potential for practical use nanofluids caused in recent years a considerable
intensification of research into their properties. The most widely studied of physical parameters include
the fluid rheology, thermal conductivity and electrical properties. Paper presents electrical properties of
aluminium oxide (Al2O3) nanofluid based on ethylene glycol (EG). Nanoparticles used in this mixture
have size between 100-300 nm. Electrical properties was investigated in a wide range of temperatures
and frequencies using a measuring LCR bridge (LCR-Bridge HM 8118, HAMEG Instruments GmBH,
A Rohde & Schwarz, Mainhausen, Germany) connected to a temperature stabilization system based on
liquid nitrogen and Peltier element (T94 - controllers, THM600 - stages, Linkam Scientific Instruments
Ltd., Tadworth, UK). The paper also presents a detailed description of the measuring position for study
of the electrical properties of nanosuspensions newly established in Department of Physics on Rzeszow
University of Technology.
SSPCM-32
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Thermodynamics of the exactly solvable spin-electron tetrahedral chain
L UCIA G ÁLISOVÁ1
1
Department of Applied Mathematics and Informatics, Faculty of Mechanical Engineering, Technical University, Letná 9, 042 00 Košice,
Slovak Republic
[email protected]
ABSTRACT
Exact solution of the the hybrid spin-electron tetrahedral chain, in which the Ising spins localized
at nodal lattice sites regularly alternate with three equivalent lattice sites available for one mobile electron, is provided. A possible experimental realization of this geometry is realized for Cu3 Mo2 O9 [1].
By using the generatized decoration-iteration tranformation[2] the considered 1D spin-electron model is
mapped onto the effective spin-1/2 Ising linear chain in an external magnetic field, which can be exactly
solved by applying the transfer-matrix method[3]. The studied spin-electron system exhibits either the
ferromagnetic or antiferromagnetic ground state depending on whether the ferromagnetic (J < 0) or
antiferromagnetic (J > 0) interaction between the Ising spins and mobile electrons is considered[4].
Here, we will investigate thermodynamics of the system. Namely, we will discuss in detail temperature
variations of the magnetization and specific heat. It will be shown that the two-peak structure of the
specific heat curves observed at very low magnetic fields, if J < 0, and in a vicinity of the ground state
phase transition from the antiferromagnetic ground state to the ferromagnetic one, if J > 0, is a result of
strong thermal excitations from the ground state towards the respective low-lying excited state.
References
[1] Matsumoto M., Kuroe H., Sekine T., Hase M. Magnetic Excitation and Electric Polarization in Strongly Coupled Spin
Monomer and Dimer System Cu3 Mo2 O9 , Journal of the Physical Society of Japan, 024711, 81.
[2] Fisher M.E. Transitions of Ising Models, Physical Review, New Yourk, 969, 113.
[3] Kramers H.A., Wannier G.H. Statistics of the Two-Dimensional Ferromagnet. Part I, Physical Review, New York, 252,
60.
[4] Gálisová L., Strečka J. Ground state, magnetization process and magnetocaloric effect of the exactly tractable spinelectron tetrahedral chain, will be published in Acta Physica Polonica A.
SSPCM-33
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Simulations of Guided Vortex Motion in Type II Superconductors with Asymmetric
Corrugated Channels and Oscillating Vortex Radii
RUSSELL G LAVEY1
1
Loughborough University, Loughborough, Leicestershire, LE11 3TU
[email protected]
ABSTRACT
DC electrical resistance in type II superconductors is due to the motion of Abrikosov vortices. Moreover, the electromagnetic response of superconductor-based devices to low frequency excitations is dominated by the dissipative motion of these vortices. Consequently, much research has been devoted to
guided vortex motion with the aim of gaining control of net vortex motion.[1].
In this paper we present our latest findings on guided vortex motion in type II superconductors
with asymmetric corrugated channels and oscillating vortex radii. Vortex motion was investigated in the
presence of increasing parameters of: temperature, driving force, radial amplitude and angular speed of
oscillation. The simulations used to model the overdamped dynamics of the Brownian particles in 2D
were based on the Langevin equation:
√
d~r
~
= −A(t)~e + Dξ(t),
dt
(1)
where ~r was the position vector of the particle, A(t)~e was the driving force, a dc drive, ~e = (ex ) was the
~ = [ξx (t), ξy (t)] was the zero mean Gaussian white noise
unit vector, D was the noise intensity and ξ(t)
with autocorrelation function hξi (t)ξj (t0 )i = 2δij δ(t − t0 ) with i, j = x, y.
It was found that vortex rectification occurred and could be controlled by the variation of these
parameters. It was possible to separate vortices on the basis of their distinct internal angular speed of
oscillation. This is the first time that particle geometry, as opposed to chamber geometry, has been
investigated for its affect upon rectification and particle separation.
References
[1]
Silhanek. A.V, Van de Vondel. J, and Moshchalkov. V.V, 2010. Chapter 1 Guided Vortex Motion and Vortex Ratchets in Nanostructured Superconductors. Moshchalkov. V.V, Wordenweber. R, Wolfgang. L (eds) Nanoscience and Engineering in Superconductivity,
Springer, pp. 1 - 24.
SSPCM-34
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Spin pumping and charge-spin current injection in graphene with Rashba spin-orbit
interaction
M ICHAŁ I NGLOT1 , V ITALII D UGAEV1,2 , E VGENY YA . S HERMAN3 , AND
J ÓZEF BARNA Ś4
1
Rzeszów University of Technology, Rzeszów, Poland,
[email protected]
2
Instituto Superior Técnico, Lisbon, Portugal
3
Universidad del Pais Vasco, Bilbao, Spain
4
Adam Mickiewicz University, Poznań, Poland
ABSTRACT
Graphene is one of the most promising for applications electronic materials now [1]. It was discovered
recently that graphene at certain substrates is characterized by rather strong Rashba spin-orbit (SO) intteraction, which can make it important for spinronics applications. In this work we consider a possibility
of optical spin pumping and spin and charge current injection related to the spin flip at optical transitions
between the spin-splitted bands. Our model includes the relativistic Hamiltonian of low-energy excitations in graphene, Rashba SO interaction associated with mirror symmetry breaking, and a weak in-plane
magnetic field B. Due to the Rashba SO coupling, the low-energy electronic spectrum is gapless and
consists of two parabolic bands, with two other spin-splitted bands. The magnitude of SO interaction
can be additionally controlled by the electric field of the gate. We calculated the absorption spectrum,
spin-flip transition rate at the optical transitions and the efficiency of spin pumping as a function of all
possible parameters including the variation of chemical potential. Our calculations demonstrate that both
in-plane spin components are effectively generated by the optical transitions between all four spin-splitted
bands. The efficiency of spin pumpimg is strongly nonlinear as a fucntion of the Rashba coupling, with
a peak corresponding to nearly equal magnetic and spin-orbit splitting of the bands. It means that large
efficiency (defined as the spin-flip number per one absorbed photon) of the order of 0.1 can be reached
at moderate Rashba SO coupling below 50 meV. In the absence of mean SO coupling, the effect of spin
pumping can be nonzero due to the fluctuations of SO interaction [2]. This is the case of free standing
graphene, for which the random SO inetraction is related to the surface ripples.
References
[1]
M. I. Katsnelson Graphene: Carbon in Two Dimensions, Cambridge, 2012.
[2]
V. K. Dugaev, E. Ya. Sherman, J. Barnaś, Phys. Rev. B, 83 pp. 085–306, 2005.
SSPCM-35
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Some exact results in the one-dimensional attractive Hubbard model.
D OROTA JAKUBCZYK1
1
The Faculty of Mathematics and Applied Physics, Rzeszow University of Technology, al. Powstańców Warszawy 8, Poland
[email protected]
ABSTRACT
The exact solution of the Hubbard Hamiltonian exists only for one spatial dimension, given in year
1968 by Lieb and Wu [1], and is not easy to analyze. We continue the work with one spatial dimension,
which may become more important due to its possible applications in intensively studied carbon nanotubes, one-dimensional organic superconductors, or one-dimensional organic ferromagnet [2]. There is
also possibility of modelling the one-dimensional Hubbard model of fermionic quantum gas loaded into
an optical lattice [3], which is a promising candidate for quantum information processing. We consider
one-dimensional attractive Hubbard model (U << 0) [4-5] assuming periodic boundary conditions and
the half-filling case. The considered chains have N nodes, the same number of electrons, where N − 1
of them have the same spin projection. We provide a thorough analysis of the eigenproblem resulting in
obtaining the general analytical formulas for the eigenvalues and the eigenvectors, for any number N .
References
[1] E. H. Lieb and F. Y. Wu, Phys. Rev. Let. 20, 1445 (1968).
[2] D. Jerome and C.R. Pasquier, in: A. V. Narlikar (ed.), Frontiers in Superconducting Materials, Springer, Berlin, 183-230 (2005).
[3] S. R. J. F. Clark, Trinity College, Oxford (2007).
[4] D. Jakubczyk, Acta Physica Polonica B 42, 1825 (2013).
[5] D. Jakubczyk, Acta Physica Polonica B 45, 1759 (2014).
SSPCM-36
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
A partial classification of bipartite entanglement in multipartite systems
PAWEL JAKUBCZYK1
1
AND
Y EVGEN K RAVETS2
Faculty of Mathematics and Natural Sciences, University of Rzeszow, Rejtana 16A, 35-959 Rzeszow, Poland
[email protected]
2
Theoretical Physics Center (CPHT), Ecole Polytechnique, 91128 Palaiseau, France
ABSTRACT
We propose a partial classification of bipartite entanglement in multipartite systems. Our approach based
on the fact that entanglement changes with a change of the degrees of freedom of the system [1]. To
exploit this property, we construct unitary matrices designed to change degrees of freedom of the system
and develop a systematic method to monitor the change of entanglement of the state during its unitary
“rotations”.
References
[1]
A. C. de la Torre, D. Goyeneche, L. Leitao, Eur. J. Phys. 31 325-332 (2010).
SSPCM-37
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Quantum entanglement of two dipolar particles within a Harmonic Trap
P RZEMYSŁAW KO ŚCIK1
1
Institute of Physics, Jan Kochanowski University
[email protected]
ABSTRACT
We study the systems of two dipolar particles, bosons and fermions, confined in quasi-onedimensional harmonic traps. The numerical results for the dependencies of the entanglement on the
control parameters of the systems are provided and discussed in details. In the strong-interaction limit,
the occupancies and the von Neumann entropies of the bosonic and fermionic ground states are derived
in closed analytical forms by applying the harmonic approximation. The analytical results presented are
in an excellent agreement with the results obtained numerically.
SSPCM-38
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Scanning gate microscopy simulations of the quantum Hall electron interferometer
K RZYSZTOF KOLASI ŃSKI1
1
AND
BARTŁOMIEJ S ZAFRAN1
AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, al. Mickiewicza 30, 30-059 Kraków,
Poland
ABSTRACT
At high magnetic field in the integer quantum Hall (IQH) regime the transport properties of twodimensional systems are determined by currents carried by so-called edge states. The currents can propagate only in one direction on each edge and the backscattering may occur only when counter-propagating
edge channels are close enough to allow for the electron inter-edge tunneling. The edge states have very
large coherence length and thus they can be used for construction of electron interferometers of various
types. One of the methods of experimental characterization of such systems is scanning gate microscopy
(SGM), which allows to probe locally the transport properties of the system by scanning the charged tip
above the sample surface.
We simulate the scanning gate microscopy of the quantum point contact (QPC) in the IQH regime. We
consider fully coherent electron transport within the single electron approximation of Schrödinger equation. In order to calculate the conductance (G) and its changes induced by the biased tip we use our finite
difference implementation of quantum transmitting boundary method [2] and a short-range (Lorentzian
type) model of the effective tip potential. We study the conductance maps of the system with and without
a quantum Hall island (QHI) between the QPC constriction. We reproduce the features observed in a
recent paper [1] including: the circular form of the oscillations in the G maps, decreasing of the spacing
between two subsequent resonant lines along with the tip approaching the QHI and the shift of the resonant lines to lower values of B by repulsive potential. In the absence of QHI none of these experimental
features is observed. We discuss the role of the profile of the QHI potential on the observed effects.
References
[1] F. Martins, S. Faniel, B. Rosenow, H. Sellier, S. Huant, M. G. Pala, L. Desplanque, X. Wallart, V. Bayot, and B. Hackens, Nature
Scientific Reports 3, 1416 (2013).
[2] D.J. Kirkner, and C.S. Lent, Journal of Applied Physics 67, 6353 (1990). M. Leng, and C. S. Lent, Journal of Applied Physics 76,
2240 (1994).
SSPCM-39
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Two-electron resonances in quasi-one dimensional quantum dots with Gaussian
confinement
A RKADIUSZ K URO Ś1
1
Institute of Physics, Jan Kochanowski University ul. Świȩtokrzyska 15, 25-406 Kielce, Poland
ABSTRACT
An examination of the system of two Coulombically interacting electrons confined in a Gaussian trap is
carried out within the framework of the single-mode approximation of the transverse components. Apart
from bound states, such a system exhibits resonances that are related to the ionization process. We employ
the complex-coordinate rotation method and provide detailed numerical results for the dependencies of
the resonance widths and energies on the confinement anisotropy and the interaction strength.
SSPCM-40
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Spin-orbit coupling in pure and hydrogenated carbon nanotubes in a transverse
electric field
M ARCIN K URPAS1 , M ARTIN G MITRA2 , AND JAROSLAV FABIAN2
1
Institute of Physics, University of Silesia, ul Uniwersytecka 4, 40-007 Katowice, Polska
[email protected]
2
Institute for Theoretical Physics, University of Regensburg, 93040 Regensburg, Germany
ABSTRACT
Graphene based materials have attracted a great deal of interest because of their peculiar electronic
properties. Due to the absence of nuclear spin in the C atom and weak spin-orbit interaction in graphene
they are promising candidates for spin based electronics. In pristine flat graphene the intrinsic spin-orbit
coupling (SOC) is very weak ∼ 24µeV [1]. It can be however strongly enhanced by adsorption of light
adatoms that locally distort the lattice and cause sp3 hybridization [2].
Carbon nanotubes (CNT) are, in contrast, curved structures and the π electrons near the Fermi level
contain some composition of σ electrons due to σ − π coupling. This leads to much stronger SOC [3]
which is strongly asymmetric (different for π and π ∗ states) and depends on the type of CNT [3, 4].
Additionally, adsorption of H adatoms causes strong local and global deformation of the nanotube [5]
which may lead to modification of SOC.
Based on the density functional theory we perform first principles calculations of spin-orbit coupling in
single wall carbon nanotubes. We study the effect of a constant transverse electric field on SOC-induced
energy gap both for pure and hydrogen decorated CNTs in dense and diluted limits.
References
[1] M. Gmitra, S. Konschuh, C. Ertler, C. Ambrosch-Draxl, and J. Fabian, Phys. Rev. B 80, 235431 (2009).
[2] M. Gmitra, D. Kochan, and J. Fabian, Phys. Rev. Lett. 110, 246602 (2013).
[3] F. Kuemmeth, S. Ilani, D. C. Ralph & P. L. McEuen, Nature 452, 448 (2008), G.A. Steele, F. Pei, E.A. Laird, J.M. Jol, H.B. Meerwaldt
& L.P. Kouwenhoven Nature Communications 4, 1573 (2013).
[4] J. Zhou, Q. Liang, and J. Dong, Phys. Rev. B 79, 195427 (2009).
[5] Ž. Šljivancanin, Phys. Rev. B 84, 085421 (2011), K. W. Lee, C. E. Lee Adv. Mater. 24, 2019 (2012).
SSPCM-41
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Crystallographic interpretation of Galois symmetries
for magnetic pentagonal ring
J. M ILEWSKI1 , T. L ULEK2 ,
AND
M. Ł ABUZ3
1
Institute of Mathematics, Poznań University of Technology, Piotrowo 3A, 60-965 Poznań, Poland
[email protected]
2
Faculty of Physics, Adam Mickiewicz University in Poznań, Poland
3
Department of Theoretical Physics, Faculty of Mathematics and Natural Sciences, University of Rzeszow, Pigonia 1, 35-310 Rzeszów,
Poland
ABSTRACT
The eigenproblem of the Heisenberg Hamiltonian for magnetic pentagonal ring within the XXX
model can be solved exactly by immediate diagonalization within the basis of wavelets - the Fourier
transform of the basis of C5 -orbits on 25 = 32 magnetic configurations. Thus the eigenstates, presented
as density matrices, are expressible within the cyclotomic extension Q(ω), ω = exp (2πi/5), of the
prime field Q of rationals. These eigenstates, however, do not exhibit the form of famous Bethe Ansatz,
and transformation to this form requires further extension of Q(ω) by appropriate Bethe parameters
a = exp (ip) = (λ + i/2)/(λ − i/2), the so called Bethe number field B. We aim to present the analogy
of the short exact sequence of groups and homomorphisms
1mult −→ Aut (B/Q(ω)) −→ Aut (B/Q) −→ Aut (Q(ω)/Q) −→ 1mult ,
with Aut (L/K) denoting the Galois group of the number field L with respect to the subfield K, 1mult
is the trivial group in the multiplicative notation, and arrows stand for group homomorphisms η, such that
Im η1 = ker η2 for consecutive arrows, to the short exact sequence
0add −→ T −→ G −→ Q −→ 1mult
which defines the space group G in terms of its translation subgroup T and point group Q (0add is the
trivial group in additive notation). We point out explicitly the isomorphism between the action of the
Galois group Aut (B/Q) on the set of Bethe parameters with that of a space group G on the nodes
of a Bravais lattice. In particular, we show that in the case of Galois group the factor system is trivial
(symorphism), and discuss in detail the action of the active group Aut (Q(ω)/Q) ∼
= C4 on the passive
group Aut (B/Q(ω)) ∼
= D2 as an embedding into Aut D2 = GL(B/Z2 ).
SSPCM-42
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
New approach to the design of tunable THz-detector
I. T RALLE1 , G. H AŁDA Ś2 , K. M AJCHROWSKI1 , AND A. KOLEK2
1
Theoretical physics Department, Faculty of Mathematics and Natural Sciences, University of Rzeszów, Pigonia 1, Rzeszów, Poland
[email protected]
2
Department of Electronics Fundamentals, Rzeszow University of Technology, Rzeszow, Poland
ABSTRACT
In the paper we proposed an approach to the design of THz photo-detector based on the resonance
tunneling in double-barrier structure. The approach is the combination of two methods, namely ISP
method which enables to reconstruct the QW potential shape having the predetermined energy spectrum,
and the NEGF method which gives the possibility to calculate adequately such important characteristics
of the device as density of states, I-V characteristics and photo-response. We also proposed some modification of initial scheme of the device, attaching to the QW an additional barrier of smaller height which
efficiently blocks the outflow of charge carriers from the ground state of QW and enhance this way the
detector performance. It seems, that the idea of the additional barrier incorporated into detector structure
can be further explored to achieve multicolor detection without the need of changing the detector bias.
Treating it as an adjustable parameter one can tune barrier thickness to align ground state of the first QW
with the first excited state of the second QW. Then, as both energy levels that matter are filled for a bias
corresponding to 12 mV/QW, the detection of both THz frequencies would be possible for this bias. Next
THz-colors which are to be detect, could be also added this way to get a comb of frequencies useful in
sensing applications.
Fig. 1. The structure of the designed THz detector which can be produced on the basis
of Alz Ga1−z As-materials. The structure is divided into eleven sections in which the
fraction z is: I - 0:0718, II - 0:0551, III - 0:0273, IV - 0:0184, V - 0:0159, VI - 0:0139,
VII - 0:0159, VIII - 0:0184, IX - 0:0273, X - 0:0551, XI - 0:0718.
Fig. 2. The photo-current response for the structure with a 20 nm thick barrier attached
to the QW versus photon energy.
SSPCM-43
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
A method for measuring thermal conductivity of liquid by using a laser beam
JAN M AMCZUR1 , A NDRZEJ WASILEWSKI1 ,
1
AND
1
T OMASZ W I ECEK
˛
Rzeszów University of Technology, al. Powstańców Warszawy 12, Rzeszów, Poland
[email protected]
ABSTRACT
A laser beam is used to heat a portion of liquid closed in a vessel from the top of it to avoid convection.
The temperature is measured at the bottom of the vessel by a laser waveguide sensor. The heating and
measuring methods allow using a small amount of liquid of the order of a milliliter fraction. The heat flow
through the liquid as well as the surrounding vessel and space is modeled by the finite element method
to calculate the temperature at the bottom vs. time. Thus obtained dependence is then used as a fitting
function to get the liquid thermal conductivity among some other fitting parameters.
SSPCM-44
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Self-energy electronic structure renormalization effects in first-principles calculations
of solids
A LBERTO M ARMODORO1 , PAOLO T REVISANUTTO2 , L EONID S ANDRATSKII1 ,
1
AND
A RTHUR E RNST1
Max-Planck Institut fur Mikrostrukturphysik, Weinberg 2, 06120 Halle
[email protected]
2
Singapore Synchrotron Light Source / National University of Singapore
ABSTRACT
We report on our work in pursue of a suitable
rst-principles description for the evaluation of finite relaxation time and general bands structure renormalization effects for electrons in a solid. These are expressed in terms of an ad-hoc self-energy term on top
of a reference hamiltonian, modified to further include the specific higher order corrections of interest.
The problem is approached distinguishing between two regimes: a low-lying excitations one, examined
from a diagrammatic -truncated point of view; and a further-away from ground-state scenario, where
techniques closer to DMFT and methods for disorder can be employed. The latter scenario is pursued as
initial validation ground, starting from the case of chemical impurities and substitutional disorder, before
continuing towards investigation of spin uctuations and more well-defined spin waves. Deployment of the
formalism at the KKR-Green function level is intended to highlight measurable effects within transport
and ARPES experiments for real materials.
References
[1]
T. Ando, J. Phys. Soc. Jpn. 69, 1757 (2000); D.V. Bulaev, B. Trauzettel, and D. Loss, Phys. Rev. B 77, 235301 (2008); M. del Valle,
M. Margańska, and M. Grifoni, Phys. Rev. B 84, 165427 (2011), J. Klinovaja, M. J. Schmidt, B. Braunecker, and D. Loss, Phys. Rev.
B 84, 085452 (2011).
[2]
E.A. Laird, F. Pei, and L.P. Kouwenhoven, Nature Nano. 8, 565 (2013).
[3]
F. Pei, E. A. Laird, G. A. Steele, and L. P. Kouwenhoven, Nature Nano. 7, 630 (2012); G. Szechenyi, and A. Palyi, Phys. Rev. B 89,
115409 (2014).
SSPCM-45
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Semi-Classical Phase Space dynamics for the Quantum Toffoli Gate
B. M ERA1,2,3 , P. M ATEUS4,5 , N. PAUNKOVI Ć4,5 , R. L OURA4,5 ,
2
AND
V. R. V IEIRA2,3
1
Physics of Information Group, Instituto de Telecomunicações, 1049-001 Lisbon, Portugal
Centro de Fı́sica das Interacções Fundamentais, Instituto Superior Técnico, Universidade de Lisboa,, Av. Rovisco Pais 1, 1049-001
Lisboa, Portugal
3
Department of Physics, IST, University of Lisbon, 1049-001, Lisbon, Portugal
4
SQIG - Instituto de Telecomunicações, IST, University of Lisbon, 1049-001 Lisbon, Portugal
5
Department of Mathematics, IST, University of Lisbon, 1049-001, Lisbon, Portugal
ABSTRACT
To be able to compare classical and quantum complexity classes one needs to establish a relation
between quantum and classical systems. In this sense, we tried to understand the classical limit of an
arbitrary finite-dimensional quantum system undergoing unitary dynamics. To study such a limit, it is
more suitable to introduce the so-called coherent states [1] associated to the symmetry group of the
problem. The coherent states are nearest to classicality because they minimize uncertainty relations. The
quantum dynamics can then be mapped to dynamics in a symplectic manifold, CPn−1 , in analogy with
the scenario of classical mechanics, with Hamilton’s function given by the expected value in the coherent
state. The symplectic potential provides the kinetic term of the action and it is related, naturally, to the
holonomy phase accumulated on a closed path in the phase space.
The Toffoli gate is very important because it provides a minimal set of universal gates for reversible
computation. It is represented, in the context of the quantum circuit paradigm of quantum computation,
by a unitary matrix. The fact that the operation is unitary and, thus, reversible, implies that it maps coherent states to coherent states and, so, classical states to classical states. We’ve studied the Hamiltonian
dynamics in this specific case.
References
[1]
A. Perelomov. “Generalized Coherent States and their applications”. Springer-Verlag, 1985.
SSPCM-46
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Imaging localization of resonant states in antidots defined within a finite graphene
flake
A. M RE ŃCA† , K. KOLASI ŃSKI AND B. S ZAFRAN
AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, al. Mickiewicza 30, 30-059 Kraków,
Poland
†
[email protected]
ABSTRACT
Confinement of electrons in structures defined electrostatically in graphene is suppressed due to
the Klein phenomenon [1]. However, for certain (e.g. circularly symmetric) types of confinement, the
localized resonant states can be formed [2]. In our work we study the graphene flake with a cirular antidot
defined on it by an external potential. The flake is connected to long nanoribbons that play a role of leads.
Using the tight binding approach, we study the transport of electrons through the system. We find narrow
peaks in the transmission probability for the resonant energies of the antidot and cavity. In those states,
electrons are quasi-bound in the system, forming current loops within the antidot and cavity, or focused
by the antidot, with the current flowing through the center of the antidot.
We investigate the influence on the system of a scanning gate microscope, modeled by a short range
potential [3]. We find that the resonances’ energies are shifted and get broadened or narrowed, which
translates into the change of the resonance lifetime.
References
[1] P.E. Allain and J.N. Fuchs Eur. Phys. J. B 83, 3017 (2011).
[2] J. H. Bardarson, M. Titov, and P. W. Brouwer Phys. Rev. Lett. 102, 226803 (2009).
[3] H. Sellier, B. Hackens, M. G. Pala, F. Martins, S. Baltazar, X. Wallart, L. Desplanque, V. Bayot, S. Huant, Semicond. Sci. Technol.
26, 064008 (2011); D. K. Ferry, A. M. Burke, R. Akis, R. Brunner, T. E. Day, R. Meisels, F. Kuchar, J. P. Bird, and B. R. Bennett,
Semicond. Sci. Technol. 26, 043001 (2011).
SSPCM-47
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Spin polarization without magnetic field
in a spin-orbit-coupled quantum point contact
M ICHAŁ P. N OWAK1
1
AND
BARTŁOMIEJ S ZAFRAN1
AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, al. Mickiewicza 30 30-059 Kraków,
Poland
[email protected]
ABSTRACT
We study electron transport through a quantum point contact (QPC) and show that in the presence of
spin-orbit interaction the QPC can serve as a source of spin polarized current that operates in the absence
of magnetic fields [1]. Spin-orbit interaction has been already used for electrical spin manipulation of
confined electron [1]. For a propagating electron spin-orbit coupling acts as an effective magnetic field
that splits the subbands of lateral quantization with the opposite spin polarizations. We explain that due to
lateral confinement of the QPC the subbands become mixed and as a result the degree of spin polarization
of some modes is reduced. When the electron propagates through the narrowing the transmission of the
input modes whose spin do not match the dominating spin polarization in the constriction is damped.
This in turn leads to non-zero spin polarization of – initially spin-degenerate – electron current flowing
out from the QPC. The spontaneous spin polarization appears particularly strong on the last conductance
step G0 ≤ 2e2 /h. The latter result corresponds with the breaking of the spin symmetry that leads
to formation of nonzero magnetic moment in the constriction that is considered [4] as responsible for
formation of G ' 0.7G0 anomalous plateau present in the experimental data [5].
References
[1]
Nowak M. P., Szafran B., Spin current source based on a quantum point contact with local spin-orbit interaction, Applied Physics
Letters, pp. 202404-1 – 202404-5, 103.
[1]
Nowack K. C., Koppens F. H. L., Nazarov Yu. V. and Vandersypen L. M. K., Coherent Control of a Single Electron Spin with Electric
Fields, Science, 1430-1433, 318; Nadj-Perge S., Frolov S. M., Bakkers E. P. A. M. and Kouwenhoven L. P., Spin–orbit qubit in a
semiconductor nanowire, Nature (London), 1084-1087, 468 (2010).
[4]
Rejec T. and Meir Y., Magnetic impurity formation in quantum point contacts, Nature, 900-903, 442.
[5]
Wang C. K. and Bergeren K. F., Local spin polarization in ballistic quantum point contacts, Physical Revew B, 4552-4556, 57.
SSPCM-48
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Simulations of spin-valley transitions in single and double quantum dots defined in
carbon nanotube
E DYTA N. O SIKA1 , A LINA M RE ŃCA1 , AND BARTŁOMIEJ S ZAFRAN1
1
AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, al. Mickiewicza 30, 30-059 Kraków,
Poland
ABSTRACT
One of the greatest obstacle on the way to coherent spin manipulation in semiconductor nanostructures is a short coherence time, mainly due to presence of the nuclear spin field. Very promising materials
in this context seem to be carbon nanotubes (CNTs), in which decoherence originating from nuclear field
is negligible. Other attractive feature of semiconducting CNTs is possibility to confine charge carriers
within electrostatically defined quantum dots and presence of additional, similar to spin, valley degreee
of freedom. The significant spin-orbit interaction [1], which appears in CNT due to folding of graphene
plane, couples the spin and valley degrees of freedom splitting the four-fold degenerate ground state into
Kramers doublets, which are further split by external magnetic field. Transitions between the spin-valley
states in CNT quantum dots have been observed recently in EDSR experiments [2].
We present simulations of the spin-valley transitions driven by external AC electric field. Using tightbinding approximation, we calculate CNT states localized in quantum dot defined by external potential
and use them as a basis for the solution of the time-dependent Schrödinger equation. In the model we
take into account curvature-induced spin-orbit interaction and external fields. Additionally we introduce
bend of the tube, atomic disorder and electric field component perpendicular to the axis of the CNT and
we discuss the impact of each of these effects on appearance and rates of transitions. We demonstrate
lifting of transitions’ selection rules by perturbation of angular symmetry of CNT eigenstates. We report
on observation of first order transitions as well as fractional resonances [3]. Apart from complete analysis
for one electron in single quantum dot, we present first results of anologous simulations for electron pair
in a double quantum dot, i.e. the system which is studied experimentally [2] by lifting the Pauli (spin)
and valley blockade of the current flow.
References
[1]
T. Ando, J. Phys. Soc. Jpn. 69, 1757 (2000); D.V. Bulaev, B. Trauzettel, and D. Loss, Phys. Rev. B 77, 235301 (2008); M. del Valle,
M. Margańska, and M. Grifoni, Phys. Rev. B 84, 165427 (2011), J. Klinovaja, M. J. Schmidt, B. Braunecker, and D. Loss, Phys. Rev.
B 84, 085452 (2011).
[2]
E.A. Laird, F. Pei, and L.P. Kouwenhoven, Nature Nano. 8, 565 (2013).
[3]
F. Pei, E. A. Laird, G. A. Steele, and L. P. Kouwenhoven, Nature Nano. 7, 630 (2012); G. Szechenyi, and A. Palyi, Phys. Rev. B 89,
115409 (2014).
SSPCM-49
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Majorana Fermions in Disordered Multichannel Wires
BARIŞ P EKERTEN1 , Ö ZG ÜR B OZAT1 , AYKUT T EKER1 , M ICHAEL W IMMER2 , AND İ NANÇ A DAGIDELI1
1
Faculty of Engineering and Natural Sciences Sabanci University Tuzla, 34956, Istanbul
[email protected]
2
Instituut-Lorentz, Universiteit Leiden, 9506, 2300 RA Leiden, the Netherlands
ABSTRACT
In this work, we investigate the effect of disorder on the topological properties of multi- channel
Rashba wires in contact with an s-wave superconductor. In a clean wire, all channels separate and form
effective (topological or otherwise) 1d wires. Although the general expec- tation is that the disorder will
destroy topological order by either simply mixing edge states (even number of channels) or by localization
(odd number of channels), we find that disorder can force a wire with even number of channels to a
topologically nontrivial state. Thus we show that disorder creates reentrant topoligcal states and can even
increase the chemical po- tential range of the topological state. We obtain analytical formulas for the
phase boundary of Rashba-superconductor wires, generalizing our earlier results of Adagideli et al. [1]
and and Rieder et al. [2]. Finally we perform numerical simulations to demonstrate our results. [3].
References
[1]
Adagireli, İ., Wimmer, M., Teker, A. Inducing topological order in dirty wires: Majorana fermions from scattering, Phys.Rev. 89,
144506 (2014)
[2]
Rieder, M.-T., Brouwer, P. W. and Adagideli, İ. Reentrant topological phase transitions in a disordered spinless superconducting
wire, Phys. Rev. B 88, 060509(R) (2013)
[3]
Pekerten, B., Bozat, Ö., Teker, A., Wimmer, M. and Adagideli, İ. Topological States in multichannel nanowires, To be submitted as
an invited paper for the special Topological Insulators issue of New Journal of Physics.
SSPCM-50
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Transport properties of twisted bilayer nanoribbon systems
M. P ELC1,2 , L. C HICO2 , E. S U ÁREZ M ORELL3 , M. PACHECO3 , AND L. B REY2
1
Nicolaus Copernicus University, Toruń, Poland
[email protected]
2
Instituto de Ciencia de Materiales de Madrid (ICMM), Consejo Superior de Investigaciones Cientı́ficas (CSIC), Madrid, Spain
3
Departamento de Fı́sica, Universidad Tecnı́ca Federico Santa Marı́a, Valparaı́so, Chile
ABSTRACT
The low-energy band structure of bilayer graphene depends strongly on the stacking sequence. While
AA stacking preserves the linear dispersion around the Fermi level, typical for a single layer, the AB type
stacked graphene has a parabolic dispersion relation [1]. In the case of twisted bilayer graphene, the two
layers are rotated an angle smaller than 30◦ . For small rotation angles, a moire pattern appears. In this
case, we may distinguish regions with both types of stacking, AA and AB, as well as displaced graphene
layers, called slip regions. The relative angle between layers determines the electronic properties of the
system. It has been shown that for large angles (10◦ − 30◦ ) with respect to the original AB stacking,
the system properties are similar to two non-interacting graphene monolayers. While in the case of small
angles, the Fermi velocity decreases, dropping to zero around the angle of 1◦ [2]. Here we consider the
twisted bilayer nanoribbons, which are the stripes of a bilayer graphene with rotated layers. Although
there is no controllable way to produce them, twisted bilayer structures appear naturally in some growth
methods [3]. Moreover, unzipping multiwall nanotubes could be used to obtain twisted nanoribbons [4].
We investigate the electronic and transport properties of twisted bilayer ribbons. We have performed
calculations of conductance and local density of states using the Green function matching technique. The
ribbons are described with a tight binding Hamiltonian. We show the dependence of transport properties
on the size of the bilayer region. We also investigate the appearance of localized states that appear in
these systems.
References
[1] E. McCann et al., Solid State Communications 143, 110 (2007); M. Aoki et al., Solid State Communications 142, 123 (2007).
[2] E. Suarez Morell et al., Phys. Rev. B 84, 195421 (2011); G. Trambly de Laissardiere et al., Nano Letters 10, 804 (2010); E. Suarez
Morel et al., Phys. Rev. B 82, 121407 (2010).
[3] G. Li, A. Luican et al., Nature Physics 6, 109 (2010).
[4] D. V. Kosynkin et al., Nature 458, 872 (2009); L. Xie et al., Journal of the American Chemical Society 133, 10394 (2011).
SSPCM-51
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Spin dynamics in asymmetric and macroscopically symmetric (110)-grown quantum
wells
A. V. P OSHAKINSKIY1
1
AND
S. A. TARASENKO1
Ioffe Physical-Technical Institute, 194021 St. Petersburg, Russia
[email protected]
ABSTRACT
We present the microscopic theory of electron spin dephasing for (110)-grown quantum wells (QWs).
Both QWs with asymmetric heteropotential, where the Rashba field is homogeneous, and macroscopically symmetric QWs where the Rashba field fluctuates in the quantum well plane due to domain structure
or inhomogeneous distribution of charged impurities in the doping layers [1] are considered. Structures
of such a crystallographic orientation are attracting much attention due to extremely long and controllable
spin lifetime.
It is shown that the Dresselhaus field, which is always present in zinc-blende-type structures and points
along the growth direction in (110)-grown QWs, increases the lifetime of the out-of-plane spin component [2]. In asymmetric structures, the interplay of the Rashba and Dresselhaus fields leads to a dynamic
coupling of the in-plane and out-of-plane spin components. In particular, the optical orientation of electron spins by circularly polarized light along the QW normal will generate an in-plane spin component.
We also demonstrate that the spin lifetime non-monotonously depends on the electron mobility reaching
the minimum in structures where the scattering time is comparable to the period of spin precession in the
effective magnetic field.
An external magnetic field applied along the growth axis leads to the cyclotron motion of electrons as well
as the Larmor precession of electron spin. Due to low symmetry of (110)-grown QWs, the interplay of
these effects results in a non-monotonous dependence of the spin lifetime on the magnetic field: the lifetime decreases in small fields, reaches a minimum, and grows in high fields. Such a non-trivial magneticfield-induced spin dynamics has been observed in experiments on (110)-grown GaAs/Al0.3 Ga0.7 As
QWs [3].
References
[1]
M. Glazov, E. Sherman, and V. Dugaev, Physica E 42, 2157 (2010).
[2]
A.V. Poshakinskiy and S.A. Tarasenko, Phys. Rev. B 87, 235301 (2013).
[3]
G. Wang, A. Balocchi, A.V. Poshakinskiy, C.R. Zhu, S.A. Tarasenko, T. Amand, B.L. Liu, and X. Marie, New J. Phys. 16, 045008
(2014).
SSPCM-52
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Focussing of electrons in graphene by n-p and n-p-n junctions
KOEN R EIJNDERS1
1
AND
M IKHAIL K ATSNELSON1
Radboud University Nijmegen, Institute for Molecules and Materials, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands
[email protected]
ABSTRACT
We study how electrons in graphene, emitted from a pointlike contact, are focussed by stepwise np and n-p-n junctions. It is known that such junctions act as a Veselago lens, because of the negative
refraction at the junction interface [1]. We investigate the exact Green’s function for this process in
detail, and find that the center of the focus is not located at the point where one would expect it based
on a classical ray picture. Instead, the center is slightly shifted in the direction parallel to the junction
interface. The size of this shift strongly depends on the (pseudo)spin polarization, but only very weakly
depends on the distance of the electron source to the junction interface.
To gain more insight in the Green’s function, we evaluate it in the semiclassical limit with the help of
the stationary phase approximation. This approximation diverges near the focus, because the second
derivative of the action vanishes at this point. Therefore, we have to expand the action to higher orders to
obtain a finite result. To correctly reproduce the shift of the focus, we also have to take the second term
in the expansion of the amplitude into account. Combining different approximations, we find a result that
is in very good agreement with the exact Green’s function. We believe that our predictions can be tested
by STM experiments.
References
[1]
V. V. Cheianov, V. Falko, and B. L. Altshuler, The focusing of electron flow and a Veselago lens in graphene p-n junctions, Science
315, 1252–1255, 2007.
SSPCM-53
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Supercapacity of soft-expanded graphite in Li-intercalational electric current
generation
R. YA . S HVETS1 , I. I. G RYGORCHAK1 , A. S. K UREPA1 , N. T. P OKLADOK1 , Y U . I. S EMENTSOV2 , G. I. D OVBESHKO3 , Y E .
S HEREGII4 , AND B. S EREDYUK5
1
Lviv Polytechnic National University, Bandera Str. 12, Lviv, 79013, Ukraine
Chuiko Surface Institute of Chemistry National academy of sciences of Ukraine, General Naumov str. 17, Kyiv, 03164, Ukraine
3
Institute of Physics of NAS of Ukraine, Prospect Nauky, 46, Kyiv, 03028, Ukraine
4
University of Rzeszow, Center of micro- and nanoelectronics, Poland, Rzeszow
5
Academy of land Forces named after Hetman Petro Sahajdachnyj, Faculty of Rocket Troops and Artillery, Gwardiyska str., bld. 32, Lviv
79012, Ukraine
[email protected]
2
ABSTRACT
In resent works, a very interesting and promising approach is suggested in materials science for
autonomous power engineering devices. From the point of view of universalization of processes of devise
making for autonomous power engineering, the possibility of application of multilayered graphen-bind
structures for Li- intercalation current generation is of interest without a doubt.
In this paper microwave-intercalation modification of natural graphite which ensures its effective use
as a cathode material of Li-based sources of electric current is developed. We have found that:
1. The possibility of application of hydrolyzed intercalated by sulphuric acid graphite of the first
stage of stage ordering after its expansion by means of microwave electromagnetic radiation
for super electric power generation according to lithium-intercalation mechanism of currentgeneration reaction has been proved. For 60-second regime, huge value of specific capacity
resource Q = 2250 mA*hour/g was obtained, which is more than the analogical parameter of
cathode materials of lithium-based power sources which are now available in market.
2. The kinetics of intercalation process for all regimes of expansion is characterized by a kineticdiffusive limitation. The equivalent electronic circuit is a modified by two Warburg impedances
de Levie circuit; they represent parallel proceeding diffusive processes of intercalation into unexpended (more weakly expanded) and into more strongly expanded intergraphene domains.
3. In more strongly expanded intergraphene domains, coefficients of diffusion are the highest for 60second regime. At the same time, for this regime, the coefficient of diffusion in more weakly
expanded domains is lower than, even that, in unexpended matrix.
4. Data of Raman scattering of light indicate that different regimes of expansion lead to considerable
changes of D-band.
SSPCM-54
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
An influence of dephasing processes on the ’2kF ‘ scattering mechanism of conduction
electrons in the three-dimensional structurally disordered systems.
B. J. S PISAK1
1
AND
M. W OŁOSZYN1
AGH University of Science and Technology Faculty of Physics and Applied Computer Science Al. Mickiewicza 30 30-059 Krakow Poland
[email protected]
ABSTRACT
In the structurally disordered systems the conduction electrons may be prone to weak localisation which
is regarded as a precursor of the Anderson localisation. The weak localisation manifests itself by the
singularity for the multiple backward scattering of carriers on the Fermi surface. The singularity can be
removed by mechanisms which describe the interaction of the carriers with an effective thermal field due
to the dynamics of ions.
The coherent backscattering is considered within the framework of the generalised kinetic equation for
the Wigner distribution function and effective medium approximation. It has been shown that a proper
explanation of the low-temperature dependence of electrical resistivity requires taking into account the
dephasing mechanism, which is proportional to the square root of temperature. On the other hand, the
high-temperature dependence of the electrical resistivity requires the dephasing mechanisms, which are
proportional to the second, third and fourth power of temperature.
The results of calculations are compared with the experimental data of resistance measurements as a
function of temperature for a typical metallic glass.
References
[1]
Morgan, G. J., Howson, M. A. and Saub, K. A generalised kinetic equation for electrons in disordered solids J. Phys. C: Solid State
Phys. 15, pp. 2157–2170, 1985.
[2]
Bruce, N. A., Morgan, G. J. Quantum interference in liquid metals Phys. Rev. B 51, pp. 12313–12321, 1995
[3]
Spisak, B. J, Paja, A. and Morgan, G. J. Influence of spin–orbit interaction on the electrical conductivity of three-dimensional
disordered systems phys. stat. solidi b 242, pp.1460–1475, 2005.
[4]
Spisak B. J. Transport properties and localisation of one-electron states in systems with disturbed translational symmetry, Libron
Press, Kraków 2013 (in polish).
SSPCM-55
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Combinatorics of Lax objects in Bethe Ansatz
RYSZARD S TAGRACZYNSKI1
1
Rzeszow University of Technology, Powstancow Warszawy, Rzeszow
[email protected]
ABSTRACT
Algebraic Bethe Ansatz (ABA) also known as Quantum Inverse Scattering Method (QISM) is an
consistent tool based on Yang-Baxter equation which allows to costruct Bethe Ansatz exact solutions.
One of the most important objects in ABA is an Monodromy matrix M which is defined as an appriopriate
product of so called ”Lax” operators L (local transition operators). Monodromy matrix as well as each
of Lex operators acts in tensor product of quantum space H with axuliary space C2 . Thus M written in
basis of axuliary space consist of four elements A, B, C, D which are operators acting in quantum space
H, where B and C are creation anihilation operators and the reamining are source of motion constatns.
This work is an proposition of constistent method of construcion Bethe Ansatz eigenstates by using ”Lax
objects” i.e. a, b, c, d - appriopriate elements of Lax operators.
SSPCM-56
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Strain designed magnetic properties in III-V semiconductors
S. S TAGRACZY ŃSKI1 , C. JASIUKIEWICZ2 , V. K. D UGAEV2 , AND J. B ERAKDAR1
1
Institute für Physik, Martin-Luther-Universität Halle-Wittenberg, 06120 Halle (Saale), Germany
[email protected]
2
Department of Physics, University of Technology, 35-959 Rzeszów, Poland
ABSTRACT
We investigate the 6-band Kane model for the valence band structure of III-V magnetic semiconductors. What is searched for is the general way to effectively control magnetic properties which are strongly
coupled with elastic properties. The aim is to find out whether uni/bi-axial strain could be used to tune
the system. We get the complicated view of total energy variations with applied magnetization and compressive/tensile strain under selected hole concentration. Later on those three parameters are intensively
used to bring a better understanding of anisotropy in the semiconductors.
In our work we perform low level numerical algorithm based on a three-dimensional grid to notice sensitive dependency on direction of magnetisation. These dependencies are strongly affected by the strain.
As an example, we have chosen GaMnAs semiconductor system. In the presence of strain the amplitude
of total energy variation and the magnetic anisotropy can increase substantially. Further, we find the
dependency of the total energy on the hole concentration in the presence of strain, magnetization and its
direction. The results showed symmetry properties, the importance of strain and magnetization in the
semiconductor system.
SSPCM-57
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Theoretical study of ferromagnetic resonance in thin composite multiferroic structures
A LEXANDER S UKHOV1 , PAUL P. H ORLEY2 , C HENGLONG J IA3 , L EVAN C HOTORLISHVILI1 , D IRK S ANDER4 , AND JAMAL
B ERAKDAR1
1
Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, Halle/Saale, GERMANY
[email protected]
2
Centro de Investigación en Materiales Avanzados (CIMAV S.C.), Chihuahua/Monterrey, MEXICO
3
Key Laboratory for Magnetism and Magnetic Materials of the Ministry of Education, Lanzhou University, Lanzhou, CHINA
4
Max Planck Institute of Microstructure Physics, Halle/Saale, GERMANY
ABSTRACT
We present a detailed theoretical study of the ferromagnetic resonance (FMR) effect, where a set of
perpendicularly oriented strong static and weak time-dependent magnetic fields is utilized, performed for
composite multiferroic interfaces such as Fe- or Co/BaTiO3 . Our theoretical tool includes the LandauLifshitz-Gilbert equation for the magnetization dynamics and the Landau-Khalatnikov equation for the
ferroelectric polarization propagation [1]. Depending on whether the magnetoelectric coupling is chargeor strain/stress-mediated, we inspect the influence of the ferroelectric interface on the magnetic response
of the entire system. In particular, the effect of the strength of the magnetoelectric coupling and an
external static electric field are shown to essentially modify the obtained FMR-spectra, which render
possible a detection of the strength of the magnetoelectric coupling [2]. Recent experimental studies
[3] confirmed the theoretical predictions revealing a strong room-temperature magnetoelectric coupling
obtained from an asymmetric angular dependence of the FMR-spectra for thin Co/BaTiO3 -films.
References
[1]
Sukhov A., Jia C.-L., Horley P.P., Berakdar J., Polarization and magnetization dynamics of a field-driven multiferroic structure,
Journal of Physics: Condensed Matter 22, 352201 (2010).
[2]
Sukhov A., Horley P.P., Jia C.-L., Berakdar J., Magnetoelectric coupling in a ferroelectric/ferromagnetic chain revealed by ferromagnetic resonance, Journal of Applied Physics 113, 013908 (2013).
[3]
Jedrecy N., von Bardelen H.J., Badjeck V., Demaille D., Stanescu D., Magnan H., Barbier A., Strong magnetoelectric coupling in
multiferroic Co/BaTiO3 thin films, Physical Review B 88, 121409(R) (2013).
SSPCM-58
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Resonant tunneling in a semiconductor structure
T. S ZCZEPA ŃSKI1
AND
V. K. D UGAEV1,2
1
Department of Physics, Rzeszów University of Technology, Al. Powstańców Warszawy 6, 35-959 Rzeszów, Poland
[email protected]
2
Department of Physics and CFIF, Instituto Superior Técnico, Technical University of Lisbon, Av. Rovisco Pais, 1049-001 Lisbon,
Portugal
ABSTRACT
Recent experiments demonstrated the possibility of an effective magnetic control of the characteristics of resonant tunneling diode [1,2]. In these experiments, the spin-polarized injected current is mostly
related to the tunneling through the resonant level in a semiconductor quantum well, and the location
of level depends on the magnetic splitting of energy bands in the injector. In our work we discuss the
properties of resonant tunneling diode in context of its conductance as a function of the localization of
resonant level. We calculated the energy of the resonant level in the quantum well of a three-layer structure with two potential barriers, taking into account two different spin channels, as a function of the spin
splitting in the injector. This calculation gives us a tunneling-induced spin splitting of the level in the
limit of small current through the structure. The energy levels are formed inside the quantum well as a
consequence of quantizing the states between two barriers of potential in semiconductor structure. For
numerical calculations we used real parameters of the structure ZnBeMnSe/ZnBeSe/ZnSe/ZnBeSe [2].
We found that at some higher magnetic field acting on the spin splitting in the ZnBeMnSe injector, the
resonant level comes into the continuous spectrum of energies on the injector side. It leads to appearance
of a quantum width of the resonant level. In these conditions we calculated both the location of the level
and its quantum width. We also have taken into account the effect of spin polarization of the current with
respect to the orientation of magnetic field in the diluted magnetic semiconductor which is situated at the
external regions of barriers. We used the methods of solving Schrödinger equations for structure with
many layers and we found the solutions for the resonant level as a function of width of the quantum well
and for different values of potential energy of the barriers.
As the electric current through the resonant diode grows, another effect of the current-induced spin splitting becomes more pronounced. It is related to the spin accumulation at the resonant level in the nonequilibrium state. We calculated the energy profile of the structure taking into account the dependence of
spin-splitted chemical potentials for up and down spin states on the coordinate across the structure. We
consider the magnetization of the well induced by spin splitting of the resonant level in equilibrium and in
nonequilibrium case. That alowed us to predict the dependence between magnetization induced by spin
polarized current carying through the resonant level and external bias. The tunneling current through
the resonant diode is calculated, along with the electron energy structure within the quantum wall. The
results of our calculations are in good agreement with the experiment of Ref. [2]
References
[1] Z.L. Fang, P. Wu, N. Kundtz, A.M. Chang, X.Y. Liu, J.K. Furdyna Appl. Phys. Lett (May 2007)
[2] Van Nam Do, P. Dollfus, V.L.Nguyen cond-mat.mes-hall (May 2006)
SSPCM-59
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Spin-transport dependence on spin-orbit interaction in MTJs
T ITOVA M.S.1 , V EDYAEV A.V.1 , RYZHANOVA N.V1 , Z HURAVLEV M. Y E1,2 , S TRELKOV N.V1 , T SYMBAL E.Y3 , AND D IENY B.4
1
Moscow State University, Physics Department, Moscow, Russia
[email protected]com
2
Kurnakov Institute for General and Inorganic Chemistry, RAS, Moscow, Russia
3
3Department of Physics and Astronomy & Nebraska Center for Materials and Nanoscience, University of Nebraska, Lincoln, Nebraska
68588, USA
4
SPINTEC-URA CEA/CNRS, 38054 Grenoble, France
ABSTRACT
In our paper we developed the theory of tunneling anisotropic magnetoresistance (TAMR) in
magnetic tunnel junction due to spin-orbit interaction of Rashba type.
This type of spin-orbit is
proportional to the gradient of voltage drop across the barrier. It was demonstrated that in adopted
spin-polarized free electron model TAMR is closely related to the usual tunnel magnetoresistance, and in
case of half-metallic ferromagnetic electrodes having antiparallel orientation of magnetizations the value
of TAMR reaches 100%. Moreover, it was shown that due to SO interaction the relative TMR value
is finite even for half-metallic FM electrodes and reaches 103 −105 (in experiment 103 was observed [1]).
Also anomalous and spin Hall effects for a magnetic tunnel junction (MTJ) where Rashba spin-orbit
coupling within the tunneling barrier layer was produces by applied voltage were theoretically investigated. The ferromagnetic electrodes are the source of the spin-polarized current. Tunneling electrons
experience a spin-orbit coupling inside the barrier due to the applied electrical field. Charge and spin Hall
currents as functions of the position inside the barrier and the angle between the magnetizations of the
electrodes were calculated. It was found out that both charge and spin Hall currents were located inside
the barrier near the interfaces. The currents dependence on magnetic configuration of the MTJ makes it
possible to manipulate the Hall currents via rotation of the electrodes magnetizations.
References
[1] Tanja Graf, Stuart S. P. Parkin, and Claudia Felser Heusler Compounds - A Material Class With Exceptional Properties, IEEE
Transactions on Magnetics 47 (2011) 367
SSPCM-60
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Interference of mobits in Quantum Cognition Models
S TANISŁAW T OPOLEWICZ
ABSTRACT
We use the Modal Quantum Theory developed by Benjamin Schumacher and Michael D. Westmoreland to investigate the interference of mobits (modal bits) in the Quantum Cognition Models.
Modal Quantum Theory exhibits the fundamental properties of the Quantum Mechanics (entanglement,
no-cloning theorem, interference) but is much simpler and easier to use in case of the Quantum Cognition
Models.
In this paper we investigate one of the most important and interesting phenomenon - quantum interference
in case of the Quantum Cognition Models.
SSPCM-61
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Density of electron states and relaxation time of intercalated layer crystals
NATALIA T OVSTYUK1
1
Ivan Franko National University of L’viv, Dragomanova str., 50, L’viv, 79005, Ukraine
[email protected]
ABSTRACT
Intercalation of layer crystal by different guest atoms, particularly, 3d-atoms, allows us to create new
materials which can be very important for using in different aspects of applied physics. Layer crystal
can be represented as the sets of mono-atomic layers bonded by ion-covalent coupling which are bonded
by weak Van der Waals bound along the anisotropy axis. These sets of mono-atomic semiconductor
layers isolate cosequence of magnetic active atomic layers, formed by intercalant placed in the van der
Waals gap, m from one another thus avoiding their coagulation. At the same time intercalation allows
obtaining information from the metallic nanolayers. The structures with alternating semiconducting and
magneto-active layers can serve as materials on the base of those one can create the spintronic elements,
particularly, as the medium structures or spin-gated transistors. That is why complex studies of such
structures provide additional opportunities to modify their magnetic properties in a wide range.
In this paper the density of electron states of layered crystal intercalated by guests of different nature
is calculated within the framework of virtual crystal considering filling of both octahedral and tetrahedral
interstitial hollows. It is found that the shift of the gap of density of states is caused firstly by the nature
of intercalant (placing of ground energy states of both intercalants) and their average concentrations. In
the case when one type of intercalant gives localized level in the forbidden gap and another intercalant
forms the resonance one in the conductive band the gap disappears. Relaxation time corresponded to the
transitions from one to another band is calculated.
SSPCM-62
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Three-component gyrotropic metamaterial
1
I. T RALLE1 , P. Z I EBA
˛
,
1
AND
W. PA ŚKO1
Theoretical physics Department, Faculty of Mathematics and Natural Sciences, University of Rzeszów, Pigonia 1, Rzeszów, Poland
ABSTRACT
We propose a comparatively simple way to fabricate a metamaterial which is both gyrotropic and of
simultaneously negative permittivity and permeability. The idea is to make a mixture of three ingredients,
where one of them would be responsible for the negativity of ν, while the other two would be responsible
for the negativity of . The first component of the mixture is the ’swarm’ of single-domain ferromagnetic
nano-particles, immersed in a mixture of other two, silver and mercury cadmium telluride. In the work
we carried out computer simulations in the frame of proposed model in order to establish the domains
of existence of such material searching through the vast parameter space. The main result of the paper
can be summarized as follows. In the framework of the model, we succeeded in establishing the domains
of gyromagnetic metamaterial existence, relative to all parameters characterizing the model, that is, temperature, external magnetic field, parameters of nano-particles, fraction of cadmium in Hg1−x Cdx Te
-compound as well as the relative concentrations of the mixture components. Negative refraction and
optical activity can be achieved only if the material is in external, however moderate magnetic field. On
the other hand, in some circumstances it could be an advantage, since switching magnetic field on and
off, one can trigger off left-handedness.
SSPCM-63
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Measuring System for Observation of Electric Parameters of Graphene in Presence of
Temperature Gradient
M ARIUSZ T RYBUS1 , B OGDAN W O Ś1 , T YMOTEUSZ C IUK2 ,
1
AND
M ICHAŁ I NGLOT1
Rzeszów University of Technology, Rzeszów, Poland,
[email protected]
2
Institute Of Electronic Materials Technology, Warsaw
ABSTRACT
Graphene is one of the most promising materials for application in electronics [1]. It has been recently
discovered that on certain substrates graphene is characterized by a rather strong SO interaction [2], which
is valuable to spintronics applications. In this paper we present an application of a newly constructed
measuring system for the research of graphene’s electrical parameters. The idea of a measuring system
originates from the measurements of the pyroelectric coefficient of ferroelectric samples [3].
After a simple modification the system can be used for various experiments related to the determination
of the electric response of samples exposed to a temperature gradient.
Exemplary measurements of graphene samples and their thermoelectric response are presented.
References
[1]
A. K. Geim and K. S. Novoselov, The rise of graphene Nature Mater. 6, 183 (2007).
[2]
C. L. Kane and E. J. Mele, Quantum Spin Hall Effect in Graphene Phys. Rev. Lett. 95, 226801 (2005)
[3]
M. Trybus, W. Proszak, B. Wos, Response of TGS ferroelectric samples to rapid temperature impulses, Infrared Physics and Technology 61 (2013) 81-87.
SSPCM-64
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Magnetic band Brillouin zone of an electron in a periodic potential and quantized
magnetic field
A NDRZEJ WAL1
1
Faculty of Mathematics and Natural Science, University of Rzeszow, Pigonia 1, 35-959 Rzeszow, Poland
[email protected]
ABSTRACT
Analysis of properties of a Brillouine zone of an itinerant electron in a periodic two-dimensional
potential and perpendicular, quantized magnetic field is presented. The description is based on the symmetry of the system given by the magnetic translation group. The irreducible representations of the group
describe the energy structure and determine nonequivalent quasimomenta forming magnetic band Brillouine zone. This zone is rarefied in both directions in comparison to Brillouine zone without magnetic
field.
SSPCM-65
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Electric and thermoelectric properties of T-shaped double quantum dots coupled to
ferromagnetic leads
K RZYSZTOF P. W ÓJCIK1
1
AND I RENEUSZ
W EYMANN1
Faculty of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland
[email protected]
ABSTRACT
We analyze transport and thermoelectric properties of interacting double quantum dots strongly coupled to two ferromagnetic leads and forming a T-shaped configuration. The calculations are performed
in linear response regime, using the numerical renormalization group procedure [1, 2], with full density
matrix of the system [3]. We find that due to the effective exchange field induced by ferromagnets, the
Fano antiresonance in the conductance [4] becomes spin-splitted. This results in enhancement of spin
polarization of the linear conductance, which reaches all values form -1 to 1, depending on the dots levels
positions, without any external magnetic field applied [5]. However, the effect is suppressed at higher
temperatures.
References
[1]
K. G. Wilson, Rev. Mod. Phys. 47, 773 (1975).
[2]
We use the open-access Budapest NRG code, O. Legeza, C. P. Moca, A. I. Tóth, I. Weymann, G. Zaránd, arXiv:0809.3143 (2008)
(unpublished). The code is available at: http://www.phy.bme.hu/dmnrg/
[3]
A. Weichselbaum, J. von Delft, Phys. Rev. Lett. 99, 076402 (2007).
[4]
R. Žitko, Phys. Rev. B 81, 115316 (2010).
[5]
K.P. Wójcik, I. Weymann, submitted to Phys. Rev. B (2014).
SSPCM-66
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
A method for measuring thermal conductivity of liquid by using a laser beam
A NDRZEJ WASILEWSKI1
1
AND
1
T OMASZ W I ECEK
˛
Rzeszów University of Technology, al. Powstańców Warszawy 12, Rzeszów, Poland
[email protected]
ABSTRACT
This work describes a new laser system to measure the dynamic Young’s modulus and logarithmic
decrement of damping for fibers varied twisting. The Impulse Mechanical Spectrometer (IMS) was
designed and built by the authors. A change of the vibration frequency is achieved by changing the length
of the fibre or the load. The dynamic Young’s modulus and logarithmic decrement of damping were also
estimated in the dynamic characterization. The experimental method does not require calibration.
SSPCM-67
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Spin and charge transport through the Fe/MgO/GaAs heterostructure
S. W OLSKI1 , V. K. D UGAEV1,2 , J. BARNA Ś3 , T. S LOBODSKYY4 , AND W. H ANSEN4
1
Department of Physics, Rzeszów University of Technology, al. Powstańców Warszawy 6, 35-959 Rzeszów, Poland
[email protected]
2
Departmento de Fı́sica and CFIF, Instituto Superior Técnico, Universidade de Lisboa, av. Rovisco Pais, 1049-001 Lisbon, Portugal
3
Faculty of Physics, Adam Mickiewicz University, ul. Umultowska 85, 61-614 Poznań, Poland
4
Institute for Applied Physics, University of Hamburg, Jungiusstraße 11, 20355 Hamburg, Germany
ABSTRACT
One of intensively investigated problems in modern spintronics is the problem of spin injection into
semiconductor through the insulating tunnel barrier. It is well known that this method provides maximum
efficiency of spin polarization of the injected electrons. The best known now insulator material for the
tunnel barrier is MgO.
Here we present our theoretical results and the results of computer simulation of the tunneling current
and spin polarization efficiency of Fe/MgO/GaAs junctions as a function of external voltage for different
parameters characterising the semiconducting GaAs. The main mechanism of the current is related to
the tunneling through the barrier changing its shape under bias voltage. We found that the resistance of
strongly doped n- or p-type GaAs usually gives relatively small correction to the tunneling resistance
for any parameters of semiconductor. However, our computer simulations show that the essential effect
can be related to some special doping of GaAs in the border region near the MgO/GaAs interface. For
example, a thin layer of nearly intrinsic semiconductor can be formed near the interface due to the deep
levels of Fe impurity atoms in GaAs. It turns out that this changes dramatically the energy diagram of the
junction making the tunneling characteristics similar to the case of tunneling to the energy gap.
Our theoretical results are in good agreement with the measurements of current-voltage characteristics of
metal-insulator-semiconductor heterostructure with Fe nanodisks at the surface of GaAs semiconductor
covered with thin MgO layer.
This work is supported by the National Center of Research and Development in Poland in frame of EU
project Era.Net.Rus ”SpinBarrier”.
SSPCM-68
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Density functional theory simulation of an electrostatic
D. P. Ż EBROWSKI1
1
AND
B. S ZAFRAN1
AGH University of Science and Technology, , Faculty of Physics and Applied Computer Science, , al. Mickiewicza 30, 30-059 Kraków,
Poland
ABSTRACT
The electronic properties of graphene akes depend strongly on its size and geometry [5]. While the
infinite graphene sheet exhibit a linear, gapless spectrum, the proper boundary and the size of the finite
sample can make it a semiconductor with a tunable band gap. The presence of an energy gap lifts the Klein
tunneling of the carriers and allows for confinement of the electrons in states bound in a quantum dot by
external potential. Good examples of the structures with these properties are the graphene nanoribbons.
It has been shown [1] that those structures open gaps if the side edges are of the armchair type. The
confinement in those kind of structures was studied both experimentally [3] and theoretically [2] for the
graphene nanoribbons. We consider a finite strip of the nanoribbon with solely armchair edges graphene,
excluding the surface states near the neutrality point present at zigzag boundaries. For that configuration
the gap is open and the electrostatic confinement is now possible. In the center of the strip we apply
the confining potential. We determine the charge density and the potential profile using the tight-binding
method in the pz orbitals basis. The electron-electron interaction is treated with the all-electron DFT
calculations with the appropriately selected XC-functional [4] suitable for the two dimensional systems.
After the convergence of the DFT self-consistent loop is achieved we calculate the chemical potential,
addition energy and the number of electrons inside the flake. By integrating the electron density in the
quantum dot region we calculate the capacitance of the dot.
References
[1] L. Brey and H. A. Fertig, Phys. Rev. B 73, 235411 (2006).
[2] M. Droth and G. Burkard, Phys. Rev. B 87, 205432 (2013).
[3] M. Y. Han and P. Kim ,Nano Convergence 2014, 1:5
[4] C. Attaccalite, S. Moroni, P. Gori-Giorgi, and G. B. Bachelet, Phys. Rev. Lett. 88, 256601 (2002).
[5] E. McCann and M. Koshino, Rep. Prog. Phys. 76, 056503 (2013).
SSPCM-69
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Changes of nanoparticles agglomerates sizes during rotation measurement of
rheological properties of MgAl2 O4 -diethylene glycol nanofluids
G AWEŁ Ż YŁA1
1
AND
M ARIAN C HOLEWA1
Department of Physics, Rzeszów University of Technology, Rzeszów, Poland,
[email protected]
ABSTRACT
Nanofluid is called a suspension of nanoparticles in a liquid base. This relatively new group of engineering materials today presents the potential for broad practical application. One of the most interesting
and most investigated nanofluids properties is the increase of its’ thermal conductivity with compare to
the base liquid. Can not be forgotten, however, that with increasing concentration of nanoparticles in the
suspension it also changes the mechanical properties (in particular rheology) of such materials.
The paper presents a complete rheological profile of MgAl2 O4 -diethylene glycol nanofluids. Dynamic
viscosity curves were measured for shear rate range from 0.01 to 1000 s−1 for the various nanoparticle
mass concentration. Thixotropic properties depending on the concentration were examined in shear rate
range from 1 to 1000 s−1 . It was determined dependence of dynamic viscosity on temperature in the
range from 0o C to 50o C and viscoelastic oscillatory structure [1]. In addition, the dynamic viscosity
curves under an anisotropic pressure of 7.5 MPa and the effect of the electric field (from 0 V/mm to
2000 V/mm) on the viscosity of the material was determined [2].
One of the unexpected results of the work on determining the viscosity curves of these materials was
the occurrence of a local maximum in dynamic viscosity curve. This phenomenon is related to the
formation of agglomerates of nanoparticles during the rotation test [3]. Based on the observations not only
determined rheological properties of MgAl2 O4 -DG nanofluids, but also demonstrated that the rotational
measurement may interfere with the sample influencing the results.
References
[1]
Żyła G., Cholewa M., Witek A., Rheological properties of diethylene glycol-based MgAl2 O4 nanofluids, RSC Advances, 3, pp.
6429–6434 (2013)
[2]
Żyła G., Grzywa J., Witek A., Cholewa M., Influence of anisotropic pressure on viscosity and electrorheology of diethylene glycolbased MgAl2 O4 nanofluids, Nanoscale Research Letters, 9, pp. 170 (2014)
[3]
Żyła G., Cholewa M., On unexpected behavior of viscosity of diethylene glycol-based MgAl2 O4 nanofluids, RSC Advances, 4, pp.
26057–26062 (2014)
SSPCM-70
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
SSPCM-71
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
Index of Authors
——/
A
/——
Agundez, Rodrigo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Araujo, Miguel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
——/
B
/——
Berakdar, Jamal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Bocian, Kacper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
——/
C
/——
Castro, Eduardo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Chotorlishvili, Levan. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27
Czyż, Henryka . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
——/
D
/——
Denisov, Konstantin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Dyrdał, Anna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Działo, Artur . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
——/
E
/——
Ernst, Arthur . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
——/
F
/——
Fabian Jaroslav . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Fal, Jacek . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Fiedler Bernd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
——/
G
/——
Glavey, Russell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Gálisová, Lucia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
——/
I
/——
Inglot, Michał . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
——/
J
/——
Jakubczyk, Dorota . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Jakubczyk, Paweł . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
——/
K
/——
Kats, Efim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Khaetskii, Alexander . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Kolasiński, Krzysztof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Kolek, Andrzej . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Kościk, Przemysław . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Kuroś, Arkadiusz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Kurpas, Marcin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Kuźma, Marian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
——/
L
/——
Labuz, Mirosław . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
Lacroix, Claudine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Lulek, Tadeusz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
——/
M
/——
Majchrowski, Klaudiusz . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Mamczur, Jan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Margańska, Magdalena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Marmodoro, Alberto . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
Mera, Bruno Miguel Santos . . . . . . . . . . . . . . . . . . . . . . . . 46
Mreńca, Alina . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
——/
N
/——
Nowak, Michal Piotr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
——/
O
/——
Osika, Edyta Natalia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
——/
P
/——
Pekerten, Barış . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
Pelc, Marta Zuzanna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
Poshakinskiy, Alexander . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
——/
R
/——
Reijnders, Koen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
——/
S
/——
Seredyuk, Bogdan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
Sherman, Evgeny . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Spisak, Bartlomiej . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
Stagraczyński, Ryszard . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
Stagraczyński, Stefan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
Sukhov, Alexander. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .58
Szczepański, Tomasz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
Szopa, Marek . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
——/
T
/——
Titova, Maria. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .60
Topolewicz, Stanisław . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
Tovstyuk, Natalia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
Tralle, Igor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15, 63
Trybus, Mariusz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
——/
V
/——
Vieira, Victor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Vourdas, Apostolos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
——/
W
/——
Wal, Andrzej . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
Wasilewski, Andrzej . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Weymann, Ireneusz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Wolski, Sławomir . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
Wysokiński, Karol Izydor . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Wójcik, Krzysztof Piotr . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
Wójs, Arkadiusz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014
——/
Z
/——
Zawadzki, Włodzimierz . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Zebrowski, Dariusz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Zipper, Elżbieta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Zi˛eba, Paweł . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Zyła, Gaweł . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
Book of abstracts of The Eleventh International School on Theoretical Physics, Rzeszów, Poland, September 1-6, 2014

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