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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 SSPCM-iii 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 SSPCM-v 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 SSPCM-viii 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 SSPCM-ix 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