Publications (52)111.73 Total impact
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ABSTRACT: Analytic technique based on Chebyshev polynomials is developed for studying twodimensional lattice ribbons with hopping anisotropy. In particular, the tightbinding models on square and triangle lattice ribbons are investigated with anisotropic nearest neighbouring hoppings. For special values of hopping parameters the square lattice becomes topologically equivalent to a honeycomb one either with zigzag or armchair edges. In those cases as well as for triangle lattices we perform the exact analytic diagonalization of tightbinding Hamiltonians in terms of Chebyshev polynomials. Deep inside the edge state subband the wave functions exhibit exponential spatial damping which turns into powerlaw damping at edgebulk transition point. It is shown that strong hopping anisotropy crashes down edge states, and the corresponding critical conditions are found.01/2014;  [Show abstract] [Hide abstract]
ABSTRACT: We show that the combination of a Dresselhaus interaction and a spatially periodic Rashba interaction leads to the formation of a helical liquid in a quantum wire when the electronelectron interaction is weakly screened. The effect is sustained by a helicitydependent effective band gap which depends on the size of the Dresselhaus and Rashba spinorbit couplings. We propose a design for a semiconductor device in which the helical liquid can be realized and probed experimentally.11/2013;  [Show abstract] [Hide abstract]
ABSTRACT: We study Anderson localization in disordered helical conductors that are obtained from onedimensional conductors with spinorbit interaction and a magnetic field, or from equivalent systems. We call such conductors “quasihelical” because the spins of the counterpropagating modes are not perfectly antiparallel and have a small spinwavefunction overlap that is tunable by the magnetic field. Due to the overlap, disorder backscattering is possible and allows a localization transition. A conductor can pass through two localization transitions with increasing field, one from the conventionally localized system to the quasihelical conductor (with localization length exceeding the system length), and one at a higher field again to a localized state, due now, however, to backscattering below the magneticfield induced pseudogap. We investigate these transitions using a unified twostep renormalization group approach.Physical Review B 02/2013; 87:075151. · 3.66 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We consider the dimerized spin1/2 Heisenberg chain with spin hexameric distortion of the exchange pattern and study the zerotemperature phase diagram in the parameter space $(J_{1}, J_{2}, J_{3})$ by continuumlimit bosonization approach and the exact diagonalization method. The phase diagram is rich and has two gaped dimer phases. We obtain an estimate of the critical line separating the different gapped dimer phases by the bosonization approach. The existence of the transition line and the difference between dimer phases is checked numerically. The behavior of the energy gap and the dimer order parameter supports the exact location of the gapless line.physica status solidi (b) 08/2012; · 1.49 Impact Factor 
Article: Magnetic properties of the spin S = 1/2 Heisenberg chain with hexamer modulation of exchange.
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ABSTRACT: We consider the spin1/2 Heisenberg chain with alternating spin exchange in the presence of additional modulation of exchange on odd bonds with period 3. We study the ground state magnetic phase diagram of this hexamer spin chain in the limit of very strong antiferromagnetic (AF) exchange on odd bonds using the numerical Lanczos method and bosonization approach. In the limit of strong magnetic field commensurate with the dominating AF exchange, the model is mapped onto an effective XXZ Heisenberg chain in the presence of uniform and spatially modulated fields, which is studied using the standard continuumlimit bosonization approach. In the absence of additional hexamer modulation, the model undergoes a quantum phase transition from a gapped phase into the only one gapless Lüttinger liquid (LL) phase by increasing the magnetic field. In the presence of hexamer modulation, two new gapped phases are identified in the ground state at magnetization equal to [Formula: see text] and [Formula: see text] of the saturation value. These phases reveal themselves also in the magnetization curve as plateaus at corresponding values of magnetization. As a result, the magnetic phase diagram of the hexamer chain shows seven different quantum phases, four gapped and three gapless, and the system is characterized by six critical fields which mark quantum phase transitions between the ordered gapped and the LL gapless phases.Journal of Physics Condensed Matter 03/2012; 24(11):116002. · 2.22 Impact Factor 
Article: The quantum group, Harper equation and the structure of Bloch eigenstates on a honeycomb lattice
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ABSTRACT: The tightbinding model of quantum particles on a honeycomb lattice is investigated in the presence of homogeneous magnetic field. Provided the magnetic flux per unit hexagon is rational of the elementary flux, the oneparticle Hamiltonian is expressed in terms of the generators of the quantum group $U_q(sl_2)$. Employing the functional representation of the quantum group $U_q(sl_2)$ the Harper equation is rewritten as a systems of two coupled functional equations in the complex plane. For the special values of quasimomentum the entangled system admits solutions in terms of polynomials. The system is shown to exhibit certain symmetry allowing to resolve the entanglement, and basic single equation determining the eigenvalues and eigenstates (polynomials) is obtained. Equations specifying locations of the roots of polynomials in the complex plane are found. Employing numerical analysis the roots of polynomials corresponding to different eigenstates are solved out and the diagrams exhibiting the ordered structure of oneparticle eigenstates are depicted.Journal of Physics A Mathematical and Theoretical 03/2012; 45(39). · 1.77 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We study the crossover from a Luttinger liquid to a quasihelical liquid state in a onedimensional system of interacting electrons with strong spinorbit interaction in the presence of a transverse magnetic field, which leads to a gap for onehalf of the conducting modes. In particular, we study the effect of gap opening by electron localization in the presence of nonmagnetic disorder. We show that the localization length has a nonuniform behavior as a function of the magnetic field. With increasing field, the localization length grows from its zerofield Luttingerliquid value to a maximum, after which it crosses over to again smaller values corresponding to the localization length of spinless fermions.02/2012; 
Article: Quantum group on a honeycomb lattice
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ABSTRACT: The tightbinding model of electrons on a honeycomb lattice is studied in the presence of a homogeneous magnetic field. Provided the magnetic flux per unit hexagon is rational of the elementary flux the oneparticle Hamiltonian is expressed in terms of the generators of the quantum group U q (sl 2 ). Employing the functional representation of U q (sl 2 ) the Harper equation is rewritten as a systems of two coupled functional equations on a complex plane. For the special values of quasimomentum the entangled system admits solution in terms of polynomials. In that case the system exhibits certain symmetry relations allowing to resolve the entanglement, and basic single equation determining the eigenvalues eigenstates (polynomials) is obtained. Equations specifying the locations of the roots of polynomials on a complex plane and consequently the oneparticle wave functions are found. Employing numeric analysis the roots of polynomials corresponding to different eigenstates are solved out and the diagrams exhibiting the ordered structure of oneparticle states are depicted.Proceedings of A. Razmadze Mathematical Institute. 01/2012; 160.  [Show abstract] [Hide abstract]
ABSTRACT: It was recently shown that a spatially modulated Rashba spinorbit coupling in a quantum wire drives a transition from a metallic to an insulating state when the wave number of the modulation becomes commensurate with the Fermi wave length of the electrons in the wire. It was suggested that the effect may be put to practical use in a future spin transistor design. In the present article we revisit the problem and present a detailed analysis of the underlying physics. First, we explore how the buildup of charge density wave correlations in the quantum wire due to the periodic gate configuration that produces the Rashba modulation influences the transition to the insulating state. The interplay between the modulations of the charge density and that of the spinorbit coupling turns out to be quite subtle: Depending on the relative phase between the two modulations, the joint action of the Rashba interaction and charge density wave correlations may either enhance or reduce the Rashba current blockade effect. Secondly, we inquire about the role of the Dresselhaus spinorbit coupling that is generically present in a quantum wire embedded in semiconductor heterostructure. While the Dresselhaus coupling is found to work against the current blockade of the insulating state, the effect is small in most materials. Using an effective field theory approach, we also carry out an analysis of effects from electron electron interactions, and show how the singleparticle gap in the insulating state can be extracted from the more easily accessible collective charge and spin excitation thresholds. The smallness of the singleparticle gap together with the antiphase relation between the Rashba and chemical potential modulations pose serious difficulties for realizing a Rashbacontrolled current switch in an InAsbased device. Some alternative designs are discussed.Physical review. B, Condensed matter 05/2011; 84. · 3.77 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We analyze the dynamics of the helical edge modes of a quantum spin Hall state in the presence of a spatially nonuniform Rashba spinorbit (SO) interaction. A randomly fluctuating Rashba SO coupling is found to open a scattering channel which causes localization of the edge modes for a weakly screened electronelectron (ee) interaction. A periodic modulation of the SO coupling, with a wave number commensurate with the Fermi momentum, makes the edge insulating already at intermediate strengths of the ee interaction. We discuss implications for experiments on edge state transport in a HgTe quantum well.Physical Review Letters 06/2010; 104(25):256804. · 7.73 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Interacting onedimensional conductors with Rashba spinorbit coupling are shown to exhibit a spinselective Peierlstype transition into a mixed spinchargedensitywave state. The transition leads to a gap for onehalf of the conducting modes, which is strongly enhanced by electronelectron interactions. The other half of the modes remains in a strongly renormalized gapless state and conducts opposite spins in opposite directions, thus providing a perfect spin filter. The transition is driven by magnetic field and by spinorbit interactions. As an example we show for semiconducting quantum wires and carbon nanotubes that the gap induced by weak magnetic fields or intrinsic spinorbit interactions can get renormalized by 1 order of magnitude up to 10  30 K. Comment: 6 pages, 5 figures; final versionPhysical Review B 04/2010; 82:045127. · 3.66 Impact Factor 
Article: Edge State Transport in a Quantum Spin Hall Insulator: Effects from Rashba SpinOrbit Coupling
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ABSTRACT: We analyze the dynamics of the helical edge modes of a quantum spin Hall insulator in the presence of a spatially nonuniform Rashba spinorbit coupling. The Rashba coupling is found to open a scattering channel which causes localization of the edge modes when the electronelectron interaction or the spatial Rashba variation is sufficiently large. We discuss implications for experiments on edge state transport in HgTe quantum wells.03/2010;  [Show abstract] [Hide abstract]
ABSTRACT: We consider theoretically transport in a spinful onechannel interacting quantum wire placed in an external magnetic field. For the case of two pointlike impurities embedded in the wire, under a small voltage bias the spinpolarized current occurs at special points in the parameter space, tunable by a single parameter. At sufficiently low temperatures complete spin polarization may be achieved, provided repulsive interaction between electrons is not too strong.Physical Review Letters 02/2010; 104(7):076401. · 7.73 Impact Factor 
Article: Metalinsulator transition in a quantum wire driven by a modulated Rashba spinorbit coupling
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ABSTRACT: We study the groundstate properties of electrons confined to a quantum wire and subject to a smoothly modulated Rashba spinorbit coupling. When the period of the modulation becomes commensurate with the band filling, the Rashba coupling drives a quantum phase transition to a nonmagnetic insulating state. Using bosonization and a perturbative renormalization group approach, we find that this state is robust against electronelectron interactions. The gaps to charge and spin excitations scale with the amplitude of the Rashba modulation with a common interactiondependent exponent. An estimate of the expected size of the charge gap, using data for a gated InAs heterostructure, suggests that the effect can be put to practical use in a future spin transistor design. Comment: 4 pages; published version (added references, typos corrected)Physical review. B, Condensed matter 04/2009; · 3.77 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The groundstate magnetic phase diagram of a spin S=1/2 twoleg ladder with alternating rung exchange J⊥(n)=J⊥[1 + (1)n δ] is studied using the analytical and numerical approaches. In the limit where the rung exchange is dominant, we have mapped the model onto the effective quantum sineGordon model with topological term and identified two quantum phase transitions at magnetization equal to the half of saturation value from a gapped to the gapless regime. These quantum transitions belong to the universality class of the commensurateincommensurate phase transition. We have also shown that the magnetization curve of the system exhibits a plateau at magnetization equal to the half of the saturation value. We also present a detailed numerical analysis of the low energy excitation spectrum and the ground state magnetic phase diagram of the ladder with rungexchange alternation using Lanczos method of numerical diagonalizations for ladders with number of sites up to N = 28. We have calculated numerically the magnetic field dependence of the lowenergy excitation spectrum, magnetization and the onrung spinspin correlation function. We have also calculated the width of the magnetization plateau and show that it scales as δν, where critical exponent varies from ν = 0.87±0.01 in the case of a ladder with isotropic antiferromagnetic legs to ν = 1.82±0.01 in the case of ladder with ferromagnetic legs. Obtained numerical results are in an complete agreement with estimations made within the continuumlimit approach.Physics of Condensed Matter 03/2009; 68(1):5966. · 1.28 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We propose and analyze a device scheme by which an electrical current can be controlled via a gateoperated spinorbit interaction. The device consists of a quasionedimensional (1D) ballistic channel in a gated semiconductor heterostructure, contacted to a source and a drain and with the gates producing an alternating Rashba spinorbit interaction. When the period of the Rashba modulation becomes commensurate with the 1D electron density, the spinorbit interaction opens a charge gap, leading to a suppression of the current. Using bosonization and a perturbative RG approach we explore how electronelectron interactions influence the effect.03/2009;  [Show abstract] [Hide abstract]
ABSTRACT: We derive an effective spin Hamiltonian for the onedimensional halffilled tetramerized ionicHubbard model in the limit of strong onsite repulsion. We show that the effective Hamiltonian which describes the lowenergy spin sector of the model is a spin S=1/2 Heisenberg Hamiltonian with alternating nearestneighbour exchange.Soobshchenii͡a Akademii nauk Gruzinskoĭ SSR (1963) 02/2008; 
Article: Magnetic Phase Diagram of a Spin Antiferromagnetic S=1/2 Ladder with Alternating Rung Exchange
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ABSTRACT: The groundstate phase diagram of a twoleg spin ladder with alternating rung exchange 0 0 ) 1 ( ) ( ⊥ ⊥ ⊥ − + = J J n J n δ under the influence of a uniform magnetic field is studied. We have used the exact diagonalization technique. In the limit where the rung exchange is dominant, we have mapped the model onto the effective quantum sineGordon model with topological term and identified two quantum phase transitions at critical magnetic fields − c H and + c H from a gapped to the gapless regime. We have shown that for interme diate values of the magnetic field, at + − < < c c H H H the magnetization curve of the system exhibits a plateau at magnetization equal to the half of the saturation value. We also present a detailed numerical analysis of the low energy excitation spectrum and the ground state magnetic phase diagram of the system using the Lanczos method of numerical diagonalizations for ladders up to N=28 sites. We have calculated numerically the mag netic field dependence of the lowenergy excitation spectrum, the magnetization, the onrung spinspin corre lation function. We have also calculated the width of the magnetization plateau and show that it scales as ν δ ,01/2008;  [Show abstract] [Hide abstract]
ABSTRACT: We study the quantum phase transition from an insulator to a metal realized at t′=tc′>0.5t in the ground state of the halffilled Hubbard chain with both nearestneighbor (t) and nextnearestneighbor (t′) hopping. The study is carried out using the bosonization approach and densitymatrix renormalizationgroup calculations. An effective lowenergy Hamiltonian that describes the insulatormetal transition is derived. We find that the gross features of the phase diagram are well described by the standard theory of commensurateincommensurate transitions in a wide range of parameters. We also obtain an analytical expression for the insulatormetal transition line tc′(U,t). We present results of densitymatrixrenormalizationgroup calculations of spin and charge distribution in various sectors of the phase diagram. The numerical results support the picture derived from the effective theory and give evidence for the complete separation of the transitions involving spin and charge degrees of freedom.Physical review. B, Condensed matter 09/2007; 76(11). · 3.77 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: A detailed study of electronic phase transitions in the ionic Hubbard model at half filling is presented. Within the dynamical mean field approximation a series of transitions from the band insulator via a metallic state to a MottHubbard insulating phase is found at intermediate values of the onebody potential $\Delta$ with increasing the Coulomb interaction $U$. We obtain a critical region in which the metallic phase disappears and a {\it novel} coexistence phase between the band and the Mott insulating state sets in. Our results are consistent with those obtained at low dimensions, thus they provide a concrete description for the charge degrees of freedom of the ionic Hubbard model. Comment: 4 pages, 4 figuresPhysical review. B, Condensed matter 03/2007; · 3.77 Impact Factor
Publication Stats
549  Citations  
111.73  Total Impact Points  
Top Journals
Institutions

2003–2013

Andronikashvili Institute of Physics
Tbilsi, T'bilisi, Georgia


2011–2012

Ilia State University
 College of Engineering
Tbilsi, T'bilisi, Georgia


2010

University of Gothenburg
 Institutionen för fysik
Göteborg, Vaestra Goetaland, Sweden


1997–2009

University of Cologne
 Institute for Theoretical Physics
Köln, North RhineWestphalia, Germany


2007

University of Brasília
Brasília, Federal District, Brazil


2006

Université de Fribourg
 Department of Physics
Freiburg, Fribourg, Switzerland


2004–2006

Georgian National Academy of Sciences
Tbilsi, T'bilisi, Georgia


1999–2003

Universität Augsburg
Augsberg, Bavaria, Germany


1995

University of Sussex
 School of Mathematical and Physical Sciences
Brighton, ENG, United Kingdom
