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Souza AMC, Almeida GMA, Mucciolo ER. Localization properties of a two-channel 3D Anderson model. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:285504. [PMID: 32191929 DOI: 10.1088/1361-648x/ab8155] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We study two coupled 3D lattices, one of them featuring uncorrelated on-site disorder and the other one being fully ordered, and analyze how the interlattice hopping affects the localization-delocalization transition of the former and how the latter responds to it. We find that moderate hopping pushes down the critical disorder strength for the disordered channel throughout the entire spectrum compared to the usual phase diagram for the 3D Anderson model. In that case, the ordered channel begins to feature an effective disorder also leading to the emergence of mobility edges but with higher associated critical disorder values. Both channels become pretty much alike as their hopping strength is further increased, as expected. We also consider the case of two disordered components and show that in the presence of certain correlations among the parameters of both lattices, one obtains a disorder-free channel decoupled from the rest of the system.
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Affiliation(s)
- Andre M C Souza
- Departamento de Física, Universidade Federal de Sergipe, 49100-000 São Cristóvão, SE, Brazil
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de Queiroz SLA, Stinchcombe RB. Driven flow with exclusion and spin-dependent transport in graphenelike structures. Phys Rev E 2017; 95:042121. [PMID: 28505791 DOI: 10.1103/physreve.95.042121] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2017] [Indexed: 11/07/2022]
Abstract
We present a simplified description for spin-dependent electronic transport in honeycomb-lattice structures with spin-orbit interactions, using generalizations of the stochastic nonequilibrium model known as the totally asymmetric simple exclusion process. Mean field theory and numerical simulations are used to study currents, density profiles, and current polarization in quasi-one-dimensional systems with open boundaries, and externally imposed particle injection (α) and ejection (β) rates. We investigate the influence of allowing for double site occupancy, according to Pauli's exclusion principle, on the behavior of the quantities of interest. We find that double occupancy shows strong signatures for specific combinations of rates, namely high α and low β, but otherwise its effects are quantitatively suppressed. Comments are made on the possible relevance of the present results to experiments on suitably doped graphenelike structures.
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Affiliation(s)
- S L A de Queiroz
- Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, 21941-972 Rio de Janeiro, Rio de Janeiro, Brazil
| | - R B Stinchcombe
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, United Kingdom
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Zhao Q, Müller CA, Gong J. Quantum and classical superballistic transport in a relativistic kicked-rotor system. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:022921. [PMID: 25215813 DOI: 10.1103/physreve.90.022921] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/26/2014] [Indexed: 06/03/2023]
Abstract
As an unusual type of anomalous diffusion behavior, (transient) superballistic transport is not well known but has been experimentally simulated recently. Quantum superballistic transport models to date are mainly based on connected sublattices which are constructed to have different properties. In this work, we show that both quantum and classical superballistic transport in the momentum space can occur in a simple periodically driven Hamiltonian system, namely, a relativistic kicked-rotor system with a nonzero mass term. The nonzero mass term essentially realizes a situation, now in the momentum space, in which two (momentum) sublattices with different dispersion relations (and hence different nature of on-site potential) are connected as a junction. It is further shown that the quantum and classical superballistic transport should occur under much different choices of the system parameters. The results are of interest to studies of anomalous transport, quantum and classical chaos, and the issue of quantum-classical correspondence.
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Affiliation(s)
- Qifang Zhao
- Department of Physics and Centre for Computational Science and Engineering, National University of Singapore, Singapore 117546, Republic of Singapore
| | - Cord A Müller
- Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Republic of Singapore and Department of Physics, University of Konstanz, 78457 Konstanz, Germany
| | - Jiangbin Gong
- Department of Physics and Centre for Computational Science and Engineering, National University of Singapore, Singapore 117546, Republic of Singapore and NUS Graduate School for Integrative Sciences and Engineering, Singapore 117456, Republic of Singapore
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Asatryan AA, Botten LC, Byrne MA, McPhedran RC, de Sterke CM. Evidence of a mobility edge for photons in two dimensions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:015601. [PMID: 17358216 DOI: 10.1103/physreve.75.015601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/05/2006] [Indexed: 05/14/2023]
Abstract
A scaling analysis of conductance for photons in two dimensions is carried out and, contrary to widely held belief, we find strong evidence of a mobility edge. Such behavior is compatible with the existence of an Anderson transition for electronic systems under symplectic symmetry, and indeed we show that the transfer matrix in the photonic system we have modelled has such a symmetry. We verify single parameter scaling of the conductance and demonstrate the transition from the metallic phase to localization. Key parameters, including the critical disorder, the conductance, and the critical exponent of the localization length are calculated, and it is shown that the value of the critical exponent is similar to that for electronic systems with symplectic symmetry.
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Affiliation(s)
- A A Asatryan
- Centre for Ultrahigh-bandwidth Devices for Optical Systems (CUDOS) and Department of Mathematical Sciences, University of Technology, Sydney NSW 2007, Australia
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Markoš P, Schweitzer L. Critical regime of two-dimensional Ando model: relation between critical conductance and fractal dimension of electronic eigenstates. ACTA ACUST UNITED AC 2006. [DOI: 10.1088/0305-4470/39/13/003] [Citation(s) in RCA: 42] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Asada Y, Slevin K, Ohtsuki T. Anderson transition in two-dimensional systems with spin-orbit coupling. PHYSICAL REVIEW LETTERS 2002; 89:256601. [PMID: 12484908 DOI: 10.1103/physrevlett.89.256601] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/28/2002] [Indexed: 05/24/2023]
Abstract
We report a numerical investigation of the Anderson transition in two-dimensional systems with spin-orbit coupling. An accurate estimate of the critical exponent nu for the divergence of the localization length in this universality class has to our knowledge not been reported in the literature. Here we analyze the SU(2) model. We find that for this model corrections to scaling due to irrelevant scaling variables may be neglected permitting an accurate estimate of the exponent nu=2.73+/-0.02.
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Affiliation(s)
- Yoichi Asada
- Department of Physics, Graduate School of Science, Osaka University, 1-1 Machikaneyama, Toyonaka, Japan
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Avishai Y, Meir Y. New spin-orbit-induced universality class in the integer quantum Hall regime. PHYSICAL REVIEW LETTERS 2002; 89:076602. [PMID: 12190544 DOI: 10.1103/physrevlett.89.076602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2001] [Indexed: 05/23/2023]
Abstract
Using heuristic arguments and numerical simulations it is argued that the critical exponent nu describing the localization length divergence at the integer quantum-Hall transition is modified in the presence of spin-orbit scattering with short-range correlations. The exponent is very close to nu=4/3, the percolation correlation length exponent, consistent with the prediction of a semiclassical argument. In addition, a band of weakly localized states is conjectured.
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Affiliation(s)
- Yshai Avishai
- Department of Physics and Ilse Katz Center for Meso- and Nanoscale Science and Technology, Ben Gurion University, Beer Sheva, Israel
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Kawarabayashi T, Ohtsuki T, Slevin K, Ono Y. Anderson Transition in Three-Dimensional Disordered Systems with Symplectic Symmetry. PHYSICAL REVIEW LETTERS 1996; 77:3593-3596. [PMID: 10062259 DOI: 10.1103/physrevlett.77.3593] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Sheng DN, Weng ZY. Topological characterization of delocalization in a spin-orbit coupling system. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:R11070-R11073. [PMID: 9984988 DOI: 10.1103/physrevb.54.r11070] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Kawarabayashi T, Ohtsuki T. Diffusion of electrons in two-dimensional disordered symplectic systems. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:6975-6978. [PMID: 9982136 DOI: 10.1103/physrevb.53.6975] [Citation(s) in RCA: 24] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Evangelou SN. Anderson transition, scaling, and level statistics in the presence of spin orbit coupling. PHYSICAL REVIEW LETTERS 1995; 75:2550-2553. [PMID: 10059340 DOI: 10.1103/physrevlett.75.2550] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Ludwig AW, Fisher MP, Shankar R, Grinstein G. Integer quantum Hall transition: An alternative approach and exact results. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:7526-7552. [PMID: 9974736 DOI: 10.1103/physrevb.50.7526] [Citation(s) in RCA: 102] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Medina E, Kardar M. Quantum interference effects for strongly localized electrons. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 46:9984-10006. [PMID: 10002836 DOI: 10.1103/physrevb.46.9984] [Citation(s) in RCA: 26] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Medina E, Kardar M. Spin-orbit scattering and magnetoconductance of strongly localized electrons. PHYSICAL REVIEW LETTERS 1991; 66:3187-3190. [PMID: 10043721 DOI: 10.1103/physrevlett.66.3187] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Ando T. Numerical study of symmetry effects on localization in two dimensions. PHYSICAL REVIEW. B, CONDENSED MATTER 1989; 40:5325-5339. [PMID: 9992560 DOI: 10.1103/physrevb.40.5325] [Citation(s) in RCA: 111] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Evangelou SN. Universal energy-level statistics for disordered metals. PHYSICAL REVIEW. B, CONDENSED MATTER 1989; 39:12895-12898. [PMID: 9948165 DOI: 10.1103/physrevb.39.12895] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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