Integer quantum Hall effect in a lattice model revisited: Kubo formalism

Dutta, Paramita; Maiti, Santanu K.; Karmakar, S. N.

doi:10.1063/1.4748312

Cited by 27 publications

(13 citation statements)

References 25 publications

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“…In this case the system becomes periodic in the remaining spatial direction and one can use the Bloch decomposition with respect to that direction. Hence, the 2-dimensional Schrödinger equation can be reduced to a 1-dimensional Harper's like equation, which has been studied computationally by various techniques [15,16,36,63,51,62,56,57,32,35,17]. As such, the rigorous error bounds reported in this section (see Theorem 6.3) can still be of interest to numerical analysts.…”

Section: Approximating Algebras: First Roundmentioning

confidence: 98%

Quantum Transport in Disordered Systems Under Magnetic Fields: A Study Based on Operator Algebras

Prodan

2012

Applied Mathematics Research eXpress

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The linear conductivity tensor for generic homogeneous, microscopic quantum models was formulated as a noncommutative Kubo formula in Refs. [6,53,54]. This formula was derived directly in the thermodynamic limit, within the framework of C * -algebras and noncommutative calculi defined over infinite spaces. As such, the numerical implementation of the formalism encountered fundamental obstacles. The present work defines a C * -algebra and an approximate noncommutative calculus over a finite real-space torus, which naturally leads to an approximate finite-volume noncommutative Kubo formula, amenable on a computer. For finite temperatures and dissipation, it is shown that this approximate formula converges exponentially fast to its thermodynamic limit, which is the exact noncommutative Kubo formula. The approximate noncommutative Kubo formula is then deconstructed to a form that is implementable on a computer and simulations of the quantum transport in a 2-dimensional disordered lattice gas in a magnetic field are presented.

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Section: Approximating Algebras: First Roundmentioning

confidence: 98%

Quantum Transport in Disordered Systems Under Magnetic Fields: A Study Based on Operator Algebras

Prodan

2012

Applied Mathematics Research eXpress

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“…The magnetic field is introduced as an phase factor 2π Bzya φo felt by an electron when moving along the x−direction, where φ o = h/e is the magnetic flux quantum. To keep the periodicity along the y-direction, the magnetic flux is chosen to be a rational number and commensurate with the width N y [28,29].…”

Section: Model Hamiltonianmentioning

confidence: 99%

Topological phase transitions in an inverted InAs/GaSb quantum well driven by tilted magnetic fields

Hsu¹,

Jhang²,

Chen³

et al. 2017

Phys. Rev. B

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The helical edge states in a quantum spin Hall insulator are presumably protected by timereversal symmetry. However, even in the presence of magnetic field which breaks time-reversal symmetry, the helical edge conduction can still exist, dubbed as pseudo quantum spin Hall effect. In this work, the effects of the magnetic fields on the pseudo quantum spin Hall effect and the phase transitions are studied. We show that an in-plane magnetic field drives a pseudo quantum spin Hall state to metallic state at a high field. Moreover, at a fixed in-plane magnetic field, an increasing out-of-plane magnetic field leads to a reentrance of pseudo quantum spin Hall state in an inverted InAs/GaSb quantum well. The edge state probability distribution and Chern numbers are calculated to verify that the reentrant states are topologically nontrivial. The origin of the reentrant behavior is attributed to the nonmonotonic bending of Landau levels and the Landau level mixing caused by the orbital effect induced by the in-plane magnetic field. The robustness to disorder is demonstrated by the numerically calculated quantized conductance for disordered nanowires within Landauer-Büttiker formalism.

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“…It should be noted that, like a conventional disordered material, the localization of energy levels always starts from the band edges, keeping the extended states towards the band centre. This phenomenon has been revisited in our recent work in the context of studying integer quantum Hall effect 56 within a tight-binding framework. It reveals that, for large enough electric field almost all the energy levels get localized, and therefore, no such crossover between a conducting zone and an insulating phase is observed.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

Electric field induced localization phenomena in a ladder network with superlattice configuration: Effect of backbone environment

2014

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Electric field induced localization properties of a tight-binding ladder network in presence of backbone sites are investigated. Based on Green's function formalism we numerically calculate two-terminal transport together with density of states for different arrangements of atomic sites in the ladder and its backbone. Our results lead to a possibility of getting multiple mobility edges which essentially plays a switching action between a completely opaque to fully or partly conducting region upon the variation of system Fermi energy, and thus, support in fabricating mesoscopic or DNA-based switching devices.

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Integer quantum Hall effect in a lattice model revisited: Kubo formalism

Cited by 27 publications

References 25 publications

Quantum Transport in Disordered Systems Under Magnetic Fields: A Study Based on Operator Algebras

Quantum Transport in Disordered Systems Under Magnetic Fields: A Study Based on Operator Algebras

Topological phase transitions in an inverted InAs/GaSb quantum well driven by tilted magnetic fields

Electric field induced localization phenomena in a ladder network with superlattice configuration: Effect of backbone environment

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