Transport in a thin topological insulator with potential and magnetic barriers

Udupa, Adithi; Sengupta, K.; Sen, Diptiman

doi:10.1103/physrevb.98.205413

Cited by 6 publications

(6 citation statements)

References 68 publications

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“…The main results obtained for this system are as follows [78]. For a potential barrier, the conductance G is an oscillatory function of the barrier strength V 0 .…”

Section: Transport On Surfaces Of Topological Insulatorsmentioning

confidence: 96%

“…An interesting problem arises in the case of thin topological insulators where the tunneling between the two surfaces cannot be neglected. Such a situation has been studied in reference [78]. In this work, the effect of potential and magnetic barriers placed on only the top surface was investigated; a schematic picture of the system is shown in figure 22.…”

Section: Transport On Surfaces Of Topological Insulatorsmentioning

confidence: 99%

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Driven quantum many-body systems and out-of-equilibrium topology

Bandyopadhyay

Bhattacharjee

Sen

2021

J. Phys.: Condens. Matter

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“…The main results obtained for this system are as follows [78]. For a potential barrier, the conductance G is an oscillatory function of the barrier strength V 0 .…”

Section: Transport On Surfaces Of Topological Insulatorsmentioning

confidence: 96%

Section: Transport On Surfaces Of Topological Insulatorsmentioning

confidence: 99%

Driven quantum many-body systems and out-of-equilibrium topology

Bandyopadhyay

Bhattacharjee

Sen

2021

J. Phys.: Condens. Matter

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show abstract

“…Such a situation has been studied in Ref. 71. In this work, the effect of potential and magnetic barriers placed on only the top surface was investigated; a schematic picture of the system is shown in Fig.…”

Section: Transport On Surfaces Of Topological Insulatorsmentioning

confidence: 99%

“…The main results obtained for this system are as follows 71 . For a potential barrier, the conductance G is an oscillatory function of the barrier strength V 0 .…”

Section: Transport On Surfaces Of Topological Insulatorsmentioning

confidence: 99%

Driven quantum many-body systems and out-of-equilibrium topology

Bandyopadhyay,

Bhattacharjee,

Sen

2021

Preprint

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In this review we present some of the work done in India in the area of driven and out-of-equilibrium systems with topological phases. After presenting some well-known examples of topological systems in one and two dimensions, we discuss the effects of periodic driving in some of them. We discuss the unitary as well as the non-unitary dynamical preparation of topologically non-trivial states in one and two dimensional systems. We then discuss the effects of Majorana end modes on transport through a Kitaev chain and a junction of three Kitaev chains. Transport through the surface states of a three-dimensional topological insulator is discussed. The effects of hybridization between the top and bottom surfaces and the application of electromagnetic radiation on a strip-like region on the top surface are described. Two unusual topological systems are mentioned briefly, namely, a spin system on a kagome lattice and a Josephson junction of three superconducting wires. We have also included a pedagogical discussion on topology and topological invariants in the appendices, where the connection between topological properties and the intrinsic geometry of quantum states is also elucidated. Contents V. Generically driven two-dimensionalChern topological systems 24 A. The unitary no-go theorem 24 B. The non-unitary no-go theorem 26 C. Dissipative preparation of mixed states 28 1. Dissipators having a finite range 28 2. Macroscopic electric polarization and mixed state Chern number 29 3. Long-range dissipators and Floquet Chern insulators 32 D. Going around the unitary no-go theorem: bilayer Chern systems 34 VI. Majorana modes in one-dimensional systems and transport 35 VII. Transport on surfaces of topological insulators 37 VIII. Other topological systems 41 IX. Summary and future directions 42 A. A pedagogical introduction to the geometry and topology of quantum states43 1. Adiabatic transformations 43 a. Topology of adiabatically connected states44 2. The underlying geometry of quantum states 45 3. Topological invariants 48 a. Chern invariants 48 b. Bott invariant 50 B. A perturbative expansion of the steady state Majorana correlations 51 References 52

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“…The total transmitted particle current I t is clearly a function of θ. Given I t (θ), the differential conductance G can be calculated as follows 48 . Suppose that the µ L and µ R denote the chemical potentials of the left and right leads assumed to be at x → −∞ and x → ∞ respectively; the chemical potential µ in a lead is related to the voltage V applied to that lead as µ = qV , where q is the charge of the electron.…”

Section: δ-Function Magnetic Barriermentioning

confidence: 99%

Transport on a topological insulator surface with a time-dependent magnetic barrier

Udupa,

Sengupta,

Sen

2019

Preprint

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We study transport across a time-dependent magnetic barrier present on the surface of a three-dimensional topological insulator. We show that such a barrier can be implemented for Dirac electrons on the surface of a three-dimensional topological insulator by a combination of a proximate magnetic material and linearly polarized external radiation. We find that the conductance of the system can be tuned by varying the frequency and amplitude of the radiation and the energy of an electron incident on the barrier providing us optical control on the conductance of such junctions. We first study a δ-function barrier which shows a number of interesting features such as sharp peaks and dips in the transmission at certain angles of incidence. Approximate methods for studying the limits of small and large frequencies are presented. We then study a barrier with a finite width. This gives rise to some new features which are not present for a δ-function barrier, such as resonances in the conductance at certain values of the system parameters. We present a perturbation theory for studying the limit of large driving amplitude and use this to understand the resonances. Finally, we use a semiclassical approach to study transmission across a time-dependent barrier and show how this can qualitatively explain some of the results found in the earlier analysis. We discuss experiments which can test our theory.

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Transport in a thin topological insulator with potential and magnetic barriers

Cited by 6 publications

References 68 publications

Driven quantum many-body systems and out-of-equilibrium topology

Driven quantum many-body systems and out-of-equilibrium topology

Driven quantum many-body systems and out-of-equilibrium topology

Transport on a topological insulator surface with a time-dependent magnetic barrier

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