Continuum theory of edge states of topological insulators: variational principle and boundary conditions

Medhi, Amal; Shenoy, Vijay B.

doi:10.1088/0953-8984/24/35/355001

Cited by 24 publications

(33 citation statements)

References 33 publications

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“…Refs. [11][12][13] analyzed dispersion dependence of SSs on the BCs for envelope functions (eigenfunctions of the kp-Hamiltonian). In this approach one should exploit a matrix form of BCs with some unknown parameters 14 that connect envelope functions and their derivatives on the interface.…”

Section: Introductionmentioning

confidence: 99%

Boundary conditions and surface state spectra in topological insulators

Enaldiev

Zagorodnev²

2015

Jetp Lett.

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We study spectra of surface states in 2D topological insulators (TIs) based on HgTe/(Hg,Cd)Te quantum wells and 3D Bi2Se3-type compounds by constructing a class of feasible time-reversal invariant boundary conditions (BCs) for an effective kp-Hamiltonian and a tight-binding model of the topological insulators. The BCs contain some phenomenological parameters which implicitly depend on both bulk Hamiltonian parameters and crystal potential behavior near the crystal surface. Space symmetry reduces the number of the boundary parameters to four real parameters in the 2D case and three in the 3D case. We found that the boundary parameters may strongly affect not only an energy spectrum but even the very existence of these states inside the bulk gap near the Brillouin zone center. Nevertheless, we reveal in frames of the tight-binding model that when surface states do not exist in the bulk gap in the Brillouin zone center they cross the gap in other points of the Brillouin zone in agreement with the bulk-boundary correspondence.

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Section: Introductionmentioning

confidence: 99%

Boundary conditions and surface state spectra in topological insulators

Enaldiev

Zagorodnev²

2015

Jetp Lett.

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“…This case is, in some sense, similar to a topological insulator (TI). TIs are electronic materials that have a bulk band gap like an ordinary insulator, but have protected conducting states on their edge or surface [2][3][4][5]. We have similar phenomenon for surface state protection as in TI, although the physical nature is different.…”

Section: Introductionmentioning

confidence: 61%

Periodic chain of disks in a magnetic field: bulk states and edge states

Grishanov¹,

Eremin²,

Ivanov³

et al. 2015

Nanosist.: fiz. him. mat.

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An explicitly solvable model for periodic chain of coupled disks in orthogonal magnetic field is considered. The spectrum for the Hamiltonian is compared with the spectrum for the corresponding chain of circles. These models are used for the comparison of the bulk and edge states. It is found that for some range of the magnetic field values the lowest band for the circles system lies below the spectrum for the corresponding disks system, i.e. the edge band is below and is separated from the lowest bulk band.

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“…This means that the solution for an isolated edge state (including the gapless dispersions) also becomes the solution for a finite ribbon, when the zeros of the transverse wave function match the width. This destructive interference has been studied before both with [51] and without [52] RSOC. Similar physics has also been discussed Table I. for thin films of 3D TIs [53][54][55].…”

Section: B the Case Of A Ribbon With Two Parallel Edgesmentioning

confidence: 99%

Generic helical edge states due to Rashba spin-orbit coupling in a topological insulator

et al. 2016

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We study the helical edge states of a two-dimensional topological insulator without axial spin symmetry due to the Rashba spin-orbit interaction. Lack of axial spin symmetry can lead to so-called generic helical edge states, which have energy-dependent spin orientation. This opens the possibility of inelastic backscattering and thereby nonquantized transport. Here we find analytically the new dispersion relations and the energy dependent spin orientation of the generic helical edge states in the presence of Rashba spin-orbit coupling within the Bernevig-Hughes-Zhang model, for both a single isolated edge and for a finite width ribbon. In the single-edge case, we analytically quantify the energy dependence of the spin orientation, which turns out to be weak for a realistic HgTe quantum well. Nevertheless, finite size effects combined with Rashba spin-orbit coupling result in two avoided crossings in the energy dispersions, where the spin orientation variation of the edge states is very significantly increased for realistic parameters. Finally, our analytical results are found to compare well to a numerical tight-binding regularization of the model.

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Continuum theory of edge states of topological insulators: variational principle and boundary conditions

Cited by 24 publications

References 33 publications

Boundary conditions and surface state spectra in topological insulators

Boundary conditions and surface state spectra in topological insulators

Periodic chain of disks in a magnetic field: bulk states and edge states

Generic helical edge states due to Rashba spin-orbit coupling in a topological insulator

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