Controlling edge state transport in a HgTe topological insulator by superlattice effect

L.-Z. Lin, F. Cheng, L. B. Zhang, D. Zhang, and Wen Yang

Phys. Rev. B 87, 245311 – Published 24 June 2013

Abstract

We investigate theoretically the edge state transport in a HgTe topological insulator under periodic electrical modulation. We find constructive interference of the backscattering amplitudes, leading to the formation of superlattice minigaps and hence complete suppression of the edge state transmission. Consequently, the edge channel can be switched on/off by appropriately tuning the modulation amplitude via gate voltages, even for wide Hall bar with a small finite size effect. We also find efficient conversion between spin-up and spin-down edge channels by the gate-induced Rashba spin-orbit interaction.

Received 1 April 2013

DOI:https://doi.org/10.1103/PhysRevB.87.245311

Authors & Affiliations

L.-Z. Lin^1,*, F. Cheng², L. B. Zhang³, D. Zhang¹, and Wen Yang^4,†

¹SKLSM, Institute of Semiconductors, Chinese Academy of Sciences, P.O. Box 912, Beijing 100083, China
²Department of Physics and Electronic Science, Changsha University of Science and Technology, Changsha 410004, China
³Department of Physics, Hunan Normal University, Hunan 410012, China
⁴Beijing Computational Science Research Center, Beijing 100089, China

^*lzlin@semi.ac.cn
^†wenyang@csrc.ac.cn

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Vol. 87, Iss. 24 — 15 June 2013

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Images

Figure 1
(a) HgTe QW with an inverted band structure in the Hall bar geometry, under $N$ periods of potential modulation. (b) The bulk energy spectra of the HgTe QW in the regions with and without the potential modulation $V_{0}$ (tunable through electric gating), respectively. Here a small gap around $E_{gap}$ is opened in the Dirac spectra of the edge states due to the finite-size effect, i.e., the finite width of the Hall bar. The green dashed line indicates the Fermi energy $E_{F}$ .Reuse & Permissions
Figure 2
Transmission probability $T = T_{sc}$ of an incident edge state on the Fermi level $E_{F} = 12.5$ meV across successively increasing $N = 1, 2, \dots, 6$ periods of potential modulation as a function of modulation amplitude $V_{0}$ . Inset: For $V_{0} = 5$ meV, the Fermi level $E_{F}$ lies in the finite-size gap of the modulated region.Reuse & Permissions
Figure 3
Contour plot of the transmission probability $T$ of an incident edge state on the Fermi level $E_{F} = 12.5$ meV as a function of modulation amplitude $V_{0}$ and number of modulation $N$ . For $V_{0} < - 0.7$ meV, the Fermi level enters the bulk energy bands in the modulation region [shaded area in Fig. 1a], as schematically shown in Fig. 1b (edge-bulk coupling). For $V_{0} > - 0.7$ meV, the Fermi level lies in the bulk gap (edge-edge coupling).Reuse & Permissions
Figure 4
(a) and (c) The solid lines show the energy spectra of the Hall bar under an infinite number $N \to \infty$ of modulations; the dotted lines show the energy spectrum of the leads, shifted upward by $V_{0} / 2$ . (b) and (d) The transmission probability $T$ of a single incident edge state with energy $E$ across the Hall bar under $N = 30$ modulations. The modulation amplitude $V_{0} = 10$ meV [corresponding to $E_{F}$ in the bulk gap, as sketch in the inset of (b)] for (a), (b) and $V_{0} = - 8.5$ meV [corresponding to $E_{F}$ entering the bulk energy spectra of the modulated region, as sketched in the inset of (d)] for (c), (d).Reuse & Permissions
Figure 5
(a) Total transmission probability $T$ and (b) the spin-flip transmission probability $T_{sf}$ of an incident edge state on the Fermi level $E_{F} = 12.5$ meV across the Hall bar under $N = 30$ modulation periods. The gate-induced Rashba spin-orbit coupling strength (the linear Rashba term) is taken as $α = 50$ meV nm (orange, solid curve) and $α = 0$ (black, dashed curve), respectively. The green dashed curve indicates the spin-flip transmission probability $T_{sf}$ with including the nonlinear Rashba terms. The vertical, blue dashed line distinguishes the edge-edge coupling regime ( $E_{F}$ in the bulk gap) and the edge-bulk coupling regime ( $E_{F}$ entering the bulk energy bands of the modulated region).Reuse & Permissions
Figure 6
Division of the Hall bar into $2 N + 1$ segments (denoted by $j = 0, 1, \dots, 2 N$ ) by the $N$ periods of modulation potential. The interfaces coordinates are denoted by $x_{1}, x_{2}, \dots, x_{2 N}$ .Reuse & Permissions

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