Finite size effects on the quantum spin Hall state in HgTe quantum wells under two different types of boundary conditions

doi:10.1088/1674-1056/24/6/067304

Abstract The finite size effect in a two-dimensional topological insulator can induce an energy gap E_g in the spectrum of helical edge states for a strip of finite width. In a recent work, it has been found that when the spin–orbit coupling due to bulk-inversion asymmetry is taken into account, the energy gap E_g of the edge states features an oscillating exponential decay as a function of the strip width of the inverted HgTe quantum well. In this paper, we investigate the effects of the interface between a topological insulator and a normal insulator on the finite size effect in the HgTe quantum well by means of the numerical diagonalization method. Two different types of boundary conditions, i.e., the symmetric and asymmetric geometries, are considered. It is found that due to the existence of the interface between topological insulator and normal insulator this oscillatory pattern on the exponential decay induced by bulk-inversion asymmetry is modulated by the width of normal insulator regions. With the variation of the width of normal insulator regions, the shift of the Dirac point of the edge states in the spectrum and the energy gap E_g closing point in the oscillatory pattern can occur. Additionally, the effect of the spin–orbit coupling due to structure-inversion asymmetry on the finite size effects is also investigated.

Keywords: quantum spin Hall state finite size effect spin-orbit coupling

Received: 26 October 2014
Revised: 03 February 2015
Accepted manuscript online:

PACS:	73.43.-f	(Quantum Hall effects)
	72.25.Dc	(Spin polarized transport in semiconductors)
	85.75.-d	(Magnetoelectronics; spintronics: devices exploiting spin polarized transport or integrated magnetic fields)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11274102), the Program for New Century Excellent Talents in University of the Ministry of Education of China (Grant No. NCET-11-0960), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20134208110001).

Corresponding Authors: Zhou Bin
E-mail: binzhou@hubu.edu.cn

About author: 73.43.-f; 72.25.Dc; 85.75.-d

Cite this article:

Cheng Zhi (成志), Chen Rui (陈锐), Zhou Bin (周斌) Finite size effects on the quantum spin Hall state in HgTe quantum wells under two different types of boundary conditions 2015 Chin. Phys. B 24 067304

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Finite size effects on the quantum spin Hall state in HgTe quantum wells under two different types of boundary conditions

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