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

中国物理B ›› 2015, Vol. 24 ›› Issue (6): 67304-067304.doi: 10.1088/1674-1056/24/6/067304

• CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES • 上一篇下一篇

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

成志, 陈锐, 周斌

Department of Physics, Hubei University, Wuhan 430062, China

收稿日期:2014-10-26 修回日期:2015-02-03 出版日期:2015-06-05 发布日期:2015-06-05
基金资助:
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).

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

Cheng Zhi (成志), Chen Rui (陈锐), Zhou Bin (周斌)

Department of Physics, Hubei University, Wuhan 430062, China

Received:2014-10-26 Revised:2015-02-03 Online:2015-06-05 Published:2015-06-05
Contact: Zhou Bin E-mail:binzhou@hubu.edu.cn
About author:73.43.-f; 72.25.Dc; 85.75.-d
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: quantum spin Hall state, finite size effect, spin-orbit coupling

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.

Key words: quantum spin Hall state, finite size effect, spin-orbit coupling

中图分类号: (Quantum Hall effects)

73.43.-f

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

成志, 陈锐, 周斌. Finite size effects on the quantum spin Hall state in HgTe quantum wells under two different types of boundary conditions[J]. 中国物理B, 2015, 24(6): 67304-067304.

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[J]. Chin. Phys. B, 2015, 24(6): 67304-067304.

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

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

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