中国物理B ›› 2014, Vol. 23 ›› Issue (3): 37304-037304.doi: 10.1088/1674-1056/23/3/037304

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

Finite size effects on helical edge states in HgTe quantum wells with the spin–orbit coupling due to bulk-and structure-inversion asymmetries

成志, 周斌   

  1. Department of Physics, Hubei University, Wuhan 430062, China
  • 收稿日期:2013-09-21 修回日期:2013-11-26 出版日期:2014-03-15 发布日期:2014-03-15
  • 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 Universities, 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 helical edge states in HgTe quantum wells with the spin–orbit coupling due to bulk-and structure-inversion asymmetries

Cheng Zhi (成志), Zhou Bin (周斌)   

  1. Department of Physics, Hubei University, Wuhan 430062, China
  • Received:2013-09-21 Revised:2013-11-26 Online:2014-03-15 Published:2014-03-15
  • Contact: Zhou Bin E-mail:binzhou@hubu.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 11274102), the Program for New Century Excellent Talents in Universities, China (Grant No. NCET-11-0960), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20134208110001).

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摘要： There is a quantum spin Hall state in the inverted HgTe quantum well, characterized by the topologically protected gapless helical edge states lying within the bulk gap. It has been found that for a strip of finite width, the edge states on the two sides can couple together to produce a gap in the spectrum. The phenomenon is called the finite size effect in quantum spin Hall systems. In this paper, we investigate the effects of the spin–orbit coupling due to bulk-and structure-inversion asymmetries on the finite size effect in the HgTe quantum well by means of the numerical diagonalization method. When the bulk-inversion asymmetry is taken into account, it is shown that the energy gap Eg of the edge states due to the finite size effect features an oscillating exponential decay as a function of the strip width of the HgTe quantum well. The origin of this oscillatory pattern on the exponential decay is explained. Furthermore, if the bulk-and structure-inversion asymmetries are considered simultaneously, the structure-inversion asymmetry will induce a shift of the energy gap Eg closing point. Finally, based on the roles of the bulk-and structure-inversion asymmetries on the finite size effects, a way to realize the quantum spin Hall field effect transistor is proposed.

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

Abstract: There is a quantum spin Hall state in the inverted HgTe quantum well, characterized by the topologically protected gapless helical edge states lying within the bulk gap. It has been found that for a strip of finite width, the edge states on the two sides can couple together to produce a gap in the spectrum. The phenomenon is called the finite size effect in quantum spin Hall systems. In this paper, we investigate the effects of the spin–orbit coupling due to bulk-and structure-inversion asymmetries on the finite size effect in the HgTe quantum well by means of the numerical diagonalization method. When the bulk-inversion asymmetry is taken into account, it is shown that the energy gap Eg of the edge states due to the finite size effect features an oscillating exponential decay as a function of the strip width of the HgTe quantum well. The origin of this oscillatory pattern on the exponential decay is explained. Furthermore, if the bulk-and structure-inversion asymmetries are considered simultaneously, the structure-inversion asymmetry will induce a shift of the energy gap Eg closing point. Finally, based on the roles of the bulk-and structure-inversion asymmetries on the finite size effects, a way to realize the quantum spin Hall field effect transistor is proposed.

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)