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

doi:10.1088/1674-1056/23/3/037304

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 E_g 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 E_g 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.

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

Received: 21 September 2013
Revised: 26 November 2013
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 Universities, 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

Cite this article:

Cheng Zhi (成志), Zhou Bin (周斌) Finite size effects on helical edge states in HgTe quantum wells with the spin–orbit coupling due to bulk-and structure-inversion asymmetries 2014 Chin. Phys. B 23 037304

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

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