Finite size effects on the helical edge states on the Lieb lattice

doi:10.1088/1674-1056/25/6/067204

中国物理B ›› 2016, Vol. 25 ›› Issue (6): 67204-067204.doi: 10.1088/1674-1056/25/6/067204

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

Finite size effects on the helical edge states on the Lieb lattice

Rui Chen(陈锐), Bin Zhou(周斌)

Department of Physics, Hubei University, Wuhan 430062, China

收稿日期:2016-01-17 修回日期:2016-02-23 出版日期:2016-06-05 发布日期:2016-06-05
通讯作者: Bin Zhou E-mail:binzhou@hubu.edu.cn
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 the Higher Education of China (Grant No. 20134208110001).

Finite size effects on the helical edge states on the Lieb lattice

Rui Chen(陈锐), Bin Zhou(周斌)

Department of Physics, Hubei University, Wuhan 430062, China

Received:2016-01-17 Revised:2016-02-23 Online:2016-06-05 Published:2016-06-05
Contact: Bin Zhou 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 University of the Ministry of Education of China (Grant No. NCET-11-0960), and the Specialized Research Fund for the Doctoral Program of the Higher Education of China (Grant No. 20134208110001).

摘要/Abstract

摘要：

For a two-dimensional Lieb lattice, that is, a line-centered square lattice, the inclusion of the intrinsic spin--orbit (ISO) coupling opens a topologically nontrivial gap, and gives rise to the quantum spin Hall (QSH) effect characterized by two pairs of gapless helical edge states within the bulk gap. Generally, due to the finite size effect in QSH systems, the edge states on the two sides of a strip of finite width can couple together to open a gap in the spectrum. In this paper, we investigate the finite size effect of helical edge states on the Lieb lattice with ISO coupling under three different kinds of boundary conditions, i.e., the straight, bearded and asymmetry edges. The spectrum and wave function of edge modes are derived analytically for a tight-binding model on the Lieb lattice. For a strip Lieb lattice with two straight edges, the ISO coupling induces the Dirac-like bulk states to localize at the edges to become the helical edge states with the same Dirac-like spectrum. Moreover, it is found that in the case with two straight edges the gapless Dirac-like spectrum remains unchanged with decreasing the width of the strip Lieb lattice, and no gap is opened in the edge band. It is concluded that the finite size effect of QSH states is absent in the case with the straight edges. However, in the other two cases with the bearded and asymmetry edges, the energy gap induced by the finite size effect is still opened with decreasing the width of the strip. It is also proposed that the edge band dispersion can be controlled by applying an on-site potential energy on the outermost atoms.

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

Abstract:

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

中图分类号: (Spin polarized transport in semiconductors)

72.25.Dc

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

陈锐, 周斌. Finite size effects on the helical edge states on the Lieb lattice[J]. 中国物理B, 2016, 25(6): 67204-067204.

Rui Chen(陈锐), Bin Zhou(周斌). Finite size effects on the helical edge states on the Lieb lattice[J]. Chin. Phys. B, 2016, 25(6): 67204-067204.

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Finite size effects on the helical edge states on the Lieb lattice

Finite size effects on the helical edge states on the Lieb lattice

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