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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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Chinese Physics B 2015年第6期24卷 528-533页

作者：成志陈锐周斌 Department of Physics Hubei University

The finite size effect in a two-dimensional topological insulator can induce an energy gap Eg 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 Eg 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 Eg 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

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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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Chinese Physics B 2014年第3期23卷 498-503页

作者：成志周斌 Department of Physics Hubei University

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

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

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Chinese Physics B 2016年第6期25卷 444-457页

作者：陈锐周斌 Department of Physics Hubei University

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 ***,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 *** 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 *** spectrum and wave function of edge modes are derived analytically for a tight-binding model on the Lieb *** 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 ***,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 *** is concluded that the finite size effect of QSH states is absent in the case with the straight ***,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 *** 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

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