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Abstract: Helical edge modes are characteristic of topological insulators in twodimensions. This paper demonstrates that helical edge modes remain acrosstransitions to ordinary insulators or to semimetals under certain condition.Straight and zigzag edges are considered in a tight-binding model on squarelattice. We focus on the case of indirect gap in bulk topological insulators,and obtain the spectrum of edge modes on both sides of transitions. Forstraight edge, the helical edge mode in topological insulators with strongparticle-hole asymmetry has a reentrant region in momentum space. Edge modesshow up even in ordinary insulators, but are absent in semimetals. In zigzagedge, the helical edge mode survives in both semimetals and ordinaryinsulators. However, the edge modes are absent inside the energy gap ofordinary insulators. All results are obtained analytically.



Author: Shijun Mao, Yoshio Kuramoto

Source: https://arxiv.org/







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