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The hallmark of the spin-Hall insulator is the presence of gapless edge states of different spins moving in opposite directions. Through analytical solutions in a model calculation for a strip of finite width, we find that edge states on the two sides can couple together to produce a gap in the spectrum, destroying the quantum spin-Hall effect. The application of a magnetic field can however modify and even remove the gap by shifting the momenta of the edge states relative to each other.
Zhou et al. (Wed,) studied this question.
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