Time-reversal-symmetry-broken quantum spin Hall effect

The quantum spin Hall (QSH) state of matter is usually considered to be protected by time-reversal (TR) symmetry. We investigate the fate of the QSH effect in the presence of the Rashba spin-orbit coupling and an exchange field, which break both inversion and TR symmetries. It is found that the QSH...

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Published in:Physical review letters 2011-08, Vol.107 (6), p.066602-066602
Main Authors: Yang, Yunyou, Xu, Zhong, Sheng, L, Wang, Baigeng, Xing, D Y, Sheng, D N
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container_title Physical review letters
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Xu, Zhong
Sheng, L
Wang, Baigeng
Xing, D Y
Sheng, D N
description The quantum spin Hall (QSH) state of matter is usually considered to be protected by time-reversal (TR) symmetry. We investigate the fate of the QSH effect in the presence of the Rashba spin-orbit coupling and an exchange field, which break both inversion and TR symmetries. It is found that the QSH state characterized by nonzero spin Chern numbers C(±) = ±1 persists when the TR symmetry is broken. A topological phase transition from the TR-symmetry-broken QSH phase to a quantum anomalous Hall phase occurs at a critical exchange field, where the bulk band gap just closes. It is also shown that the transition from the TR-symmetry-broken QSH phase to an ordinary insulator state cannot happen without closing the band gap.
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