The quantum spin Hall(QSH) effect is considered to be unstable to perturbations violating the time-reversal(TR) symmetry.We review some recent developments in the search of the QSH effect in the absence of the TR symmetry.The possibility to realize a robust QSH effect by artificial removal of the TR symmetry of the edge states is explored.As a useful tool to characterize topological phases without the TR symmetry,the spin-Chern number theory is introduced.
The quantum spin Hall (QSH) effect is considered to be unstable to perturbations violating the time-reversal (TR) symmetry. We review some recent developments in the search of the QSH effect in the absence of the TR symmetry. The possibility to realize a robust QSH effect by artificial removal of the TR symmetry of the edge states is explored. As a useful tool to characterize topological phases without the TR symmetry, the spin-Chern number theory is introduced.