We have a comparative study of the quantum spin Hall (QSH) effects induced by non-magnetic and magnetic staggered potentials respectively and show that they have the same effect in driving the topological phase transition. The result implies that both time-reversal (${ \cal T}$) preserving and breaking systems can host QSH effect. We also investigate the stability of the resulting QSH effect to disorder and find that for ${ \cal T}$ invariant system the edge states are always robust while those of ${ \cal T}$ breaking system are also robust if there is additional symmetry in the system.
Categories: cond-mat.mes-hall