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We have a comparative study of the quantum spin Hall (QSH) effects induced bynon-magnetic and magnetic staggered potentials respectively and show that theyhave the same effect in driving the topological phase transition. The resultimplies that both time-reversal (${\cal T}$) preserving and breaking systemscan host QSH effect. We also investigate the stability of the resulting QSHeffect to disorder and find that for ${\cal T}$ invariant system the edgestates are always robust while those of ${\cal T}$ breaking system are alsorobust if there is additional symmetry in the system.

Quantum spin Hall effect induced by non-magnetic and magnetic staggered potentials