CT invariant quantum spin Hall effect in ferromagnetic graphene

We predict a quantum spin Hall effect (QSHE) in ferromagnetic graphene under a magnetic field. Unlike the previously reported effect, this QSHE appears in the absence of any spin-orbit interaction, and its system does not possess time-reversal (T) invariance but has CT invariance, where C is the charge conjugation operation. Due to this QSHE, the longitudinal and spin Hall resistances exhibit quantum plateaus. In particular, the plateau of the spin Hall resistance is very robust against disorder.