CT invariant quantum spin Hall effect in a ferromagnetic graphene

TL;DR

This paper predicts a novel quantum spin Hall effect in ferromagnetic graphene that arises without spin-orbit interaction, protected by CT invariance, and exhibits quantized resistance plateaus and robustness against disorder.

Contribution

It introduces a new type of QSHE in ferromagnetic graphene protected by CT invariance, independent of spin-orbit coupling, with quantized resistance plateaus.

Findings

Quantum spin Hall effect predicted in ferromagnetic graphene.

Quantum plateaus in longitudinal resistance at specific values.

Spin Hall resistance remains robust against disorder.

Abstract

We predict a quantum spin Hall effect (QSHE) in the ferromagnetic graphene under a magnetic field. Unlike the previous QSHE, this QSHE appears in the absence of any spin-orbit interaction, thus, arrived from a different physical origin. The previous QSHE is protected by the time-reversal (T) invariance. This new QSHE is protected by the CT invariance, where C is the charge conjugation operation. Due to this QSHE, the longitudinal resistance exhibits quantum plateaus. The plateau values are at 1/2, 1/6, 3/28, ..., (in the unit of $h/e^2$), depending on the filling factors of the spin-up and spin-down carriers. The spin Hall resistance is also investigated and is found to be robust against the disorder.