Spin-valley quantum Hall phases in graphene

We theoretically investigate possible quantum Hall phases and corresponding edge states in graphene by taking a strong magnetic field, Zeeman splitting M, and sublattice potential Δ into account but without spin-orbit interaction. It was found that for the undoped graphene either a quantum valley Hall phase or a quantum spin Hall phase emerges in the system, depending on relative magnitudes of M and Δ . When the Fermi energy deviates from the Dirac point, the quantum spin-valley Hall phase appears and its characteristic edge state is contributed only by one spin and one valley species. The metallic boundary states bridging different quantum Hall phases possess a half-integer quantized conductance, like e²/2h or 3e²/2h. The possibility of tuning different quantum Hall states with M and Δ suggests possible graphene-based spintronics and valleytronics applications.