Quantum Transport by Spin-Polarized Edge States in Graphene Nanoribbons in the Quantum Spin Hall and Quantum Anomalous Hall Regimes

Using the non-equilibrium Green's function method and the Keldysh formalism, we study the effects of spin-orbit interactions and time-reversal symmetry breaking exchange fields on non-equilibrium quantum transport in graphene armchair nanoribbons. We identify signatures of the quantum spin Hall (QSH) and the quantum anomalous Hall (QAH) phases in non-equilibrium edge transport by calculating the spin-resolved real space charge density and local currents at the nanoribbon edges. We find that the QSH phase, which is realized in a system with intrinsic spin-orbit coupling, is characterized by chiral counter-propagating local spin currents summing up to a net charge flow with opposite spin polarization at the edges. In the QAH phase, emerging in the presence of Rashba spin-orbit coupling and a ferromagnetic exchange field, two chiral edge channels with opposite spins propagate in the same direction at each edge, generating an unpolarized charge current and a quantized Hall conductance G = 2e(2)/h. Increasing the intrinsic spin-orbit coupling causes a transition from the QAH to the QSH phase, evinced by characteristic changes in the non-equilibrium edge transport. In contrast, an antiferromagnetic exchange field can coexist with a QSH phase, but can never induce a QAH phase due to a symmetry that combines time-reversal and sublattice translational symmetry.