Quantum transport by spin-polarized edge states in graphene nanoribbons in the quantum spin Hall and quantum anomalous Hall regimes

Abstract

Using the non-equilibrium Green\noindent '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 the 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.

References in corpus (14)

• Quantum Spin Hall Effect in Graphene
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Epitaxial Growth of Two-Dimensional Stanene
• The quantum spin Hall effect and topological insulators
• Intrinsic and Rashba Spin-orbit Interactions in Graphene Sheets
• Quantum Anomalous Hall Effect in Graphene from Rashba and Exchange Effects
• Antiferromagnetic topological insulators
• Quantum Anomalous Hall Effect in Graphene Proximity Coupled to an Antiferromagnetic Insulator
• Time-reversal-symmetry-broken quantum spin Hall effect
• Imaging mesoscopic spin Hall flow: Spatial distribution of local spin currents and spin densities in and out of multiterminal spin-orbit coupled semiconductor nanostructures
• Spatial distribution of local currents of massless Dirac fermions in quantum transport through graphene nanoribbons
• How to construct the proper gauge-invariant density matrix in steady-state nonequilibrium: Applications to spin-transfer and spin-orbit torques
• Inverse quantum spin Hall effect generated by spin pumping from precessing magnetization into a graphene-based two-dimensional topological insulator

Cited by in corpus (1)

• Chiral edge transport along domain walls in magnetic topological insulator nanoribbons