Topological state engineering by in-plane electric field in graphene nanoribbon

We investigate the electronic states of a zigzag graphene nanoribbon in the presence of mutually perpendicular electric and magnetic fields. We find that both edge and bulk states are localized in the vicinity of zero energy, leading to spin-polarized states and quantized transport in the system. A quantum spin Hall phase is characterized by helical edge and tilted bulk states. By tuning Fermi energy and in-plane electric field, a topological phase transition is also realized. The electronic states support the transport of spin and charge, and the corresponding spin and charge Hall conductivities are calculated in a four-terminal geometry.