Rashba spin-orbit coupling induced topological transitions in charge pumps based on graphene

Based on the lattice Green's function technique, we theoretically investigate the topological charge pump driven by two time-dependent staggered potentials in graphene with Rashba spin-orbit coupling. A topological transition occurs with increasing Rashba strength, where the pumped charge in a period changes from 1 to 0 per spin. The transition is attributed to the change of Berry phase from $\ensuremath{\pi}$ to $2\ensuremath{\pi}$ when the Rashba spin-orbit coupling is turned on. In the gap opened by the staggered potential, the Berry phase becomes the valley Chern number and very sensitive to the Rashba strength. As a consequence, the pumped current undergoes an abrupt transition from 1 to 0 even in the presence of a weak Rashba coupling. This proposal provides a scheme to realize tunable topological transitions in quantized charge pumps.