Boundary condition induced topological transitions in graphene quantum pumps: from finite to infinite

We investigate the quantized charge pumping in graphene with Rashba spin-orbit coupling (RSOC) under two time-periodic staggered potentials. Surprisingly, the quantized charge pumped per cycle exhibits a sharp dependence on the transverse boundary conditions: a zero quantized charge is obtained under periodic boundary conditions (consistent with bulk thermodynamic limits), whereas a quantized value of 1 per spin emerges under open boundary conditions. This topological transition induced by the transverse boundary conditions persists even for large system widths, revealing a discontinuous crossover from finite to infinite geometries without relying on topological edge states at the boundaries. We attribute this phenomenon to RSOC-induced intravalley reflection at transverse boundaries, which modifies the winding number of the pumping cycle. These results challenge conventional wisdom about finite-to-infinite transitions in condensed matter systems and advance the fundamental understanding of boundary-sensitive quantum transport in multivalley systems.