Reversing Berry phase and modulating Andreev reflection by Rashba spin-orbit coupling in graphene mono- and bilayers

Graphene with Rashba spin-orbit coupling (RSOC) has attracted much attention so far. However, no one has noticed the topologically nontrivial changes of Berry phase for RSOC from the absence to the presence. We demonstrate that the Berry phase of electronic wave functions changes from pi to 2 pi in graphene monolayer (GML) and from 2 pi to pi in graphene bilayer (GBL), driven by RSOC. These reversals of Berry phase result in anomalous electron-hole conversions at normal conductor-superconductor junctions. The specular Andreev reflection can be significantly reduced in GML, but obviously enhanced in GBL. Another unusual point caused by RSOC is that the spin-flipped electron reflection happens due to the spin helical structures on equal-energy surfaces. An electrically observable effect induced by RSOC is proposed such that the differential conductance at voltages below the superconducting gap decreases strongly for GML while it increases remarkably for GBL, attributed to the Berry-phase-dictated interference between incident and reflected states.