Movable Valley Switch Driven by Berry Phase in Bilayer-Graphene Resonators.

Berry phase, the geometric phase accumulated over a closed loop in parameter space during an adiabatic cyclic evolution, has been demonstrated to play an important role in many quantum systems since its discovery. In gapped Bernal bilayer graphene, the Berry phase can be continuously tuned from zero to 2π, which offers a unique opportunity to explore the tunable Berry phase on physical phenomena. Here, we report experimental observation of Berry-phase-induced valley splitting and crossing in movable bilayer-graphene p-n junction resonators. In our experiment, the resonators are generated by combining the electric field of a scanning tunneling microscope tip with the gap of bilayer graphene. A perpendicular magnetic field changes the Berry phase of the confined bound states in the resonators from zero to 2π continuously and leads to the Berry phase difference for the two inequivalent valleys in the bilayer graphene. As a consequence, we observe giant valley splitting and unusual valley crossing of the lowest bound states. Our results indicate that the bilayer-graphene resonators can be used to manipulate the valley degree of freedom in valleytronics.