Tunable and giant valley-selective Hall effect in gapped bilayer graphene

Berry curvature is analogous to magnetic field but in momentum space and is commonly present in materials with non-trivial quantum geometry. It endows Bloch electrons with transverse anomalous velocities to produce Hall-like currents even in the absence of a magnetic field. We report the direct observation of in situ tunable valley-selective Hall effect (VSHE), where inversion symmetry, and thus the geometric phase of electrons, is controllable by an out-of-plane electric field. We use high-quality bilayer graphene with an intrinsic and tunable bandgap, illuminated by circularly polarized mid-infrared light and confirm that the observed Hall voltage arises from an optically-induced valley population. Compared with molybdenum disulfide, we find orders of magnitude larger VSHE, attributed to the inverse scaling of the Berry curvature with bandgap. By monitoring the valley-selective Hall conductivity, we study Berry curvature's evolution with bandgap. This in situ manipulation of VSHE paves the way for topological and quantum geometric opto-electronic devices, such as more robust switches and detectors.