Imaging the valley and orbital Hall effect in monolayer MoS2

The topological properties of a material's electronic structure are encoded in its Berry curvature, a quantity which is intimately related to the transverse electrical conductivity. In transition metal dichalcogenides with broken inversion symmetry, the nonzero Berry curvature results in a valley Hall effect. We identify a previously unrecognized consequence of Berry curvature in these materials: an electric-field-induced change in the electrons' charge density orientation. We use first-principles calculations to show that measurements of the electric-field-induced change in the charge density or local density of states in MoS2 can be used to measure its energy-dependent valley and orbital Hall conductivity.