Angle-Resolved Berry Curvature via Nonlinear Hall Effect of Ballistic Electrons

Berry curvature fundamentally dictates the topological ground state, anomalous transport and optical properties of quantum materials. However, directly mapping its momentum-space distribution in real materials remains an outstanding experimental challenge. Here, we present an inverse method for reconstructing the abelian Berry curvature of a single band using angle-resolved measurements of the transverse conductance. Our inversion relies on a symmetry-constrained statistical model with two hyperparameters that can be inferred directly from the nonlinear Hall conductance, yielding a parameter-free inversion method. We demonstrate the feasibility of our method using simulated measurements of tight-binding models of WSe$_2$ and $ABC$-stacked trilayer graphene.