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

TL;DR

This paper introduces a novel, parameter-free inverse method to reconstruct the Berry curvature distribution in momentum space from angle-resolved nonlinear Hall conductance measurements, validated through simulations of quantum materials.

Contribution

The work presents the first symmetry-constrained statistical inversion technique for directly mapping Berry curvature from experimental conductance data.

Findings

Successfully reconstructs Berry curvature in simulated models

Provides a parameter-free, symmetry-based inversion method

Demonstrates applicability to materials like WSe₂ and trilayer graphene

Abstract

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.