Quantum Geometry Induced Third Order Nonlinear Transport Responses

TL;DR

This paper explores third-order nonlinear charge transport responses in centrosymmetric systems, revealing new contributions linked to band geometry and symmetry breaking, with implications for quantum materials.

Contribution

It uncovers the fundamental third-order transport effects in centrosymmetric systems arising from band geometric quantities, expanding understanding beyond second-order responses.

Findings

Identified two new third-order charge conductivity contributions.

Linked third-order effects to Berry curvature and symplectic connection.

Demonstrated results in antiferromagnetic monolayer SrMnBi2.

Abstract

Nonlinear transport phenomena offer an exciting probe into the band geometry and symmetry properties of a system. While most studies on nonlinear transport have looked at second-order nonreciprocal responses in noncentrosymmetric systems, the reciprocal third-order effects dominant in centrosymmetric systems remain largely uncharted. Here, we uncover two significant contributions to third-order charge conductivity: one affecting longitudinal resistance and another impacting the Hall effect. We demonstrate that these previously unexplored contributions arise in time-reversal symmetry-broken systems from band geometric quantities such as the Berry curvature and the symplectic connection. We prescribe a detailed symmetry dictionary to facilitate the discovery of these fundamental transport coefficients. Additionally, we unify our quantum kinetic results with the semiclassical wave-packet formalism to unveil all contributions to third-order charge transport. We illustrate our results in antiferromagnetic monolayer SrMnBi$_2$. Our comprehensive study significantly advances the fundamental understanding of reciprocal nonlinear responses.