Consequences of Time-reversal-symmetry Breaking in the Light-Matter Interaction: Berry Curvature, Quantum Metric and Diabatic Motion

TL;DR

This paper explores how breaking time-reversal symmetry affects nonlinear optical responses in topological materials, revealing new mechanisms involving Berry curvature, quantum metric, and diabatic motion that enhance the nonlinear anomalous Hall effect.

Contribution

The work introduces a comprehensive diagrammatic formalism for second-order optical responses considering time-reversal-symmetry breaking, highlighting three physical mechanisms and their impact on nonlinear Hall effects.

Findings

Identification of three mechanisms: Berry curvature, quantum metric, diabatic motion.

Derivation of semiclassical conductivity including intra- and interband effects.

Enhanced nonlinear anomalous Hall effect beyond Berry curvature dipole contributions.

Abstract

Nonlinear optical response is well studied in the context of semiconductors and has gained a renaissance in studies of topological materials in the recent decade. So far it mainly deals with non-magnetic materials and it is believed to root in the Berry curvature of the material band structure. In this work, we revisit the general formalism for the second-order optical response and focus on the consequences of the time-reversal-symmetry ($\mathcal{T}$) breaking, by a diagrammatic approach. We have identified three physical mechanisms to generate a dc photocurrent, i.e. the Berry curvature, the quantum metric, and the diabatic motion. All three effects can be understood intuitively from the anomalous acceleration. The first two terms are respectively the antisymmetric and symmetric parts of the quantum geometric tensor. The last term is due to the dynamical antilocalization that appears from the phase accumulation between time-reversed fermion loops. Additionally, we derive the semiclassical conductivity that includes both intra- and interband effects. We find that $\mathcal{T}$-breaking can lead to a greatly enhanced non-linear anomalous Hall effect that is beyond the contribution by the Berry curvature dipole.