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

Tobias Holder, Daniel Kaplan, Binghai Yan

Published 2019-11-13Version 1

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 appear in general for broken time-reversal symmetry and 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 inter-band effects. We find that $\mathcal{T}$-breaking generally enhances the conductivity by contributing the leading-order term ($\omega^{-2}$, where $\omega$ is the light frequency) while preserving $\mathcal{T}$ restricts the response to the term of next-to-leading order ($\omega^{-1}$).