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.
Highlights
The bulk photovoltaic effect (BPVE) [1,2,3] refers to the generation of a DC current from a uniform material by irradiation with strong light
While we will not attempt to solve this issue comprehensively, we offer a way to discuss both the adiabatic and the diabatic motion which arises under optical driving in connection with the so-called quantum geometric tensor [55]
Studies of the bulk photovoltaic effect were restricted to the evaluation of the complicated perturbative expressions
Summary
The bulk photovoltaic effect (BPVE) [1,2,3] refers to the generation of a DC current from a uniform material by irradiation with strong light. It gained renewed interest in topological Weyl semimetals (WSMs) [10,11], where the Berry phase is believed to generate the giant photocurrent and the second harmonic response [12,13,14,15,16,17,18,19,20]. Recent theoretical [21] and experimental [22,23,24] works on magnetic systems reveal a distinct photocurrent and second harmonic generation which cannot be merely derived from the Berry phase. We are motivated to reexamine the second-order response theory and investigate the effects of time-reversal-symmetry (T ) breaking
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