Resonant Second-Harmonic Generation as a Probe of Quantum Geometry

Nonlinear responses are actively studied as probes of topology and band geometric properties of solids. Here, we show that second harmonic generation serves as a probe of the Berry curvature, quantum metric, and quantum geometric connection. We generalize the theory of second harmonic generation to include Fermi surface effects in metallic systems, and finite scattering timescale. In doped materials the Fermi surface and Fermi sea cause all second harmonic terms to exhibit resonances, and we identify two novel contributions to the second harmonic signal: a double resonance due to the Fermi surface and a higherorder pole due to the Fermi sea. We discuss experimental observation in the monolayer of time reversal symmetric Weyl semimetal WTe2 and the parity-time reversal symmetric topological antiferromagnet CuMnAs.

Automated summary

Nonlinear responses are actively studied as probes of topology and band geometric properties of solids. In this study, the theory of second harmonic generation is generalized to include Fermi surface effects and finite scattering timescale in metallic systems. The experimental observation in monolayer Weyl semimetal and topological antiferromagnet is discussed.