Second Harmonic Generation in Correlated Topological Semimetals*

Nonlinear responses have proved a powerful way to reveal, understand, and tune the wavefunction geometry and/or topology, driven by the recent discovery and engineering of quantum materials. On the other hand, the interplay between topology and electronic correlations may offer a rich avenue for discovering emergent quantum phenomena in condensed matter systems. In this work, we explore the role of electronic correlation on the nonlinear optical response, specifically, the second harmonic generation (SHG). We identify six distinct contributions (e.g., shift, injection, Berry curvature dipole) to the SHG within the quantum kinetic theory framework. Furthermore, we apply our analysis to the Weyl-Hubbard system to explore the effect of electron-electron correlation on the various components of the SHG signal. Our study reveals the possible mechanisms for correlation-driven SHG enhancement, which have direct experimental consequences.