Regularized lattice theory for spatially dispersive nonlinear optical conductivities

Optical conductivities at nonlinear order in the electric field are powerful probes of symmetry breaking in quantum materials. In many scenarios, the dipole approximation for light-matter coupling is sufficient, which forbids responses like second harmonic generation in systems with inversion symmetry. This assumption is expected to fail in many systems of recent interest, such as artificial lattices with inflated lattice constants or materials whose bands support nontrivial quantum geometry. In these systems, contributions from electric quadrupole and magnetic dipole couplings are present and may even dominate the response. In this presentation, we describe how to calculate first-order spatially dispersive corrections to nonlinear optical conductivities, and illustrate the effects with models that demonstrate guiding principles for finding systems where these anomalous responses are strong.