Second harmonic Hall responses of insulators as a probe of Berry curvature dipole

Diverse nonlinear optical responses of metallic band states have been characterized in terms of the Berry curvature dipole (BCD) or other multipole structures of Berry curvature. Here, we find that the second harmonic optical responses of insulators to sub-bandgap light are also delicately associated with the interband BCD. We performed real-time time-dependent density functional theory calculations and theoretically analyzed the second harmonic generation susceptibility tensors. The two-band term of the second-order susceptibility is precisely proportional to the interband BCD, which is particularly significant for low-symmetric systems with a small bandgap. We show that higher-order responses to nonperturbative strong fields can be associated with higher poles of Berry curvature. We suggest that the consequences of symmetry lowering can be detected by nonlinear optical responses through adjustments of the dipole or other multipole structures of the Berry curvature texture.