Tracing out the Berry curvature dipole and multipoles in second harmonic Hall responses of time-reversal symmetric insulators

TL;DR

This paper investigates how the Berry curvature dipole and multipoles in time-reversal symmetric insulators influence their second harmonic generation, proposing a method to extract band structure geometry from nonlinear optical responses.

Contribution

The study demonstrates that the nonlinear Hall response in insulators can be used to trace Berry curvature dipoles and multipoles via second harmonic generation, using real-time density functional theory.

Findings

Two-band susceptibility term is proportional to interband BCD

Nonlinear Hall component can reveal band structure geometry

Method enables extraction of Berry curvature multipoles

Abstract

Various nonlinear characteristics of solid states, such as the circular photogalvanic effect of time-reversal symmetric insulators, the quantized photogalvanic effect of Weyl semimetals, and the nonlinear Hall effect of time-reversal symmetric metals, have been associated with the Berry curvature dipole (BCD). Here, we explore the question of whether the Berry curvature dipole and multipoles of time-reversal symmetric insulators can be traced in the nonlinear optical responses. We performed real-time time-dependent density functional theory calculations and examined the second harmonic generation susceptibility tensors. The two-band term of the susceptibility tensor is sharply proportional to the interband BCD, dominating over the Hall response once the cancellation effect of the multiple reflection symmetries is lifted. We suggest that the nonlinear Hall component of the second-harmonic spectra of insulators can also be utilized as an effective tool to extract the band structure geometry through Berry curvature dipole and possibly multipoles.