Detection of quantum geometric tensor by nonlinear optical response

TL;DR

This paper demonstrates how nonlinear optical responses, specifically the photogalvanic effect, can be used to detect and interpret the quantum geometric tensor, including quantum metric and Berry curvature, in multi-band systems.

Contribution

It provides a novel theoretical framework linking the quantum geometric tensor to observable nonlinear optical effects, offering a new method for QGT detection.

Findings

Integral of gradient of quantum metric relates to linear photogalvanic effect.

Integral of gradient of Berry curvature relates to circular photogalvanic effect.

Proposes an alternative interpretation of photogalvanic effects via QGT.

Abstract

Quantum geometric tensor (QGT), including a symmetric real part defined as quantum metric and an antisymmetric part defined as Berry curvature, is essential for understanding many phenomena. We studied the photogalvanic effect of a multiple-band system with time-reversal-invariant symmetry by theoretical analysis in this work. We concluded that the integral of gradient of the symmetric part of QGT in momentum space is related to the linearly photogalvanic effect, while the integral of gradient of Berry curvature is related to the circularly photogalvanic effect. Our work afforded an alternative interpretation for the photogalvanic effect in the view of QGT, and a simple approach to detect the QGT by nonlinear optical response.