Optical detection of quantum geometric tensor in intrinsic semiconductors

Quantum geometric tensor, including a symmetric real part defined as quantum metric and an antisymmetric part defined as Berry curvature, is essential for understanding many phenomena. In this study, we investigated the photogalvanic effect of semiconductors with time-reversal-invariant and spatial inversion symmetries using the quantum kinetic equation. We concluded that the integral of the symmetric (antisymmetric) part of quantum geometric tensor on the equal energy surface in momentum space, satisfying the resonance condition, is related to the generation rate of carriers in semiconductors under linearly (circularly) polarized light. Under additional bias voltage, the dc photocurrent is proportional to the bias voltage. Our study provided an alternative interpretation for the photogalvanic effect in the view of quantum geometric tensor. Additionally, it classified the intrinsic difference between linearly and circularly polarized optical fields.