  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.
