  Motivated by the nonlinear Hall effect observed in topological semimetals, we
studied the photocurrent by the quantum kinetic equation. We recovered the
shift current and injection current discovered by Sipe et al., and the
nonlinear Hall current induced by Berry curvature dipole (BCD) proposed by Inti
Sodemann and Liang Fu. Especially, we further proposed that 3-form tensor can
also induce photocurrent, in addition to the Berry curvature and BCD. This work
will supplement the existing mechanisms for photocurrent. In contrast to the
shift current induced by shift vector, all photocurrents induced by
gradient/curl of Berry curvature, and high rank tensor require circularly
polarized light and topologically non-trivial band structure, viz.
non-vanishing Berry curvature.
