Semiclassical dynamics and nonlinear charge current

Electron conductivity is an important material property that can provide a wealth of information about the underlying system. Especially, the response of the conductivity with respect to electromagnetic fields corresponds to various nonlinear charge currents, which have distinct symmetry requirements and hence can be used as efficient probes of different systems. To help the band-structure engineering of such nonlinear currents, a universal treatment of electron dynamics up to second order expressed in the basis of the unperturbed states are highly useful. In this work, we review the general semiclassical framework of the nonlinear charge currents.