  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.
