How the local density of states and total photoemission spectra change due to a pumped electric field

Single-band models of noninteracting electrons can be solved exactly in the presence of an electric field pump (for a pump/probe experiment) by employing the Peierls substitution. Because this transformation simply relabels momentum wavevectors as a function of time, the instantaneous spectrum is unchanged by the pump pulse. But the local density of states and the total photoemission spectrum both display significant time dependence due to the field. This occurs for two reasons: first, the time-dependent change of the momentum label changes the relationship between momentum and bandstructure, which, in turn, changes the density of states and second, the time-dependent wavefunctions affect the density of states through the equation of motion for the Green's functions. We describe how these effects determine what appears as a field-dressed bandstructure which changes with time. For example, these effects can create spectra outside of the range of the instantaneous bandstructure. We describe what impact this has on the interpretation of time-resolved photoemission spectra.