Insignts into non-equilibrium spectroscopy from the theoretical perspective

Time-resolved angle-resolved photoemission spectroscopy is one of the most powerful pump–probe measurements of materials driven far from equilibrium. Unlike the linear-response regime, where the frequency-dependent response function is independent of time, in a far-from-equilibrium experiment, responses functions depend on two times in the time domain. We describe how one can transition from the two independent times to time-dependent frequency response functions and how they involve contributions from times that are near to each other. However, they should not be thought of as a frequency-dependent response at a single definite time. Instead, the Fourier uncertainty relations show that they involve contributions from ranges of times and must be interpreted in this light.

With this is mind, we examine the problem of how excited populations of electrons relax after they have been excited by a pump. We include three of the most important relaxation processes: (i) impurity scattering; (ii) Coulomb scattering; and (iii) electron-phonon scattering. The relaxation of an excited population of electrons is one of the most fundamental processes measured in pump/probe experiments, but its interpretation can be complicated. We show how to resolve four common and incorrect misconceptions about non-equilibrium relaxation.

We use these insights to help understand what time-resolved photoemission measurements actually measure.