Improved Understanding of Gap Dynamics from Time- and Angle-Resolved Photoemission Spectroscopy of a Nonequilibrium Superconductor*

Time- and angle- resolved photoemission spectroscopy (tr-ARPES) has shown to be a useful tool in studying non-equilibrium states of matter. However, the absence of time-translation invariance presents a challenge to understanding the underlying dynamics of the system from the measurements in a straightforward manner. In equilibrium, ARPES intensity is understood to be I(k, ω) ∝ f(ω) A(k, ω) with broadening, where f(ω) is the Fermi-Dirac distribution, and A(k, ω) is the electronic spectral function. Here we study how one should interpret I(k, ω, t), now as a function of time t. We focus our study on tr-ARPES measurements of a non-equilibrium superconducting system where the superconducting gap changes with time. With a focus on situations where the standard quasi-static analysis method fails, we present a possible better way to obtain superconducting gap dynamics.