Coexistence of excited polarons and metastable delocalized states in photo-induced metals

We study how polaronic states form as a function of time due to strong electron-phonon coupling, starting from a hot electron distribution which is representative of a photo-induced metallic state immediately after laser excitation. For this purpose we provide the exact solution of the single-electron Holstein model within nonequilibrium dynamical mean-field theory. In particular, this allows us to reveal key features of the transient metallic state in the numerically most challenging regime, the adiabatic regime, in which phonon frequencies are smaller than the electronic bandwidth: Initial coherent phonon oscillations are strongly damped, leaving the system in a mixture of excited polaron states and metastable delocalized states. We compute the time-resolved photoemission spectrum, which allows to disentangle two contributions. The existence of long-lived delocalized states suggest ways to externally control transient properties of photo-doped metals.