The Interplay of Thermal Melting and Pump Driven Melting of Charge Order: A Two-Temperature Study of the Holstein Model
Charge order driven by electron-phonon coupling is well understood at equilibrium but pump-probe experiments raise a new question: how does this order melt and recover after strong photoexcitation? A pump pulse promotes carriers across the charge-order gap and creates a nonequilibrium high-energy electronic population. In a closed system the subsequent dynamics is constrained by energy conservation. In an `open system' - where the system is coupled to a thermal bath at some temperature $T_{\rm bath}$ - there are new fluctuation and dissipation processes at play. One can attempt a computational scheme that incorporates coupling of electrons to a laser pump, the coupling of system phonons to a thermal bath, and the Holstein interaction that couples electrons and phonons. We attempt an approximation where the pump induced electronic excitations are modeled by a slowly time varying `electron temperature', $T_{\rm el}(t)$, indicative of a quasi-equilibrium electronic state. We solve the problem for different combinations of $T_{\rm el}$ and $T_{\rm bath}$, probing the order parameter dynamics, the static properties and excitations in the long time `quasi steady state', and establish a `phase diagram' in terms of bath temperature and electron temperature.