Phonon branch-resolved electron-phonon coupling and the multitemperature model

Abstract

Electron-phonon $(e\text{\ensuremath{-}}p)$ interaction and transport are important for laser-matter interactions, hot-electron relaxation, and metal-nonmetal interfacial thermal transport. A widely used approach is the two-temperature model (TTM), where $e\text{\ensuremath{-}}p$ coupling is treated with a gray approach with a lumped coupling factor ${G}_{ep}$ and the assumption that all phonons are in local thermal equilibrium. However, in many applications, different phonon branches can be driven into strong nonequilibrium due to selective $e\text{\ensuremath{-}}p$ coupling, and a TTM analysis can lead to misleading or wrong results. Here, we extend the original TTM into a general multitemperature model (MTM), by using phonon branch-resolved $e\text{\ensuremath{-}}p$ coupling factors and assigning a separate temperature for each phonon branch. The steady-state thermal transport and transient hot electron relaxation processes in constant and pulse laser-irradiated single-layer graphene (SLG) are investigated using our MTM respectively. Results show that different phonon branches are in strong nonequilibrium, with the largest temperature rise being more than six times larger than the smallest one. A comparison with TTM reveals that under steady state, MTM predicts 50% and 80% higher temperature rises for electrons and phonons respectively, due to the ``hot phonon bottleneck'' effect. Further analysis shows that MTM will increase the predicted thermal conductivity of SLG by 67% and its hot electron relaxation time by 60 times. We expect that our MTM will prove advantageous over TTM and gain use among experimentalists and engineers to predict or explain a wide ranges of processes involving laser-matter interactions.