Extended Multi-Temperature Model for Electron--Phonon Coupling and Ultrafast Thermal Transport in Graphene

Abstract

Ultrafast thermal transport in low-dimensional materials challenges traditional diffusive models due to reduced scattering, strong electron-phonon coupling, and pronounced non-equilibrium effects. To address these complexities, we extend the macroscopic multi-temperature model by incorporating non-diffusive and non-local phenomena, treating electrons, optical phonons, and acoustic phonons as coupled but thermally distinct subsystems. We benchmark this enhanced framework against the multi-temperature Boltzmann transport equation, enabling detailed resolution of branch-dependent energy relaxation and identifying bottlenecks in thermalization. This approach provides a more accurate and comprehensive description of heat flow in emerging materials, offering novel insights into phonon dynamics and electron-phonon interactions. These theoretical advances pave the way for the improved design and optimization of next-generation nanoelectronic and photothermal devices.

Figures (4)

• Figure 1: Schematic illustration of electron-phonon (e-ph) coupling in photoexcited graphene exp_photon_excitation2021nano_letters_2017_non_equilibriumDistinguishing_AdvSci_2020beardo_hydrodynamic_EP_2025ZHANG2024Lu2018. The ultrafast laser pulse rapidly heats electrons, which subsequently transfer energy to optical and acoustic phonon modes.
• Figure 2: (a) Hot-spot generation in single-layer graphene induced by ultrafast laser pulse. (b) Evolutionary history of electron–phonon coupling heat-conduction models, emphasizing the progression from the standard TTM to modern extended MTM formulations.. Temporal evolution of the temperatures at spatial positions (c) $y = 1$ nm and (d) $y = 5$ nm, respectively, from the center of the ultrafast laser excitation.
• Figure 3: Effective thermal conductivity the electron and different phonon branches.
• Figure 4: Temperature contours originating from the hot spot. Figures 4(a), (c), and (e) are obtained using the eMTM-BTE, while Figures 4(b), (d), and (f) are obtained using the eMTM-GKE.