Electron-Phonon Temperature Inversion in Nanostructures under Pulsed Photoexcitation

Abstract: Photoexcitation of metallic nanostructures with short optical pulses can drive non-thermal electronic states, which, upon decay, lead to elevated electronic temperatures ($T_e \gtrapprox 1000\,\mathrm{K}$) eventually equilibrating with the lattice ($T_p$) through electron-phonon scattering. Here, we show that, in spatially extended nanostructures, the lattice temperature can locally exceed that of the electrons, a seemingly counterintuitive transient effect termed hereafter ``temperature inversion'' ($T_p > T_e$). This phenomenon, fundamentally due to inhomogeneous absorption patterns and absent in smaller particles, emerges from a complex spatio-temporal interplay, between the electron-phonon coupling and competing electronic thermal diffusion. By combining rigorous three-dimensional (3D) finite-element-method-based simulations with practical reduced zero-dimensional (0D) analytical models, we identify the electron-phonon coupling coefficient ($G_{e-p}$) as the critical parameter governing this behavior. An optimal $G_{e-p}$ range allows the inversion, whereas a weak or overly strong coupling suppresses it. Among common plasmonic metals, platinum (Pt) exhibits the most pronounced and long-lived inversion, while gold (Au) and silver (Ag) show no significant inversion. Moreover, the close agreement between the 0D and 3D results, once an appropriate characteristic length is selected, highlights that the essential physics governing the inversion can be captured without full spatial complexity. These results provide insights for optimizing nanoscale energy transfer and hot-carrier-driven processes, guiding the strategic design of materials, geometries, and excitation conditions for enhanced ultrafast photothermal control.