Electron-Phonon Dephasing in Ultrathin Disordered Films: From Power Laws to Diagnostic Maps

Abstract

Electron-phonon dephasing in ultrathin disordered metallic films is often summarized by a power law, $\tau_{e-ph}^{-1}=AT^p$. However, thin metals, alloys, and superconducting films exhibit effective exponents close to 2, 3, and 4, as well as intermediate nonuniversal values. We argue that in ultrathin supported films, the exponent should be treated not as a universal material constant, but as a crossover observable. Its interpretation requires several coordinates: the clean-to-dirty parameter $q_T l$, phonon confinement and film-substrate acoustic coupling, and the microscopic character of disorder. The diagnostic picture is illustrated using Ar-ion-irradiated Au films as a controlled-disorder series. In these films, the fitted electron-phonon exponent remains near $p\simeq 2$ for low values of the pure-dirty crossover temperature $T_{tr}\simeq \hbar s/(k_B l)$ and increases toward $p\simeq 2.8$ as disorder increases. At the same time, the prefactor trend indicates suppression of electron-phonon scattering with decreasing mean free path, consistent with dirty-limit weakening rather than static-disorder enhancement. The persistence of $p<4$ points to the role of thin-film or film-substrate phonon effects. The resulting diagnostic map provides a compact framework for comparing electron-phonon dephasing data in ultrathin disordered films.