Inelastic phase-coherence time in thin metal films

Abstract

We obtain the inelastic phase-coherence time ${\tau }_{\phi }$ for thin metal films above helium temperature by considering Coulomb and electron-phonon scattering contributions. In this temperature regime, we find the asymptotic expansion used so far for the electron-phonon contribution to be invalid. The resulting $T$ dependence is not a power law, but mimics $T^p$ with $p\simeq 2$ for $T=4-20\mathrm{}$ K. Our calculated disorder dependence is very weak. We interpret the experimental results of Bergmann and collaborators as a superposition of Coulomb and a two-dimensional electron-phonon contribution. We obtain good agreement between theory and experiment for ${\tau }_{\phi }$ as a function of both temperature and resistivity.