Inelastic phase-coherence time in thin metal films

We obtain the inelastic phase-coherence time ${\ensuremath{\tau}}_{\ensuremath{\varphi}}$ 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 $p\ensuremath{\simeq}2$ for $T=4\ensuremath{-}20$ 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 ${\ensuremath{\tau}}_{\ensuremath{\varphi}}$ as a function of both temperature and resistivity.

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