Intraband optical conductivityσ(ω,T)of Cu, Ag, and Au: Contribution from electron-electron scattering

The intraband optical conductivity of all the noble metals has been measured at the temperatures 77, 295, and 425 K. In all the cases the Drude scattering rate ${\tau }^{-1\mathrm{}}=\alpha \mathrm{}\left(T\right)+\beta {\left(\hslash \omega \right)}^2$ for $\hslash \omega$ less than about 2 eV. The temperature-dependent intercept $\alpha \mathrm{}\left(T\right)\mathrm{}$ may be attributed to electron-phonon scattering. The quadratic dependence on $\omega$, with $\beta$ found to be temperature independent, is suggestive of electron-electron scattering. However, the observed values of $\beta$ exceed current theoretical estimates by a factor of 2 or 3. Moreover, $\beta$ should be related to the dc electrical and thermal resistivities (in the limited temperature regimes in which electron-electron scattering contributes appreciably). If this comparison is made, the discrepancy worsens to an order of magnitude. We briefly discuss other mechanisms which might account for the large observed values of $\beta$, but none looks sufficient. We conclude that the frequency dependence in the Drude scattering rates of the noble metals, while qualitatively suggestive of electron-electron scattering, is quantitatively not understood.