Electron-electron scattering in the intraband optical conductivity of Cu, Ag, and Au

The predictions of the Drude dielectric function are compared with measured room-temperature reflectivities of the noble metals in the near infrared and visible regions. The electron scattering frequency $\frac{1}{\tau }$ is assumed to be the sum solely of electron-phonon scattering as calculated by Holstein and electron-electron scattering according to Gurzhi. The latter accounts for an important quadratic frequency dependence of $\frac{1}{\tau }$. Although Gurzhi's coefficient is too small by a factor of 2 to 4, an improved calculation by Lawrence gives more reasonable agreement with the data. In this comparison it is essential to consider the contribution to ${\epsilon }_1$ from interband transitions at higher frequencies, which we derive from transmissivity measurements. The resulting reflectivity is in reasonable agreement with a selection of data for Cu and Au between 0.4 and 2.0 eV and for Ag between 0.4 and 3.3 eV, if the data are corrected for the anomalous skin effect, assuming some fraction of the electrons is diffusely scattered at the surface.