Optical properties of the alkali-metal-doped superconducting fullerenes: ${\mathrm{K}}_3$${\mathrm{C}}_{60}$ and ${\mathrm{Rb}}_3$${\mathrm{C}}_{60}$

We have measured the optical reflectivity over a broad spectral range of single-phase ${\mathrm{K}}_3$${\mathrm{C}}_{60}$ and ${\mathrm{Rb}}_3$${\mathrm{C}}_{60}$ compounds, and have evaluated the optical conductivity both below and above the superconducting transition temperature. We identify various features in the excitation spectrum of the normal state: a Drude contribution at low frequency, a midinfrared absorption, and several interband transitions. In the superconducting state our results are in full agreement with a BCS singlet ground state, with the measured gap values consistent with the weak-coupling limit. We also evaluate several intrinsic parameters characterizing both the normal and superconducting state, such as the plasma frequency, the relaxation scattering rate, and the mean free path, besides the superconducting gaps and the penetration depth. We compare these quantities with similar ones from other experiments and find satisfactory agreement. Moreover, we present our calculation of the electrodynamic response above and below ${\mathit{T}}_{\mathit{c}}$ with the standard Eliashberg electron-phonon theory of superconductivity, which strongly supports a pairing mechanism mediated by high-frequency intramolecular phonon modes.