Implications of Reflectance Measurements on the Mechanism for Superconductivity inMgB2

Recent optical studies in $c$-axis oriented superconducting ${\mathrm{MgB}}_2$ films indicate that the electron-phonon coupling is weak. We reinforce this conclusion by examining the raw reflectance data; its frequency dependence is incompatible with strong electron-phonon scattering. This is further strengthened by analysis of the real part of the conductivity, and by the temperature dependence of the effective Drude scattering rate. Using a realistic electron-phonon spectral shape, we find ${\lambda }_{\mathrm{tr}}\approx 0.15$. To the extent that ${\lambda }_{\mathrm{tr}}\approx \lambda$, this disagrees sharply with model calculations, and is far too low to provide the means for $T_c=39\mathrm{}\mathrm{K}$. A simple model is constructed with coupling to a high frequency excitation, which is consistent with both the low frequency optical data and the high $T_c$.