Optical properties and electron-phonon interactions in superconducting transition metals

The infrared optical properties of various high-temperature superconductors are analyzed using a Drude form of the dielectric function $\epsilon (q,\omega )$. By plotting the imaginary part $\omega {\epsilon }_2$ vs ${\epsilon }_1$, we identify the interband contributions, and estimate the plasmon damping $\Gamma$ from the slope in the frequency range where the Drude form is justified. Thus we estimate the electron-phonon coupling parameter $\lambda$ which enters the BCS expression for the superconducting transition temperature $T_c$. Independently we estimate $\lambda$ from resistivity data, for temperatures $T>\mathrm{}300\mathrm{}$ °K using the plasma frequency extracted from the optical data. For Nb the analysis gives good agreement for $\lambda \simeq 0.7$ obtained from optical, resistance, and $T_c$ data. For the $A-15\mathrm{}$ compounds ${\mathrm{Nb}}_3$Ge, ${\mathrm{Nb}}_3$Sn, and ${\mathrm{V}}_3$Si the $\lambda$ values estimated from the optical data are in accord with the resistance measurements but generally are found to be much too small, typically $\lambda <~0.2$, to account for the high superconducting temperatures ($T_c\sim 20$ °K) of these materials.