Electron-phonon coupling in the transition metals: Electronic aspects

The electron-phonon coupling parameter $\lambda$ may be written as the product of three factors: the Fermi-energy density of states, $N\left(E_F\right)$, the Fermi-surface average of the electron-phonon interaction, $〈I^2〉$, and an effective inverse lattice force constant $\Phi$. We have calculated $〈I^2〉$ and $N\left(E_F\right)$ for 11 $4d$ transition-metal systems using the rigid muffin-tin approximation. We find a large but understandable variation in $〈I^2〉$ which is in good agreement with the empirical variation in $〈I^2〉$. $〈I^2〉$ varies approximately as the inverse second power of the atomic volume and as the first power of the amount of $l=3\mathrm{}$ Fermi-energy state density within the Wigner-Seitz cell. We discuss the implications of our findings in regard to the search for systems with higher superconducting transition temperatures.