Angular Momentum and Transition-Metal Superconductivity

The relation between the systematics of superconductivity in the transition metals and the Periodic Table suggests that the transition temperature is chiefly a short-range or "chemical" property. When a local representation of phonons and an angular momentum decomposition of electron wave functions are used, the conventional description of electron-phonon interactions contains chiefly scatterings which change the angular momentum of the electron. This selection rule makes possible the writing of the electron-phonon coupling constant $\lambda$ as the quotient of two parameters, each of which is of a chemical nature. This simplification is possible for materials having a high density of $d$ states at the Fermi energy. For such materials, $\lambda$ is little affected by the density of states. The theory is compared with the superconducting transition temperatures of transition metals and their alloys.