Soft phonon modes and localization of d-electrons in superconducting vanadium

A few years ago, Matthias1 attempted to find some empirical relation between the superconducting transition temperature Tc and the number of electrons per atom in the transition metals and their alloys. To elucidate the relation, we present a theoretical investigation of the dependence of the soft phonon modes associated with the high Tc of superconducting vanadium on the degree of localization of its d electron and on the strength of the s-d resonant interaction, using the transition-metal model potential method in the self-consistent field and harmonic approximations.2 We find that, as the number of d-electrons localized at the vanadium ion varies from zero in V5+ to three in V2+, the longitudinal and the transverse phonon modes soften significantly, signaling lattice instability; and we discuss the implications of the results for the systems V, V3Ga and V3Si in which different valence states may be a factor determining the magnitude of Tc.