Phonon Anomalies in d-Band Metals and their Relationship to Superconductivity

Abstract

Many high Tc d- and f-band superconductors exhibit actual or incipient lattice instabilities as evidenced by structural transitions or anomalous dips in their phonon dispersion curves. We present a theory demonstrating that the dips and high Tc’s in these materials are likely manifestations of the characteristic response (screening) by d-electrons near the Fermi level. In materials with a relatively large density of localized states at the Fermi level there is a tendency towards a collective electronic instability characterized by a periodic charge redistribution. However a charge density wave does not form because these charge fluctuations are strongly coupled to the lattice giving rise to anomalies in the phonon spectrum and in some cases eventually driving the lattice into a structural transformation. By including relaxation of the fluctuations the central peak observed by neutron diffraction in many of these materials can also be understood. In regions of \(\vec q\)-space where such incipient electronic instabilities are present there is lessened screening or relative enhancement of the electron- phonon matrix elements - giving rise to larger λ’s and thus greater Tc ’s. The details of the theory are sketched and the physical ideas explained. A simplified application of the theory to Nb and NbC shows that the positions of the dips are readily accounted for and that the size or depth of these anomalies is very sensitive to the density of states at EF. The relationship to other work is discussed.