Role of electronic structure on observed phonon anomalies of transition-metal carbides

The possible role of electronic structure on observed phonon anomalies in high-temperature superconducting transition-metal carbides is studied by means of accurate ab initio calculations of the conduction electron response function. From augmented-plane-wave determinations of the electronic band structure, density of states, and Fermi surface of NbC and TaC, the wave-vector-dependent generalized susceptibility, χ(q→), is calculated in the constant-matrix-element approximation. For both NbC and TaC, χ(q→) has strong maxima at precisely those q→ values at which soft modes were observed by Smith and Gläser. Maxima in χ(q→) are predicted for other directions. The locus of these q→max values can be represented by a warped cube of dimension ∼1.2(2πa) in momentum space-in striking agreement with the soft-mode surface proposed phenomenologically by Weber. In sharp contrast, the χ(q→) calculated for both ZrC and HfC-for which no phonon anomalies have been observed-fall off in all symmetry directions away from the zone center. In agreement with Phillips, we thus interpret the phonon anomalies in the transition-metal carbides as due to an "overscreening" effect resulting from an anomalous increase of the response function of the conduction electrons.