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

Abstract

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, $\ensuremath{\chi}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}})$, is calculated in the constant-matrix-element approximation. For both NbC and TaC, $\ensuremath{\chi}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}})$ has strong maxima at precisely those $\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}$ values at which soft modes were observed by Smith and Gl\"aser. Maxima in $\ensuremath{\chi}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}})$ are predicted for other directions. The locus of these ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}}_{max}$ values can be represented by a warped cube of dimension $\ensuremath{\sim}1.2(\frac{2\ensuremath{\pi}}{a})$ in momentum space---in striking agreement with the soft-mode surface proposed phenomenologically by Weber. In sharp contrast, the $\ensuremath{\chi}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}})$ 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.