Electronic susceptibility of niobium

Abstract

The static electronic susceptibility $\chi \left(\overrightarrow{\mathrm{q}}\right)$ is calculated for niobium along the [100] direction both with and without matrix elements. The energy bands are generated by a fitted second neighbor, $s-p-d$ Slater-Koster model, and matrix elements are approximated by using the Slater-Koster wave-function coefficients with radial integrals of Fermi-level Korringa-Kohn-Rostoker wave functions within the muffin tin. The Brillouin-zone integration is carried out by the combined linear-quadratic method of Cooke and Wood. Contrary to the work of Evenson, Fleming, and Liu our constant-matrix-element calculation yields a result for $\chi \left(\overrightarrow{\mathrm{q}}\right)$, which is relatively featureless. The major effects of including the band and momentum dependence of the matrix elements are to make $\chi \left(\overrightarrow{\mathrm{q}}\right)$ a generally decreasing function of $\left|\overrightarrow{\mathrm{q}}\right|$, and to bring out some structure not seen in the constant-matrix-element calculation. The static susceptibility has a noticeable hump around the same wave vector as the observed [100] LA-phonon anomaly. The frequency dependence of the real part of the dynamic susceptibility appears to be small for $\omega$ in the phonon-frequency range.