Electron band structure, resistivity, and the electron-phonon interaction for niobium under pressure

Accurate measurements of the electrical resistance of Nb are presented as a function of temperature and pressure in the region 0-40°C and 0-1 GPa. From these measurements and published results for the compressibility and the pressure dependence of the superconducting transition temperature $T_c$ we evaluate the pressure dependence of the electron-gas plasma frequency $\omega \mathrm{}\left(p\right)\mathrm{}$. The electronic structure of Nb is calculated from a self-consistent linear muffin-tin orbital method and results are obtained for the pressure dependence of the density of states at the Fermi surface, the root mean square over the Fermi surface of the Fermi velocity, the optical mass, and the plasma frequency. The experimental and calculated results for the pressure dependence of $\omega \mathrm{}\left(p\right)\mathrm{}$ are both close to $\frac{d\ln {\omega }^2}{d\ln V}=-1.9\mathrm{}$. This agreement suggests that measurements of the electrical resistance as a function of temperature and pressure provide a new test of band-structure calculations. From our measurements of the resistance and calculations of $\omega \mathrm{}\left(p\right)\mathrm{}$ and from published results for the compressibility we obtain the pressure dependence of the electron-phonon interaction $\lambda \mathrm{}\left(p\right)\mathrm{}$. With $p$ given in gigapascals, the result is $\frac{d\ln \lambda }{\mathrm{dp}}=-0.0047\mathrm{}$.