Electronic Structure of Niobium and Tantalum

The band structures and Fermi surfaces of niobium and tantalum have been calculated via the augmented-plane-wave (APW) method. Relativistic effects have been included in the tantalum but not the niobium calculation. The resulting niobium and tantalum Fermi surfaces are similar to a Fermi-surface model for the vanadium-group transition metals that was proposed previously by the author. This model contains closed hole pockets centered at the symmetry points $\ensuremath{\Gamma}$ and $N$ of the bcc Brillouin zone plus a multiply connected hole sheet which extends from $\ensuremath{\Gamma}$ to $H$ along $〈100〉$ directions. Areas and cyclotron masses of closed extremal orbits on the niobium and tantalum Fermi surfaces have been calculated as a function of magnetic field direction in the {100} and {110} planes. The calculated areas are in quantitative agreement with recent experimental results. The maximum discrepancies are 18 and 10% for niobium and tantalum, respectively. The effect of niobium Fermi-surface anisotropy on the temperature dependence of the upper critical field has been evaluated in terms of the Hohenberg-Werthamer theory. The results of this calculation overestimate the experimentally observed effect by a factor of about 2.5.