Electronic Structure of Niobium and Tantalum

TLDR

The vanadium‑group transition‑metal model predicts closed hole pockets at Γ and N and a multiply connected sheet extending from Γ to H along 〈100〉 directions. The authors calculated niobium and tantalum band structures and Fermi surfaces using the APW method (including relativistic effects for Ta), computed extremal orbit areas and cyclotron masses versus field direction, and evaluated the impact of Fermi‑surface anisotropy on the upper critical field via Hohenberg‑Werthamer theory. The calculated Fermi surfaces agree with the vanadium‑group model, the extremal orbit areas match experiments within 10–18%, and the predicted upper‑critical‑field anisotropy overestimates the measured effect by about 2.5‑fold.

Abstract

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.