First-principles calculation of the superconducting properties of Niobium

We report results for the superconducting transition temperature and anisotropic energy gap for pure Niobium based on Eliashberg's equations and electron and phonon band structures computed from Density Functional Theory. The Fermi surface and the Fermi velocity are also calculated. The phonon bands are in excellent agreement with inelastic neutron scattering data. The phonon density of states and electron-phonon coupling define the electron-phonon spectral function, α²F(p,p';ω), and the electron-phonon pairing interaction, which is the basis for computing the superconducting properties. The electron-phonon spectral function is overall agreement with tunneling spectroscopy data. The strong-coupling gap at T=0 is modestly enhanced, Δ=1.55 meV, compared to weak-coupling BCS value. The superconducting gap exhibits strong anisotropy on the Fermi surface. This leads to violation of Anderson's theorem for non-magnetic impurity scattering in conventional isotropic superconductors. We analyze the distribution of gap anisotropy and compute the suppression of the superconducting transition temperature using a self-consistent T-matrix theory for quasiparticle-impurity scattering to describe Niobium doped with non-magnetic impurities.