Calculation of the superconducting transition temperature in niobium

Abstract

We present calculations of the superconducting transition temperature ${T}_{c}$, the electron-phonon coupling constant $\ensuremath{\lambda}$, and the spectral function ${\ensuremath{\alpha}}^{2}f(\ensuremath{\omega})$, for niobium. Our calculations are based on an empirical-pseudopotential-method band structure. Phonon linewidths are also given for longitudinal and transverse branches along different directions. The necessary electron-phonon matrix elements are evaluated using only the rigid-ion approximation and applying Green's theorem to the nonlocal pseudopotential. The calculated value of ${T}_{c}$ is 8.4 K and the calculated $\ensuremath{\lambda}$ is 1.02. The spectral function and linewidths are compared to experimental and previous theoretical results.