We report on quantitative calculations of the upper critical field $H_{ c2}$ for clean type-II superconductors Nb, NbSe$_{ 2}$, and MgB$_{ 2}$ using Fermi surfaces from { \em ab initio} electronic structure calculations. The results for Nb and NbSe$_2$ excellently reproduce both temperature and directional dependences of measured $H_{ c2}$ curves without any adjustable parameters, including marked upward curvature of NbSe$_{ 2}$ near $T_{ c}$. As for MgB$_2$, a good fit is obtained for a $\pi / \sigma$ gap ratio of $\sim 0.3$, which is close to the value from a first-principles strong-coupling theory [H. J. Choi \textit{ et al}. Nature, \textbf{ 418} 758 (2002)]. Our results indicate essential importance of Fermi surface anisotropy for describing $H_{ c2}$.
Categories: cond-mat.supr-con cond-mat.mtrl-sci