Effect of Orbital Quantization on the Critical Field of Type-II Superconductors

Abstract

We discuss the effect of the discreteness of the Landau levels on the upper critical field of a type-II superconductor. At $T=0\ifmmode^\circ\else\textdegree\fi{}$K an ideal superconductor will remain superconducting in an arbitrarily large magnetic field. However, the high-field state is destroyed by a minute amount of impurity scattering or by a small misalignment of up- and down-spin Landau levels. The residual effects are (a) a small shift in the low-temperature critical field [$\frac{\ensuremath{\Delta}{H}_{c2}}{{H}_{c2}}\ensuremath{\approx}{({k}_{F}{\ensuremath{\xi}}_{0})}^{\ensuremath{-}1}$] and (b) oscillatory structure in the transition temperature ${T}_{c2}(H)$ for temperatures $T\ensuremath{\lesssim}\frac{\ensuremath{\hbar}{\ensuremath{\omega}}_{c}}{2{\ensuremath{\pi}}^{2}k}$.