Microscopic Description of the Vortex State near the Upper Critical Field

We solve the BCS-Gor'kov equations for a pure, isotropic type-II superconductor near the upper critical field. Corrections to the semiclassical results lower the value of the upper critical field and cause $H_{c2\mathrm{}}\left(T\right)$ to vanish quadratically near $T_c$. This form leads to positive curvature in the critical field, which has been seen in a range of materials, and means that a type-II superconductor will convert to type I at a temperature close to $T_c$.