We derive solutions of the Gorkov equations for a type-II superconductor using the fact that the vortex lattice is a consequence of translation and gauge covariance. We thus generalize the Abrikosov solutions of the vortex lattice to include Cooper pairing in higher-order Landau indices relevant to low temperatures and high quantizing second critical fields where the semiclassical assumptions of the Ginzburg-Landau theory break down. Detailed calculations of the pairing amplitudes are presented for triangular and square lattices in a diagonal Landau-state approximation illustrating the effects of temperature and magnetic field on the vortex lattices. These solutions are also of interest because they give a purely microscopic view of the vortex lattice and the correlations responsible for it.

• Received 18 November 1992

DOI:https://doi.org/10.1103/PhysRevB.47.8843