Bulk Solution of Ginzburg-Landau Equations for Type II Superconductors: Upper Critical Field Region

Abstract

A solution is described of the Ginzburg---Landau equations of the Abrikosov type for a homogeneous type II superconductor just below the upper critical field. This solution is characterized by magnetic field maxima corresponding to an equilateral triangular lattice and a value $\ensuremath{\beta}=1.16$ of Abrikosov's parameter. Abrikosov's square-lattice solution with $\ensuremath{\beta}=1.18$ has a higher free energy and is unstable with respect to the triangular lattice solution.