Ginsburg‐Landau Theory of the Vortex Lattice in Type‐I1 Superconductors for All Values of ϰ and <i>B</i>

Abstract

Abstract A two‐dimensional variational method is established which permits the solution of the Ginsburg‐Landau equations for type‐II superconductors to any desired accuracy. Free energy, magnetization curves, GL function, microscopic magnetic field and current density are calculated for hexagonal and tetragonal lattice symmetries and for all values of the GL parameter ϰ and the induction B . The hexagonal lattice is found to be stable throughout. As a further result simple approximate expressions are found for the free energy (with en error &lt;5 × 10 −5 ) and for the magnetization as functions of ϰ and B or the external field H e .