The wall energy and the critical current of an anisotropic high-temperature superconductor using modified Ginzburg-Landau theory

Abstract

The modified Ginzburg-Landau theory (MGL) for strongly anisotropic high-temperature superconductors (HTS's) is reviewed, and the MGL equations are rederived and used in solving two important fundamental problems. The first one concerns the evaluation of the domain-wall energy problem by a complete solution of the derived equations. The modified free energy functional is used to calculate the maximum supercurrents in both HTS's and the conventional superconductors. Our calculations show that the surface energy vanishes at the critical value of the GL parameter$\kappa _c = \left( {{1 \mathord{\left/ {\vphantom {1 {\sqrt 2 }}} \right. \kern-\nulldelimiterspace} {\sqrt 2 }}} \right)\left\{ {\left( {1 - M} \right)\left( {1 + \left( {{M \mathord{\left/ {\vphantom {M 3}} \right. \kern-\nulldelimiterspace} 3}} \right)} \right)} \right\}^{1/2}$, where 0≤M<1. Therefore, the transformation from type II to type I superconductivity is possible at temperatures very close to the transition critical one, at which κ(T) becomes zero. The generalized formulas of the superconducting current allowed us to calculate the maximum supercurrents for both the HTS's and the conventional one. The possible maximum currents are anisotropic and have higher values for HTS's. Our results are in good agreement with the related theoretical works as well as with the experimental data.