Boundary condition for Ginzburg-Landau theory of superconducting layers

TL;DR

This paper derives and compares boundary conditions for the Ginzburg-Landau theory of superconducting layers, linking electrostatic effects to critical temperature changes and validating approximations with the Budd-Vannimenus theorem.

Contribution

It introduces a new derivation of the boundary condition from the principle of minimum free energy, aligning with de Gennes' approach from BCS theory.

Findings

Derived boundary condition from free energy minimization.

Compared new boundary condition with de Gennes' form.

Validated approximations using the Budd-Vannimenus theorem.

Abstract

Electrostatic charging changes the critical temperature of superconducting thin layers. To understand the basic mechanism, it is possible to use the Ginzburg-Landau theory with the boundary condition derived by de Gennes from the BCS theory. Here we show that a similar boundary condition can be obtained from the principle of minimum free energy. We compare the two boundary conditions and use the Budd-Vannimenus theorem as a test of approximations.