Microscopic derivation of superconductor-insulator boundary conditions for Ginzburg-Landau theory revisited. Enhanced superconductivity at boundaries with and without magnetic field

TL;DR

This paper revisits the microscopic derivation of superconductor-insulator boundary conditions within Ginzburg-Landau theory, incorporating magnetic fields and higher-order effects, revealing boundary states with enhanced superconductivity.

Contribution

It provides a revised derivation of boundary conditions from BCS theory, including effects of magnetic fields and higher-order derivatives, showing boundary states with increased critical temperature.

Findings

Boundary conditions follow from order parameter reflection.

Boundary states with higher critical temperature exist.

H_{c3} is higher than de Gennes prediction in magnetic fields.

Abstract

Using the standard Bardeen-Cooper-Schrieffer (BCS) theory, we revise microscopic derivation of the superconductor-insulator boundary conditions for the Ginzburg-Landau (GL) model. We obtain a negative contribution to free energy in the form of surface integral. Boundary conditions for the conventional superconductor have the form $\textbf{n} \cdot \nabla \psi = \text{const} \psi$. These are shown to follow from considering the order parameter reflected in the boundary. The boundary conditions are also derived for more general GL models with higher-order derivatives and pair-density-wave states. It shows that the boundary states with higher critical temperature and the boundary gap enhancement, found recently in BCS theory, are also present in microscopically-derived GL theory. In the case of an applied external field, we show that the third critical magnetic-field value $H_{c3}$ is higher than what follows from the de Gennes boundary conditions and is also significant in type-I regime.