Surface Induced Anomalous Superconductivity

TL;DR

This paper generalizes the Ginzburg-Landau theory to include surface effects, revealing new anomalous superconducting states and analyzing their properties, including critical currents, especially in thin superconducting slabs.

Contribution

It introduces a surface energy term into the GL theory, enabling the discovery of anomalous superconducting states and providing analytical solutions for various surface-induced phenomena.

Findings

Existence of anomalous superconducting states for all sign combinations of parameters.

Analytical solutions for generalized GL equations in thin slabs.

Critical current dependencies on surface parameters and state ratios.

Abstract

The Ginzburg-Landau (GL) theory is recast using a Hamiltonian involving the complete kinetic energy density which requires that the surface energy must contain a term \nabla |\psi|^2 to support superconducting (SC) states. The GL equations contain two temperature, t, dependent parameters \alpha(t) and \beta(t), which are respectively the coefficients of the SC pair density \propto |\psi|^2, and the pair interaction term \propto |\psi|^4 in the free energy density. The sign of these parameters, which define distinct solution classes, and the ratio s(t) = \sqrt{|\alpha|/|\beta|} are governed by the characteristics of the surface energy density. In addition to the conventional bulk superconducting states with (\alpha < 0, \beta > 0), anomalous superconducting states exist for all other sign combinations, including cases with \beta < 0 which may exist only when surface pair interactions are significant. All possible solutions of our generalized nonlinear, one dimensional GL equations are found analytically and applied to a thin superconducting slab which manifests the possibility of states exhibiting enhanced, diminished, and pre-wetting superconductivity. Critical currents are determined as functions of s(t) and surface parameters. The results are applied to critical current experiments on SNS systems.