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 ∇|ψ|2 to support superconducting (SC) states. The GL equations contain two temperature t dependent parameters α(t) and β(t), which are respectively the coefficients of the SC pair density ∝|ψ|2, and the pair interaction term ∝|ψ|4 in the free energy density. The sign of these parameters, which defines distinct solution classes, and the ratio [Formula: see text] are governed by the characteristics of the surface energy density. In addition to the conventional bulk superconducting states with (α < 0, β > 0), anomalous superconducting states exist for all other sign combinations, including cases with β < 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.
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