Surface Induced Anomalous Superconductivity

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.