On a Generalized Ginzburg-Landau Energy for Superconducting/Normal Composite Materials

We review and extend some results for a generalized Ginzburg-Landau energy functional, introduced in the physics literature to model composite superconducting/normal body. In this formulation, the order parameter is defined everywhere in the composite system, with the intention to capture the effect of superconducting electrons pairs diffusing in the normal parts. For suitable choices of the materials conductivities, one can show that a superconductor in contact with a normal material may not exhibit surface superconductivity in decreasing applied fields.