High-temperature Versus Low-temperature Superconductors:

A Mathematical Description

(Abstract)

We discuss the Ginzburg-Landau model for homogeneous (low-temperature) superconductors and the Lawrence-Doniach model for anisotropic layered (high-temperature) superconductors. The Larence-Doniach model features nonlinear Josephson coupling among a stack of parallel superconducting layers, which results in less regularity of minimizers and fundamental differences in critical phenomena. We discuss similarities and differences for minimizers of these models and how they relate to the Josephson coupling in the Lawrence-Doniach model.