Ginzburg-Landau Theory

Abstract

We have seen in Sect.2 that a superconductor often resides in a state of high spatial inhomogeneity. Here the intermediate state and the situation near a domain wall are just an example showing spatial variations of the order parameter. Spatial inhomogeneity is displayed perhaps even more importantly in the case of the vortex state in type-II superconductors. A phenomenological theory particularly suited for dealing with such inhomogeneous situations has been developed by GINZBURG and LANDAU [1.4]. The Ginzburg-Landau (GL) theory is based on LANDAU’S [1.2] theory of second- order phase transitions, in which LANDAU introduced the important concept of the order parameter. This concept, originally developed for treating structural phase transitions, has since proved extremely useful in many systems where phase transitions take place. Depending on the physical system, the order parameter can have different dimensions. In order-disorder phase transitions the order parameter is a scalar. In a ferromagnetic and ferro-electric phase transition the order parameter is a vector, namely the magnetization and the polarization, respectively. In the superconducting phase transition the order parameter is the density of the superconducting electrons (pair wave function) or the energy-gap parameter. More recently, the concept of the order parameter has been extended to nonequilibrium phase transitions [3.1]. Here an example is the laser near threshold pumping power which can be treated using the light field or the photon number as the order parameter.