Ginzburg–Landau Theory and High T c Superconductivity

Abstract

In many ways, condensed matter theory is based on the art of making uncontrolled approximations guided by experiment. A remarkable property of such theories is that they often turn out to be much more robust than was thought at the time they were put forward, such as the BCS theory of superconductivity, or Laughlin’s Fractional Quantum Hall effect theory. One such uncontrolled approximation is the class of theories put forward by Ginzburg and Landau. Of course the idea of coarse graining comes from a long tradition based on work by Euler, Navier, Stokes, Curie, Weiss, Lennard–Jones, Devonshire and many others. In this note I will make some comments on the application of Ginzburg–Landau (GL) theory to the properties of the high Tc superconductors at the phenomenological level. Starting with the work of Abrikosov, the GL description of superconductivity (and before that the London description) was central to the understanding of the reaction of superconductors to applied magnetic fields. This (and similar work in liquid 4He) led to the idea of flux quantization and eventually to the description of the thermodynamics and kinetics of superconductors in terms of vortex degrees of freedom. In conventional superconductors, the Abrikosov theory leads to the kinetic properties associated with the thermally activated movement of vortices which is restricted by pinning centers. In three-dimensional superconductors at low temperatures the vortices are very slow to equilibrate owing to their macroscopic character. In thin films, however, the creation of vortex– antivortex pairs costs energy on the order of a few KBT, so that the vortices behave as true thermo-