The berezinskii-Kosterlitz-Thouless transition in superconductors

The Berezinskii-Kosterlitz-Thouless (BKT) transition occurs in thin superconducting films and Josephson junction arrays in a manner closely analogous to what is found for superfluid helium films. Initially it was believed that a BKT thermodynamic instability in which vortex-antivortex pairs, bound at low temperatures dissociate into free vortices at a characteristic temperature, would not occur in superconductors. The reason for this was that the vortex-antivortex interaction potential in bulk superconductors falls offas 1/r, and the requirement for a BKT transition is that the interaction potential between vortex-antivortex pairs be a logarithmic function of their separation. Once it was realized that a logarithmic vortex-antivortex interaction occurs in thin films to a characteristic distance that can be macroscopic, systematic experiments were carried out on such systems establishing the existence of such a transition. In this chapter, we review the elementary theory of the BKT transition in superconductors along with the earliest experimental results leading to the establishment of its existence in thin films and Josephson junction arrays. At the present time, the BKT paradigm plays a central role in the understanding of thin film superconductors, Josephson junction arrays, and complex compounds which have weakly coupled layers, such as many of the high temperature superconductors. The limitations of space preclude a discussion of many issues that are of contemporary interest.