The Berezinskii–Kosterlitz–Thouless Transition in Superconductors

Abstract

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 off as 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 vortexantivortex 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. 4.

An introduction to spontaneous symmetry breaking

“…Simultaneously, the energy cost of vortices grows and starts to depend on the system size again, pushing the BKT transition temperature up from zero. This explains the experimental observation of BKT transitions in both thin type-II superconductors and in Josephson junction arrays [102].…”

“…Vortices can thus interact over large distances through the electromagnetic fields that they create in the vacuum surrounding the superconducting film. This can be described by introducing an effective penetration depth of magnetically mediated interactions within the two-dimensional superconductor, which turns out to be [102]:…”

An Introduction to Spontaneous Symmetry Breaking

“…Simultaneously, the energy cost of vortices grows and starts to depend on the system size again, pushing the BKT transition temperature up from zero. This explains the experimental observation of BKT transitions in both thin type-II superconductors and in Josephson junction arrays [97].…”

“…Vortices can thus interact over large distances through the electromagnetic fields that they create in the vacuum surrounding the superconducting film. This can be described by introducing an effective penetration depth of magnetically mediated interactions within the two-dimensional superconductor, which turns out to be [97]:…”

Density induced BCS-Bose evolution in gated two-dimensional superconductors: The Berezinskii-Kosterlitz-Thouless transition as a function of carrier density

“…The physics of two-dimensional (2D) superconductors is a fascinating subject with a long history [1]. The theoretical prediction that 2D Fermi systems can exhibit superconductivity can be inferred from the seminal papers of Berezinskii [2], Kosterlitz and Thouless [3], where the mechanism of vortex-antivortex unbinding was proposed.…”