Two-Dimensional Transition in Superconducting Films and Junction Arrays

Abstract

In two-dimensional systems a special phase transition is possible which has become known as the Kosterlitz-Thouless transition. The original authors1 characterized the transition as the breakdown of topological long range order. Below a critical temperature T topological excitations, vortices, occur only as bound vortexc-antivortex pairs. Above the critical temperature single vortices and anti-vortices are present in thermodynamic equilibrium. A renormalization procedure was developed to account for the influence of bound pairs with small separation on pairs with larger separation. A Kosterlitz-Thouless phase transition occurs only if the energy of a bound vortex-antivortex pair depends logarithmically on the separation r. As the number of free vortices grows extremely slowly with temperature above Tc, the transition is not very pronounced from an experimental point of view.