Vortex loops in the critical Casimir effect in superfluid and superconducting films

Abstract

Vortex-loop renormalization techniques are used to calculate the magnitude of the critical Casimir forces in superfluid and superconducting thin films. The force is found to become appreciable when the size of the thermally excited vortex loops is comparable to the film thickness, and the results for T< T c are found to match very well with perturbative renormalization-group theories that can only be carried out for T> T c. In helium films the Casimir force leads to a change in the film thickness close to T c that has been observed experimentally. A similar effect is predicted to occur near the transition temperature of high- T c superconducting films, which is also a vortex-loop phase transition. In this case the Casimir force takes the form of a voltage difference that will appear at the junction between a thin film and a bulk sample. Estimates show that this voltage can be appreciable (tens of microvolts), and it may be possible to observe the effect by measuring the voltage across two Josephson tunnel junctions to the film and to the bulk, using a SQUID voltmeter.