Vortex Fluctuations in the Critical Casimir Effect of Superfluid and Superconducting Films

Vortex-loop renormalization techniques are used to calculate the magnitude of the critical Casimir forces in superfluid films. The force is found to become appreciable when size of the thermal vortex loops is comparable to the film thickness, and the results for T < Tc are found to match very well with perturbative renormalization theories that have only been carried out for T > Tc. When applied to a high-Tc superconducting film connected to a bulk sample, the Casimir force causes a voltage difference to appear between the film and bulk, and estimates show that this may be readily measurable.