Long-range interaction of fluctuating vortices with a parallel surface in layered superconductors

In extremely anisotropic layered superconductors randomly fluctuating vortex lines are attracted to a planar specimen surface by a long-range interaction decreasing as 〈(Formula presented)〉/(Formula presented), where (Formula presented)≫:λ is the average vortex distance to the surface oriented perpendicular to the layers and 〈(Formula presented)〉 is the mean square vortex displacement, e.g., 〈(Formula presented)〉∝kT for thermal fluctuations. This long-range force exceeds the short-range exponential interaction ∝exp(-(Formula presented)/λ) of straight vortices with their image vortex, where λ=(Formula presented) is the penetration depth of supercurrents in the layers. The long-range attraction originates from the dipole-dipole interaction between each displaced pancake vortex and its image. It is analogous to the Casimir effect, which predicts an attraction between two closely spaced metal plates. The energy contribution of the additional stray field generated by the distorted vortex is calculated. For short-wavelength distortions this term decreases more rapidly with increasing surface distance (Formula presented) and may be disregarded; for long-wavelength distortions the stray-field contribution is comparable to the energy of the dipole-dipole interaction, compensating it partly.