Casimir Force between Vortex Matter in Anisotropic and Layered Superconductors

TL;DR

This paper introduces a novel method to compute the long-range vortex-vortex Casimir interaction in anisotropic layered superconductors by mapping the problem onto a 2D quantum mechanics framework, confirming previous van der Waals force results.

Contribution

It presents a new approach linking vortex interactions in superconductors to a 2D Casimir problem, providing a theoretical foundation for calculating vortex-vortex forces.

Findings

Derived the Casimir force between vortex matter layers.

Confirmed the force matches previous van der Waals calculations.

Established a new theoretical framework for vortex interactions.

Abstract

We present a new approach to calculate the attractive long range vortex-vortex interaction of the van der Waals type present in anisotropic and layered superconductors. The mapping of the statistical mechanics of vortex lines onto the imaginary time quantum mechanics of two dimensional charged bosons allows us to define a 2D Casimir problem: Two half-spaces of (dilute) vortex matter separated by a gap of width R are mapped to two dielectric half-planes of charged bosons interacting via a massive gauge field. We determine the attractive Casimir force between the two half-planes and show, that it agrees with the pairwise summation of the van der Waals force between vortices previously found by Blatter and Geshkenbein [Phys. Rev. Lett. 77, 4958 (1996)]