Vortex interactions in a thin platelet superconductor

TL;DR

This paper investigates vortex interactions in thin platelet superconductors by mapping vortex fluctuations to a 1D quantum boson system, analyzing how surface effects influence low-energy interactions and the Luttinger parameter.

Contribution

It provides a detailed analysis of vortex interactions in thin superconducting platelets, applying Luttinger liquid theory to determine the scattering length and interaction parameters.

Findings

Determined the vortex scattering length as a function of platelet thickness.

Showed how surface interactions affect the low-energy vortex dynamics.

Connected the scattering length to the Luttinger parameter g.

Abstract

The thermal fluctations of vortices in a superconductor can be usefully mapped onto the quantum fluctations of a collection of bosons at T=0 moving in 2 dimensions. When the superconductor is a thin platelet with the magnetic field parallel to its surface, the interacting quantum bosons are effectively moving in 1 dimension, allowing for powerful Luttinger liquid methods to be applied. Here we consider how this 1 dimensional limit is approached, studying the interaction of vortices with the platelet surfaces and each other. Using realistic parameters and vortex interactions for an underdoped YBCO platelet we determine the scattering length, a, characterizing the low energy interaction of a vortex pair as a function of the platelet thickness. a determines the Luttinger parameter, g, for the quantum system at low densities, n_0: g -> 1-2an_0.