Vortex interactions in a thin platelet superconductor

The thermal fluctuations of vortices in a superconductor can be usefully mapped onto the quantum fluctuations of a collection of bosons at T = 0 moving in two dimensions. When the superconductor is a thin platelet with the magnetic field parallel to its surface, the interacting quantum bosons are effectively moving in one dimension, allowing for powerful Tomonaga–Luttinger liquid methods to be applied. Here we consider how this one-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 (yttrium–barium–copper oxide) 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, n0: .