Abstract
The thermal fluctuations of vortices in a superconductor can be usefullymapped onto the quantum fluctuations of a collection of bosons atT = 0 moving in two dimensions. When the superconductor is a thin platelet with themagnetic field parallel to its surface, the interacting quantum bosons are effectivelymoving in one dimension, allowing for powerful Tomonaga–Luttinger liquid methodsto 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 theLuttinger parameter, g, for the quantum system at low densities,n0: .
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