Finite size effects as the explanation of ``freezing'' in vortex liquids

TL;DR

This paper explains the observed 'freezing' in vortex liquids as a finite size crossover effect in three-dimensional superconductors, accounting for experimental features like entropy and magnetization jumps.

Contribution

It provides a theoretical framework linking finite size effects and phase correlation length growth to the experimental 'freezing' phenomena in vortex liquids.

Findings

Crossover effect mimics first-order transition in experiments

Calculated entropy, magnetization, specific heat jumps agree with data

Phase correlation length grows exponentially as temperature decreases

Abstract

We investigate the effect of thermal fluctuations on the (mean-field) Abrikosov phase. The lower critical dimension of the superconducting phase is three, indicating the absence of the Abrikosov phase for dimensions d<3. Within the d=3 vortex liquid, the phase correlation length along the magnetic field direction grows exponentially rapidly as the temperature is lowered. For a finite bulk system, there is a 3D-2D crossover effect when the phase correlation length becomes comparable to the sample thickness. Such a crossover effect takes place over a very narrow temperature interval and mimics the ``first order transition'' seen in experiments on clean YBCO and BSCCO crystals. We calculate the jumps in the entropy, magnetization and specific heat due to the crossover and find reasonably good agreement with experiments on both YBCO and BSCCO.