Phase-coherence and the boson-analogy of vortex liquids

TL;DR

This paper investigates the vortex liquid phase in extreme type-II superconductors using a 3D XY-model, revealing a percolation transition driven by thermally induced vortex loops that leads to lattice melting and loss of phase coherence.

Contribution

It introduces a finite-field vortex-loop transition framework and analyzes the impact of thermal vortex loops on flux-line lattice melting and phase coherence loss.

Findings

Vortex liquid phase is dominated by thermally induced vortex loops, not well-defined vortex lines.

The critical region near the transition is about 10% of T_c for certain anisotropies.

The entropy jump at melting is approximately 0.1k_B per vortex pancake, lower than experimental values.

Abstract

The statistical mechanics of the flux-line lattice in extreme type-II super- conductors is studied within the framework of the uniformly frustrated anisotropic 3D XY-model. A finite-field counterpart of an Onsager vortex-loop transition in extreme type-II superconductors renders the vortex liquid phase- incoherent when the Abrikosov vortex lattice undergoes a first order melting transition. For the filling fractions considered in this paper $f$ given by $1/f=12,14,16,20,25,32,48,64,72,84,96,112$, and 128, the vortex liquid phase is not describable as a liquid of well-defined field induced vortex lines. This is due to the proliferation of thermally induced closed vortex-loops with dia- meters of order the magnetic length in the problem, resulting in a "percolation transition" driven by non-field induced vortices also transverse to the direc- tion of the applied magnetic field. This immediately triggers flux-line lattice melting and loss of phase-coherence in all direction. In a non-relativistic 2D boson-analogy picture, this latter feature would correspond to a vanishing mass of the bosons. Scaling functions for the specific heat are calculated in zero and finite magnetic field. From this we conclude that the critical region is of order 10% of $T_c$ for a mass anisotropy $\sqrt{M_z/M}=3$, and increases with increasing mass anisotropy. The entropy jump at the melting transition is cal- culated as a function of magnetic field for a mass-ansitropy slightly lower than that in $YBCO$, and found to be $\Delta S=0.1k_B$ per vortex panncake, independent of the magnetic field for the filling fractions considered here. This is slightly lower than experimental values of $\Delta S \approx 0.4k_B$ found experimentally for $YBCO$. We attribute this to the slightly lower mass anisotropy used in our simulations.