Two-Dimensional Vortex Lattice Melting

TL;DR

This study uses Monte-Carlo simulations to investigate the melting transition of a two-dimensional vortex lattice in superconductors, revealing a first-order phase transition with measurable latent heat.

Contribution

Introduces an efficient Fourier-based quantity for Monte-Carlo sampling and provides quantitative estimates of latent heat in vortex lattice melting.

Findings

Evidence for a first-order melting transition

Quantitative estimate of latent heat (~0.38 k_B T_M)

Development of a sum rule for the superfluid density Fourier transform

Abstract

We report on a Monte-Carlo study of two-dimensional Ginzburg-Landau superconductors in a magnetic field which finds clear evidence for a first-order phase transition characterized by broken translational symmetry of the superfluid density. A key aspect of our study is the introduction of a quantity proportional to the Fourier transform of the superfluid density which can be sampled efficiently in Landau gauge Monte-Carlo simulations and which satisfies a useful sum rule. We estimate the latent heat per vortex of the melting transition to be $\sim 0.38 k_B T_M$ where $T_M$ is the melting temperature.