A Simple Analytical Model of Vortex Lattice Melting in 2D Superconductors

TL;DR

This paper presents an analytical model for vortex lattice melting in 2D superconductors, revealing a weak first order transition driven by phase fluctuations, with results aligning with Monte Carlo simulations.

Contribution

It introduces a simple analytical framework to describe vortex lattice melting, emphasizing phase fluctuations and shear modulus behavior, advancing understanding beyond numerical methods.

Findings

Melting occurs via a weak first order transition at temperature T_m.

Residual shear modulus decreases to zero as temperature approaches T_m.

Quasi-long range order persists above T_m with growing superconducting crystallites.

Abstract

The melting of the Abrikosov vortex lattice in a 2D type-II superconductor at high magnetic fields is studied analytically within the framework of the phenomenological Ginzburg-Landau theory. It is shown that local phase fluctuations in the superconducting order parameter, associated with low energies sliding motions of Bragg chains along the principal crystallographic axes of the vortex lattice, lead to a weak first order 'melting' transition at a certain temperature $T_{m}$, well below the mean field $T_{c\text{}}$, where the shear modulus drops abruptly to a nonzero value. The residual shear modulus above $T_{m}$ decreases asymptotically to zero with increasing temperature. Despite the large phase fluctuations, the average positions of Bragg chains at fimite temperature correspond to a regular vortex lattice, slightly distorted with respect to the triangular Abrikosov lattice. It is also shown that a genuine long range phase coherence exists only at zero temperature; however, below the melting point the vortex state is very close to the triangular Abrikosov lattice. A study of the size dependence of the structure factor at finite temperature indicates the existence of quasi-long range order with $S(\overrightarrow{G}) \sim N^{\sigma}$, and $1/2<\sigma <1$, where superconducting crystallites of correlated Bragg chains grow only along pinning chains. This finding may suggest a very efficient way of generating pinning defects in quasi 2D superconductors. Our results for the melting temperature and for the entropy jump agree with the state of the art Monte Carlo simulations.