Density functional theory of vortex lattice melting in layered superconductors: a mean-field--substrate approach

TL;DR

This paper develops a density functional theory-based model to analyze vortex lattice melting in layered superconductors, providing a thermodynamically consistent approach that aligns well with simulation data and explains experimental phenomena.

Contribution

It introduces a novel mean-field substrate model combined with density functional theory to describe vortex lattice melting in layered superconductors, including negative magnetization jumps.

Findings

Good agreement with simulation data

Derived a simple temperature-dependent melting field formula

Demonstrated thermodynamic consistency via Clausius-Clapeyron relation

Abstract

We study the melting of the pancake vortex lattice in a layered superconductor in the limit of vanishing Josephson coupling. Our approach combines the methodology of a recently proposed mean-field substrate model for such systems with the classical density functional theory of freezing. We derive a free-energy functional in terms of a scalar order-parameter profile and use it to derive a simple formula describing the temperature dependence of the melting field. Our theoretical predictions are in good agreement with simulation data. The theoretical framework proposed is thermodynamically consistent and thus capable of describing the negative magnetization jump obtained in experiments. Such consistency is demonstrated by showing the equivalence of our expression for the density discontinuity at the transition with the corresponding Clausius-Clapeyron relation.