Vortices in layered superconductors with columnar pins: A density functional study

TL;DR

This study uses a density functional approach to analyze how columnar pinning centers influence vortex structures and phase transitions in layered superconductors, revealing a first-order melting line ending at a critical point.

Contribution

It provides a detailed numerical analysis of vortex behavior and phase transitions in layered superconductors with columnar pins, including the effects of temperature and pinning strength.

Findings

First-order vortex lattice melting transition line identified.

Critical point where transition becomes a crossover.

Dependence of vortex trapping on temperature and pinning strength.

Abstract

We use numerical minimization of a model free energy functional to study the effects of columnar pinning centers on the structure and thermodynamics of a system of pancake vortices in the mixed phase of highly anisotropic layered superconductors. The magnetic field and the columnar pins are assumed to be perpendicular to the layers. Our methods allow us to study in detail the density distribution of vortices in real space. We present results for the dependence of the average number of vortices trapped at a pinning center on temperature and pinning strength, and for the effective interaction between nearby pinned vortices arising from short-range correlations in the vortex liquid. For a commensurate, periodic array of pinning centers, we find a line of first order vortex lattice melting transitions in the temperature $T$ vs. pin concentration $c$ plane, which terminates at an experimentally accessible critical point as $c$ is increased. Beyond this point, the transition is replaced by a crossover. Our results should also apply, with little change, to thin-film superconductors with strong point pinning.