Continuous Melting of a "Partially Pinned" Two-Dimensional Vortex Lattice in a Square Array of Pinning Centers

TL;DR

This paper investigates the continuous melting transition of a partially pinned two-dimensional vortex lattice in a square array of pinning centers, combining numerical simulations and a symmetry-based spin model.

Contribution

It introduces a detailed numerical analysis of the melting process and develops a spin model to explain the critical behavior at the transition.

Findings

The vortex lattice exhibits a continuous melting transition.

The low-temperature state is partially pinned with one periodicity.

A symmetry-based spin model reproduces the critical behavior.

Abstract

The structure and equilibrium properties of a two-dimensional system of superconducting vortices in a periodic pinning potential with square symmetry are studied numerically. For a range of the strength of the pinning potential, the low-temperature crystalline state exhibits only one of the two basic periodicities (in the $x$- and $y$-directions) of the pinning potential. This ``partially pinned'' solid undergoes a continuous melting transition to a weakly modulated liquid as the temperature is increased. A spin model, constructed using symmetry arguments, is shown to reproduce the critical behavior at this transition.