Melting and structure of the vortex solid in strongly anisotropic layered superconductors with random columnar pins

TL;DR

This study investigates the melting transition of vortex solids in anisotropic layered superconductors with sparse columnar pins, revealing a two-step melting process involving Bragg glass, Bose glass, and interstitial liquid phases.

Contribution

It introduces a numerical minimization method of a free energy functional to analyze detailed vortex density structures and phase transitions in the presence of random columnar pins.

Findings

The stable low-temperature phase is a topologically ordered Bragg glass.

Melting occurs in two steps: Bragg glass to Bose glass, then Bose glass to interstitial liquid.

Both transitions are first-order, with spatially varying local melting temperatures.

Abstract

We study the melting transition of the low-temperature vortex solid in strongly anisotropic layered superconductors with a concentration of random columnar pinning centers small enough so that the areal density of the pins is much less than that of the vortex lines. Both the external magnetic field and the columnar pins are assumed to be oriented perpendicular to the layers Our method, involving numerical minimization of a model free energy functional, yields not only the free energy values at the local minima of the functional but also the detailed density distribution of the system at each minimum: this allows us to study in detail the structure of the different phases. We find that at these pin concentrations and low temperatures, the thermodynamically stable state is a topologically ordered Bragg glass. This nearly crystalline state melts into an interstitial liquid (a liquid in which a small fraction of vortex lines remain localized at the pinning centers) in two steps, so that the Bragg glass and the liquid are separated by a narrow phase that we identify from analysis of its density structure as a polycrystalline Bose glass. Both the Bragg glass to Bose glass and the Bose glass to interstitial liquid transitions are first-order. We also find that a local melting temperature defined using a criterion based on the degree of localization of the vortex lines exhibits spatial variations similar to those observed in recent experiments.