Two-Phase Region of the Vortex-Solid Melting Transition: 3D XY Theory

TL;DR

This paper analyzes the vortex-solid melting transition in high-$T_c$ superconductors using 3D XY theory, predicting the two-phase coexistence region and relating it to experimental data.

Contribution

It develops thermodynamic formulae for the vortex phase transition and applies 3D XY scaling to predict the coexistence region boundaries in high-$T_c$ materials.

Findings

Predicted the width of the two-phase vortex region.

Related experimental data to physical parameters in the 3D XY model.

Provided detailed boundary predictions for vortex-solid melting.

Abstract

In clean enough samples of the high-$T_c$ oxide materials, the phase transition into the superconducting state occurs along a first order line in the $H$-$T$ plane. This means that a two-phase region occurs in the B-$T$ plane, in which the liquid and solid vortex phases coexist. We discuss the thermodynamics of this two-phase region, developing formulae relating experimental quantities of interest. We then apply the 3D XY scaling theory to the problem, obtaining detailed predictions for the boundaries of the coexistence region. By using published data, we are able to predict the width of the two-phase region, and determine the physical parameters involved in the 3D XY description.