Defect induced melting of vortices in high-${\bf T_c} $ superconductors: A model based on continuum elasticity theory

TL;DR

This paper develops a continuum elasticity-based model to predict vortex lattice melting in high-temperature superconductors, aligning well with experimental data and providing insights into entropy and magnetic induction changes.

Contribution

It introduces a Gaussian melting model incorporating defect fluctuations via a vortex gauge field, offering a novel theoretical approach for vortex lattice melting.

Findings

Predicted melting temperatures match experimental data for YBa2Cu3O7−δ.

Model estimates the Lindemann number size.

Calculated entropy and magnetic induction jumps at melting.

Abstract

We set up a melting model for vortex lattices in high-temperature superconductors based on the continuum elasticity theory. The model is Gaussian and includes defect fluctuations by means of a discrete-valued vortex gauge field. We derive the melting temperature of the lattice and predict the size of the Lindemann number. Our result agrees well with experiments for $ {\rm YBa}_2 {\rm Cu}_3 {\rm O}_{7-\delta} $, and with modifications also for $ {\rm Bi}_2 {\rm Sr}_2 {\rm Ca} {\rm Cu}_2 {\rm O}_8 $ . We calculate the jumps in the entropy and the magnetic induction at the melting transition.