Effect of pinning on the vortex-lattice melting line in type-II superconductors

TL;DR

This paper derives a theoretical model for the vortex-lattice melting line in type-II superconductors considering pinning effects, providing insights into phase diagram features and the influence of defects.

Contribution

It introduces a new equation for the melting line that incorporates pinning effects and compares it with previous criteria, enhancing understanding of vortex phase transitions.

Findings

Derived a melting line equation accounting for pinning effects

Identified the upper critical point where entropy jump vanishes

Analyzed phase diagrams for different pinning strengths and types

Abstract

The vortex-lattice melting line in three-dimensional type-II superconductors with pinning is derived by equating the free energies of the vortex system in the solid and liquid phases. We account for the elastic and pinning energies and the entropy change that originates from the disappearance of the phonon shear modes in the liquid. The pinning is assumed to be caused by point defects and to be not too strong so that the melting line lies inside the so-called bundle-pinning region. We show that the derived equation for the melting line is equivalent to some Lindemann criterion, which however differs from that used previously. Estimating the effect of pinning on the entropy jump at melting, we find the upper critical point of the melting line from the condition that this jump vanishes. We also consider the H-T phase diagrams of type-II superconductors for different strengths and types of pinning and analyze the two recently discussed scenarios how the melting line and the order--disorder line merge.