Topological Order in the Phase Diagram for High-Temperature Superconductors with Point Defects

TL;DR

This paper estimates the conditions under which a topologically ordered vortex glass phase in high-temperature superconductors becomes unstable due to disorder, using a Lindemann-like criterion to analyze vortex lattice stability.

Contribution

It applies a Lindemann-like criterion to determine the stability boundary of the vortex glass phase in high-$T_c$ superconductors with point defects, connecting it to a phenomenological approach.

Findings

Calculated the positional correlation length of the vortex glass.

Estimated the magnetic field and temperature thresholds for phase instability.

Validated the criterion's equivalence to a conventional Lindemann criterion.

Abstract

Applying a Lindemann-like criterion obtained previously by Kierfeld, Nattermann and Hwa [Phys. Rev. B 55, 626 (1997)], we estimate the magnetic field and temperature for a high-$T_c$ superconductor, at which a topologically ordered vortex glass phase becomes unstable with respect to a disorder-induced formation of dislocations. The employed criterion is shown to be equivalent to a conventional phenomenological Lindemann criterion including the values for the numerical factors, i.e., for the Lindemann-number. The positional correlation length of the topologically ordered vortex glass is calculated.