Topological Defects in the Abrikosov Lattice of Vortices in Type-II Superconductors

TL;DR

This paper investigates the energy costs of various topological defects in the vortex lattice of type-II superconductors using the lowest Landau level approximation, revealing insights into vortex entanglement and stability.

Contribution

It introduces calculations of defect energies in the Abrikosov lattice and explores the stability of vortex braids, challenging assumptions about vortex entanglement in superconductors.

Findings

Stable two- and three-line braids do not exist.

High energy cost for six-line braids suggests limited vortex entanglement.

Vortex entanglement is unlikely below the irreversibility line in high-$T_c$ superconductors.

Abstract

The free energy costs for various defects within an Abrikosov lattice of vortices are calculated using the lowest Landau level approximation (LLL). Defect solutions with boundary conditions for lines to meet at a point (crossing defect) and for lines to twist around each other (braid defect) are sought for 2, 3, 6, and 12 lines. Many results have been unexpected, including the nonexistence of a stable two- or three-line braid. This, and the high energy cost found for a six-line braid lead us to propose that the equilibrium vortex state is not entangled below the irreversibility line of the high-$T_c$ superconductors or in a large part of the vortex-liquid phase above this line. Also, the solution for an infinite straight screw dislocation is found, and used to give a limiting form for the free energy cost of very large braids. This depends on the area enclosed by the braid as well as its perimeter length.