Energy cost associated with vortex crossing in superconductors

TL;DR

This paper estimates the energy involved in vortex crossing in type II superconductors using Ginzburg-Landau theory, revealing its dependence on magnetic field and temperature, and linking it to experimental observations.

Contribution

It introduces a method to calculate vortex crossing energy in superconductors under the lowest Landau level approximation, considering different boundary conditions.

Findings

Vortex crossing energy is similar on a sphere and a plane, indicating localization.

Crossing energy depends on magnetic field and temperature, with specific values at melting lines.

The results help explain recent transport experiments in superconductors.

Abstract

Starting from the Ginzburg-Landau free energy of a type II superconductor in a magnetic field we estimate the energy associated with two vortices crossing. The calculations are performed by assuming that we are in a part of the phase diagram where the lowest Landau level approximation is valid. We consider only two vortices but with two markedly different sets of boundary conditions: on a sphere and on a plane with quasi-periodic boundary conditions. We find that the answers are very similar suggesting that the energy is localised to the crossing point. The crossing energy is found to be field and temperature dependent -- with a value at the experimentally measured melting line of $U_\times \simeq 7.5 k T_m \simeq 1.16/c_L^2$, where $c_L$ is the Lindemann melting criterion parameter. The crossing energy is then used with an extension of the Marchetti, Nelson and Cates hydrodynamic theory to suggest an explanation of the recent transport experiments of Safar {{\em et al.}\ }.