A simple model for dynamical melting of moving vortex lattices interacting with periodic pinning

TL;DR

This paper introduces a simplified dynamical model to analyze the melting behavior of moving vortex lattices in superconducting films with periodic pinning, capturing thermal and pinning effects on vortex stability.

Contribution

It presents a mean-field 'cage' model that describes vortex lattice melting and V-I characteristics at high velocities, extending understanding of vortex dynamics with periodic pinning.

Findings

Dynamical melting temperature depends on vortex velocity.

The model predicts anisotropic V-I curves for strong pinning.

Results qualitatively agree with numerical simulations.

Abstract

Melting of moving vortex lattices in clean superconducting films with periodic pinning is studied by a dynamical "cage" model, based on a mean-field treatment of Langevin's equations for the whole vortex lattice, assuming elastic flow. In the frame moving with the velocity of the vortex lattice center of mass, the model describes forced vibrations of a single vortex tied to a spring. The vortex displacements due to thermal fluctuations and to the periodic pinning force, and the relationship between the driving force and the vortex velocity (V-I curves) are obtained by a perturbation method, valid for high velocities and for both weak and strong periodic pinning. The dynamical melting temperature is calculated as a function of the vortex velocity using Lindemann's criterion. Application to a square defect lattice gives, for strong pinning, dynamical melting lines and anisotropic V-I curves that agree qualitatively with numerical results.