The elastic depinning transition of vortex lattices in two dimensions

TL;DR

This study uses large-scale simulations to analyze the elastic depinning transition of two-dimensional vortex lattices in disordered media, revealing critical exponents and scaling behaviors characteristic of a second order phase transition.

Contribution

It provides the first detailed numerical characterization of the elastic depinning transition, including critical exponents and finite-size scaling, distinguishing it from plastic depinning.

Findings

Critical velocity exponent β = 0.29 ± 0.03

Critical force distribution governed by a diverging length with exponent ν = 1.04 ± 0.04

Existence of a scaling relation between velocity and temperature

Abstract

Large scale numerical simulations are used to study the elastic dynamics of two-dimensional vortex lattices driven on a disordered medium in the case of weak disorder. We investigate the so-called elastic depinning transition by decreasing the driving force from the elastic dynamical regime to the state pinned by the quenched disorder. Similarly to the plastic depinning transition, we find results compatible with a second order phase transition, although both depinning transitions are very different from many viewpoints. We evaluate three critical exponents of the elastic depinning transition. $\beta = 0.29 \pm 0.03$ is found for the velocity exponent at zero temperature, and from the velocity-temperature curves we extract the critical exponent $\delta^{-1} = 0.28 \pm 0.05$. Furthermore, in contrast with charge-density waves, a finite-size scaling analysis suggests the existence of a unique diverging length at the depinning threshold with an exponent $\nu= 1.04 \pm 0.04$, which controls the critical force distribution, the finite-size crossover force distribution and the intrinsic correlation length. Finally, a scaling relation is found between velocity and temperature with the $\beta$ and $\delta$ critical exponents both independent with regard to pinning strength and disorder realizations.