Theory of disordered flux-line liquids

TL;DR

This paper investigates the static and dynamic properties of flux line liquids in disordered environments, revealing how disorder affects their elastic properties and dynamics, and providing a theoretical framework consistent with experiments.

Contribution

It introduces a replica Gaussian variational approach to analyze disorder effects and derives a coarse-grained equation of motion that matches unpinned vortex behavior with renormalized parameters.

Findings

Disorder increases the tilt modulus and confining mass, reducing thermal wandering.

The structure factor remains similar to the disorder-free case, contrary to previous hydrodynamic results.

The static structure factor aligns with experimental data and vortex lattice elasticity theory.

Abstract

We study the equilibrium statics and nonequilibrium driven dynamics of flux line liquids in presence of a random pinning potential. Under the assumption of replica symmetry, we find in the static case using a replica Gaussian variational method that the only effect of disorder is to increase the tilt modulus and the confining "mass" of the internal modes of the flux lines, thus decreasing their thermal wandering. In the nonequilibrium, driven case, we derive the long scale, coarse-grained equation of motion of the vortices in presence of disorder, which apart from new Kardar-Parisi-Zhang nonlinearities, has the same form as the equation of motion for unpinned vortices, with renormalized coefficients. This implies, in particular, that the structure factor of a disordered vortex liquid has the same functional form as in the absence of pinning, in disagreement with the results of previous hydrodynamic methods. The expression of the static structure factor derived within our approach is consistent both with experimental data and with the standard theory of elasticity of vortex lattices.