Moving glass theory of driven lattices with disorder

TL;DR

This paper introduces the Moving Glasses concept, analyzing the behavior of driven periodic structures in disordered media, revealing new phases, critical forces, and stability conditions through RG techniques.

Contribution

It provides a comprehensive theoretical analysis of moving glass phases, including the Moving Bragg Glass and Moving Transverse Glass, with predictions on their stability and properties.

Findings

Existence of transverse critical force at T=0.

Logarithmic and algebraic displacement growth in 3D and 2D.

Prediction of a Moving Bragg Glass state with topological order.

Abstract

We study periodic structures, such as vortex lattices, moving in a random potential. As predicted in [T. Giamarchi, P. Le Doussal Phys. Rev. Lett. 76 3408 (1996)] the periodicity in the direction transverse to motion leads to a new class of driven systems: the Moving Glasses. We analyse using several RG techniques the properties at T=0 and $T>0$: (i) decay of translational long range order (ii) particles flow along static channels (iii) the channel pattern is highly correlated (iv) barriers to transverse motion. We demonstrate the existence of the ``transverse critical force'' at T=0. A ``static random force'' is shown to be generated by motion. Displacements grow logarithmically in $d=3$ and algebraically in $d=2$. The persistence of quasi long range translational order in $d=3$ at weak disorder, or large velocity leads to predict a topologically ordered ``Moving Bragg Glass''. This state continues the static Bragg glass and is stable at $T>0$, with non linear transverse response and linear asymptotic behavior. In $d=2$, or in $d=3$ at intermediate disorder, another moving glass exist (the Moving Transverse Glass) with smectic quasi order in the transverse direction. A phase diagram in $T$ force and disorder for static and moving structures is proposed. For correlated disorder we predict a ``moving Bose glass'' state with anisotropic transverse Meissner effect and transverse pinning. We discuss experimental consequences such as anomalous Hall effect in Wigner crystal and transverse critical current in vortex lattice.