Moving glass theory of driven lattices with disorder

We study periodic structures, such as vortex lattices, moving in a random pinning potential under the action of an external driving force. As predicted in T. Giamarchi and P. Le Doussal, Phys. Rev. Lett. 76, 3408 (1996) the periodicity in the direction transverse to motion leads to a different class of driven systems: the moving glasses. We analyze using several renormalization-group techniques, the physical properties of such systems both at zero and nonzero temperature. The moving glass has the following generic properties (in $d<~3$ for uncorrelated disorder) (i) decay of translational long-range order, (ii) particles flow along static channels, (iii) the channel pattern is highly correlated along the direction transverse to motion through elastic compression modes, (iv) there are barriers to transverse motion. We demonstrate the existence of the transverse critical force at $T=0\mathrm{}$ and study the transverse depinning. A “static random force” both in longitudinal and transverse directions is shown to be generated by motion. Displacements are found to grow logarithmically at large scale in $d=3\mathrm{}$ and as a power law in $d=2.\mathrm{}$ The persistence of quasi-long-range translational order in $d=3\mathrm{}$ at weak disorder, or large velocity leads to the prediction of the topologically ordered moving Bragg glass. This dynamical phase which is a continuation of the static Bragg glass studied previously, is shown to be stable to a nonzero temperature. At finite but low temperature, the channels broaden and survive and strong nonlinear effects still exist in the transverse response, though the asymptotic behavior is found to be linear. In $d=2,$ or in $d=3\mathrm{}$ at intermediate disorder, another moving glass state exists, which retains smectic order in the transverse direction: the moving transverse glass. It is described by the moving glass equation introduced in our previous work. The existence of channels allows us to naturally describe the transition towards plastic flow. We propose a phase diagram in temperature, force, and disorder for the static and moving structures. For correlated disorder we predict a “moving Bose glass” state with anisotropic transverse Meissner effect, localization, and transverse pinning. We discuss the effect of additional linear and nonlinear terms generated at large scale in the equation of motion. Generalizations of the moving glass equation to a larger class of nonpotential glassy systems described by zero temperature and nonzero temperature disordered fixed points (dissipative glasses) are proposed. We discuss experimental consequences for several systems, such as the anomalous Hall effect in the Wigner crystal, transverse critical current in the vortex lattice, and solid friction.