Devil's Staircase and Disordering Transitions in Sliding Vortices and   Wigner Crystals on Random Substrates with Transverse Driving
  Using numerical simulations we show that, in the presence of random quenched disorder, sliding superconducting vortices and Wigner crystals pass through a variety of dynamical phases when an additional transverse driving force is applied. If the disorder is weak, the driven particles form a moving lattice and the transverse response shows a devil's staircase structure as the net driving force vector locks with the symmetry directions of the moving lattice, in agreement with the predictions of Le Doussal and Giamarchi. For strong disorder, and particularly for smoothly varying potential landscapes, the transverse response consists of a sequence of disordering transitions with an intervening formation of stable channel structures. 
C. Reichhardt and C.J. Olson Reichhardt