Complete mode locking in models of charge-density waves

Mode locking in ac-driven charge-density waves is studied numerically in two and three dimensions, using both continuous equations of motion and a cellular automaton model. As the system size is increased, a complete devil’s staircase of steps is approached. The fractal dimension of the set of gaps in the staircase is found to be ${\mathit{D}}_0$=0.75±0.04 (0.88±0.05) in two (three) dimensions in the automaton model. The spectrum of singularities f(α) is calculated and is related to the dynamic critical exponent ζ for the charge-density-wave depinning transition.