Nonlinear dynamics, avalanches, and noise for driven Wigner crystals

We consider the driven dynamics of Wigner crystals interacting with random disorder. Using numerical simulations, we find a rich variety of transport phenomena as a function of charge density, drive, and pinning strength. For weak pinning, the system forms a defect-free crystal that depins elastically. When the pinning is stronger, a pinned glass phase appears that depins into a filamentary flow state, transitions at higher drives into a disordered flow phase, and finally forms a moving smectic. Within the filamentary flow phase, the conduction curves can show switching dynamics as well as negative differential conductivity in which switching events cause some flow channels to be blocked. The velocity noise in the filamentary flow regime exhibits narrow band characteristics due to the one-dimensional nature of the motion, while the moving smectic has narrow band velocity noise with a washboard frequency. In the disordered flow state, the noise power reaches a peak value and the noise has a $1/f$ character. Our transport results are consistent with recent experimental transport studies in systems where Wigner crystal states are believed to be occurring. Below the conduction threshold, we find that avalanches with a power-law size distribution appear when there are sudden local rearrangements of charges from one pinned configuration to another.