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We consider a two-dimensional Wigner crystal coupled to aquasi-one-dimensional asymmetric potential under ac or dc driving. As afunction of electron density, substrate strength, and ac amplitude, we findthat the system exhibits ordered and disordered pinned and dynamical states.Ratchet effects can appear under an applied ac drive and can be associated withpronounced structural changes from a disordered state to a one-dimensionalsmectic-like state. We observe a pinned phase, a diode-like ratchet wheremotion only occurs along the easy direction of the substrate asymmetry, aplastic ratchet where motion occurs in both directions but there is only a netdrift in the easy direction, and an elastic ratchet where the system forms acrystal without plastic deformation that can still undergo ratcheting. At highfilling, we find that there can be a ratchet reversal in which the net drift isalong the hard direction of the substrate asymmetry. For weak disorder, thereis an Aubry transition to a floating phase where the ratchet effects are lost.We map out the different dynamical phases as a function of substrate strength,filling, ac amplitude, and ac frequency. The ratchet effect on strongsubstrates is enhanced by thermal fluctuations, but is destroyed when thefluctuations become too large. Based on our results, we suggest new ways todetect Wigner crystals as well as methods for creating new types of devices tocontrol disordered charge flow.

Collective Dynamics and Defect Generation for Wigner Crystal Ratchets