Bragg-Cherenkov scattering and nonlinear conductivity of a two-dimensional Wigner crystal

We show that the conductivity of 2D Wigner crystals displays strong nonlinearity. It arises from coherent many-electron Cherenkov emission of surface waves in the substrate (e.g., ripplons on helium) with the wave vectors q close to the reciprocal lattice vectors G of the electron solid. The rate of such Bragg-Cherenkov scattering sharply increases with the Wigner crystal velocity v as v . G approaches the surface wave frequency omega(G). The results are compared with recent experiments.