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 $\mathbf{q}$ close to the reciprocal lattice vectors $\mathbf{G}$ of the electron solid. The rate of such Bragg-Cherenkov scattering sharply increases with the Wigner crystal velocity $v$ as $\mathbf{v̇}\mathbf{G}$ approaches the surface wave frequency $\omega \left(G\right)$. The results are compared with recent experiments.