Nonlinear conductivity of the two-dimensional Wigner solid on the free surface of normal and superfluid 3He

The theory of nonlinear conductivity of the 2D Wigner solid (WS) formed on the surface of normal and superfluid He-3 is presented. We show that extremely strong damping of the Fermi-liquid He-3 greatly affects the dimple sublattice of surface displacements moving along with the WS, which induces the nonlinear conductivity of surface electrons long before the conventional Bragg-Cherenkov condition is achieved. Both the hydrodynamic and Iona mean-free-path regimes are considered in order to find the velocity induced transformation of the dimple sublattice and field-velocity characteristics of the WS. Depending on the regime of measurement the theory describes dynamic decoupling of the WS from surface dimples, or the field-velocity characteristics which has regions with negative differential conductivity.