The magnetoconductivity ${\sigma }_{\mathrm{xx}}\left(B\right)$ of a classical two-dimensional electron crystal on superfluid ${}^4$He is nonlinear. Experimentally, we find a contribution to ${\sigma }_{\mathrm{xx}}\left(B\right)$ which, at constant field $B$, gives ${\sigma }_{\mathrm{xx}}\left(B\right)\propto J_x$, the current density, while at constant current, ${\sigma }_{\mathrm{xx}}\left(B\right)\propto 1/B$. For increasing $J_x$, the Hall velocity ${\upsilon }_H$ slowly approaches the ripplon velocity ${\upsilon }_l$ at the first reciprocal lattice vector, due to strong electron-ripplon interactions with the helium. The magnetoconductivity then decreases sharply for ${\upsilon }_H>{\upsilon }_1$.

• Received 28 December 1995

DOI:https://doi.org/10.1103/PhysRevLett.77.1350