Electron mobility on thin He films

We have investigated the electron mobility on the surface of ${\mathrm{H}}_2$ crystals coated with a thin He film. The mobility is found to be smaller than on the bare ${\mathrm{H}}_2$ or on the bulk He surfaces. The extra electron scattering is due to the He gas atoms, the ripplons, and the density fluctuations in the uppermost He monolayer. The scattering from the density fluctuations is a direct measure of ${\mathrm{K}}_2$, the two-dimensional compressibility of the He monolayer.