Non-Ohmic Electron Transport on Liquid Helium

The transport coefficients in high electric fields are obtained for electrons bound in image-potential-induced surface states on a dielectric liquid surface. A two-dimensional Boltzmann equation is solved in the diffusion approximation, assuming the principle electron scatterers are gas atoms and surface waves. At high temperatures, where gas-atom scattering dominates both energy and momentum relaxation, the transport coefficients are field independent even though the average electron energy is much higher than the product of Boltzmann's constant and the liquid temperature. At low temperatures, where surface-wave scattering dominates the momentum relaxation, the conductivity and Hall mobility increase rapidly with increasing electric field. For ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ this non-Ohmic transport should occur below 1 K at fields below 0.1 V/cm.