Generic electron mobility in surface states on helium films

We study the mobility of electrons adsorbed to thin ⁴He films. Utilizing the time-dependent version of the Euler-Lagrange, hypernetted chain variational theory, we compute the inelastic scattering rate of an electron due to collisions with film excitations (third sound). We obtain an analytic result valid in the long wavelength limit. In agreement with experiment, the mobility shows oscillations due to the underlying transverse film structure. The oscillations are explicitly due to the appearance of the third sound speed in the scattering rate since the third sound speed itself oscillates in conjunction with the ⁴He film structure. The mobilities tend to be higher than reported mobilities on thin films, which we attribute to substrate structure. We interpret our results as generic mobilities that are valid in the limit of perfectly smooth, structureless substrates.