Electron Conductivity on Helium Films

Electrons on liquid helium films form a two-dimensional (2D) array with a wide range of electron density. This system is also very interesting for applications in restricted geometry. The conductivity σ of the electron arrays, however, strongly depends on the thickness d of the helium films adsorbed above solid substrates. This behaviour of σ is discussed in detail for a randomly rough substrate. It turns out that for the dependence of the conductivity σ ( d ) there exist three regions of helium thicknesses: d > d min , d ∼ d min , and d < d min . Here d min is the helium film thickness which corresponds to a relatively deep minimum of the 2D conductivity. In the first interval, d > d min , a two-fraction scenario determines the behaviour of σ ( d ). In the vicinity of d min percolation phenomena develop and the conductivity exhibits different types of the so-called dip effect. For even thinner helium films, i.e., when d < d min , an activation type of mobility is stimulated. The presented model fits quite well to existing data of ac and dc electron mobility.