Electron Conductivity on Helium Films

Abstract

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 > dmin, d ∼ dmin, and d < dmin. Here dmin is the helium film thickness which corresponds to a relatively deep minimum of the 2D conductivity. In the first interval, d > dmin, a two-fraction scenario determines the behaviour of σ(d). In the vicinity of dmin percolation phenomena develop and the conductivity exhibits different types of the so-called dip effect. For even thinner helium films, i.e., when d < dmin, an activation type of mobility is stimulated. The presented model fits quite well to existing data of ac and dc electron mobility.