High-frequency conductivity of electrons on a helium film in the presence of localization at substrate potential nonuniformities

We have studied the superhigh frequency conductivity of surface electrons on a helium film wetting a dielectric substrate with a large dielectric constant (ϵs ≈9.6) in the temperature range 1.7−2.1 K with an electron density of 1010 cm−2. The conductivity was determined from the decrease in the Q of a superconducting resonator when the liquid helium film was charged with electrons. It is shown that the effective high-frequency mobility of electrons on a helium film, defined as μ(ω) = σ /ne (σ is the conductivity of the electron layer, n is the electron density, and e is the electron charge), is much lower than the mobility on bulk helium. The quantity μ (ω) increases as the temperature decreases, and in the region 1.7−2 K μ (ω)−1 is approximately proportional to the density N of atomic vapor. When positive ions are present on the substrate, μ (ω) decreases to about 70 cm2/V-sec, and its temperature dependence changes. When the temperature is in the range 1.9−2.1 K μ (ω) is approximately proportional to the density of rotons, μ (ω) increases with the thickness d of the helium film, growing in order of magnitude when d≈5×10−6 cm. These results are explained by localization of electrons on nonuniformities in the potential of the substrate caused by defects and roughness or positive charges present on its surface. Electron localization produces deformations of the underlying helium films and causes holes to form (a sort of additional self-localization). These effects produce a unique behavior in the superhigh frequency conductivity of the electron layer.

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