Electrons floating above liquid helium form an ideal two-dimensional system with an extremely high mobility. However, the mobility can change substantially when decreasing the thickness of the helium film from bulk to a thin film of a few hundred Å. Furthermore it is observed that for certain film thicknesses there is a pronounced dip in the mobility. We present theoretical investigations and measurements concerning this problem. Taking into account the roughness of the substrate, which supports the helium film, we find theoretically a discontinuity in the chemical potential of the electrons which results in a diplike behavior in the electron current and hence in the electron mobility. This scenario is supported by direct measurements of the electron current on substrates with different roughness and at different electron densities. A two-dimensional ͑2D͒ electron sheet, localized on the surface of a liquid helium film, forms a well-defined Coulomb system. The mobility of such a charge system strongly depends on the thickness of the helium film. Whereas on bulk helium the electron mobility can reach extremely high values up to 10 4 m 2 /V s, 1 for a thin van der Waals film the mobility can drastically decrease and usually depends on the surface quality of the underlying substrate.One of the qualitative questions in the 2D electron kinetics is the so-called dip problem in the electron mobility on a thin liquid helium film. The first indication of this phenomenon was given by mobility measurements of electrons on relatively thick helium films ͑around 10 Ϫ4 cm) on a sapphire substrate.2 Later, a similar behavior was observed in the mobility of electrons on very thin helium films ͑around 10 Ϫ6 cm) adsorbed on a quench-condensed solid hydrogen substrate.3,4 However, so far it is not clear whether there is any correlation between the data of Refs. 2 and Refs. 3,4.There exist several interpretations for the dip effect. In a paper by Peeters and Jackson 5 the electron mobility on helium films above a flat substrate is calculated. It predicts the monotonic mobility decrease versus the coupling constant, which is sensitive to the helium film thickness, and the nonmonotonic mobility behavior due to the self-trapping effect. However, the authors conclude that self-trapping of the electrons can not explain the dip behavior in Ref. 2, because in this case the self-trapping energy is too small with respect to the experimental temperature. Various experiments with electrons on helium films ͑see the review article by Dahm 6 ͒ show the monotonic decrease of electron mobility versus the coupling constant. But there is no indication of the dip effect, which should be more probable in the self-trapping scenario, 5 when the helium film thickness becomes small enough.The second interpretation for the dip effect is given for a nonflat substrate. As shown in Refs. 4 and 7 a diplike behavior of the electron mobility versus helium film thickness can develop in the presence of substrate corrugation. 8 Such a situation is only possible, if ...
Electrons on liquid helium film 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 film 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 fil thickness which corresponds to a relatively deep minimum of the 2D conductivity. In the firs 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 fit quite well to existing data of ac and dc electron mobility.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.