Dip problem of the electron mobility on a thin helium film

Abstract

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 ...

Generic electron mobility in surface states on thin helium films

“…We will suggest that, in line with the explanation of Ref. 19, most of the disparity may be due to the neglected effects of scattering due to substrate defects and inhomogeneities.…”

“…The authors also noted that a 3 He sample displayed qualitatively similar modulations. However, as pointed out by Shikin et al, 19 there is a many orders of magnitude difference between free-surface ͑ripplon-limited͒ mobilities and thin-film mobilities. Indeed, Shirahama et al 20 report 4 He freesurface, ripplon-limited mobilities on the order of 10 7 -10 8 cm 2 / V s. Building on a previous model introduced by Monarkha et Theoretical support for the important role played by substrate inhomogeneities and defects in determining the electron mobility on helium films can be found in the work of Studart and co-workers.…”

“…al.,21 the authors of Ref 19. argue that the mobilities being measured in the thin-film experiments may be dominated by surface impurities or inhomogeneities.…”

Electrons Above Helium Films on Metal Substrates

“…Their stability as well as lateral transport properties are extremely surface dependent, some substrates showed very good stability and transport abilities, on others transport is hardly possible. We believe that pinned electrons [12] near the isolating gap play a dominant role for the transport properties, sometimes preventing electrons from lateral transport due to their electrostatic repulsion.…”

The Helium Field Effect Transistor (II): Gated Transport of Surface-State Electrons Through Micro-constrictions

“…The larger width of the channel can only partly explain the difference, meaning that the mobility of the electrons in the channel must have been higher in this rur1. A variation in mobility is not unusual for electrons on thin helium films; details of the substrate roughness and local potential fluctuations can play an important role [ 15,16]. Also, a variation of the helium film thickness, which was not very precisely controlled in our experiment, can have a major effect on the mobility [lfr 18].…”