Theory of electron transport in a two-dimensional layer on the solid hydrogen surface

Abstract

The mobility of electrons localized over solid hydrogen is investigated theoretically using the Boltzmann equation. It is shown that the electron mobility for temperatures above 5 K is dominated by the interface roughness scattering of the hydrogen surface, which is described by the two-parameter model of Gaussian correlations. Prom detailed comparison between theory and experiment it is determined that the hydrogen surface has a roughness with the height of about 1 -2 atomic sizes and a lateral width in the mesoscopic scale (about 10 cm). The theoretical dependences of the mobility on the temperature obtained are in excellent agreement with the experimental high-temperature data available. However, for temperatures below 5 K, our results reproduce only qualitatively the overall temperature dependence of the mobility.

Ripplon-limited mobility of surface electrons on thick films ofHe3overHe

“…For liquid 4 He, which is the most used substrate, the electron-ripplon interaction provides the main scattering mechanism at temperatures TϽ1 K. 1 The sensibility of SE's to surface phenomena of substrates arose great interest for studying SE properties over condensed phases of quantum systems in addition to liquid 4 He. 2 Other substrates like solid hydrogen 3 and solid neon 4 have been used and SE's have also been trapped at the interface of the 3 He-4 He mixtures. 5 On the other hand, for the case of the free surface of pure 4 He at very low temperatures, Andreev 6 predicted that an added 3 He atom would occupy a bound state at the free surface of 4 He.…”

“…2 Other substrates like solid hydrogen 3 and solid neon 4 have been used and SE's have also been trapped at the interface of the 3 He-4 He mixtures. 5 On the other hand, for the case of the free surface of pure 4 He at very low temperatures, Andreev 6 predicted that an added 3 He atom would occupy a bound state at the free surface of 4 He. The existence of this surface state was confirmed through surface tension measurements and the energy of the state was determined.…”

“…The existence of this surface state was confirmed through surface tension measurements and the energy of the state was determined. 7 If more 3 He atoms are adsorbed on 4 He, a weakly interacting two-dimensional ͑2D͒ gas of quasiparticles is formed when the surface density of 3 He is less than a monolayer. Interesting experimental studies about the properties of 2D 3 He over 4 He have been reported.…”

“…Interesting experimental studies about the properties of 2D 3 He over 4 He have been reported. 8 As one increases further the density of 3 He atoms, the adsorbed layer of 3 He on the surface becomes thicker and thicker in a microstratification process until the saturation value of 6.6% of 3 He is reached in the bulk and the upper phase consists of a macroscopic film. At low temperatures the upper phase is very nearly pure 3 He and the experimental data by Guo et al 9 are consistent with a theory by Saam.…”

“…8 As one increases further the density of 3 He atoms, the adsorbed layer of 3 He on the surface becomes thicker and thicker in a microstratification process until the saturation value of 6.6% of 3 He is reached in the bulk and the upper phase consists of a macroscopic film. At low temperatures the upper phase is very nearly pure 3 He and the experimental data by Guo et al 9 are consistent with a theory by Saam. 10 Figure 1 shows a schematic view of the system under consideration which consists of two liquid phases: the upper phase 1 with the thickness d composed by near pure 3 He and the semiinfinite lower phase 2 formed by a weak solution of 3 He in 4 He.…”