Escape rate of surface state electrons on liquid helium below 1 K

The escape rate of surface state electrons on liquid helium was measured in the temperature interval 0.56<T<1.0 K for electron areal density below 5×10⁷ cm^–2, where the rate is independent of density. It is found that the escape rate is dominated by the scattering from the helium gas atoms in the vapor phase above 0.8 K, while it is dominated by that from ripplons (surface wave quanta) below 0.8 K. Quantitative agreement is obtained between our experiment and the theoretical calculation by Nagano et al.Preliminary results were published inSurface Sci. 98, 17 (1980).     

Quantum transport of surface electrons over liquid helium in magnetic field

The magnetoconductivity _xx of surface electrons over liquid helium at electron densities (1–9) × 10⁸ cm^–2 is measured at temperatures down to 0.5 K and magnetic fields H up to 25 kOe. _xx is shown to decrease with increasing H. For rather high temperatures and low magnetic fields dependence _xx ^–1 on H displays a classical behavior, but as the temperature is reduced or H is increased, a transition to the quantum magnetotransport regime occurs. It is shown that _xx decreases at lowering temperature, passes through a minimum and then slightly increases in the region of electron-ripplon scattering. The measured data are in good agreement with the theoretical results taking into account the preferable contribution of electron scattering on ripplons with wavelength near magnetic length. At the region of electron crystal _xx is weakly dependent on T. At low magnetic field _xx ^–1 increases with H linearly and, at H>17kOe, _xx ^–1 ~ H ^1.5.     

Conductivity of electrons on a liquid helium surface in high magnetic fields

The elementary processes of electron scattering on a liquid helium surface in the limit of a high magnetic field are considered. For the scattering on helium vapor atoms, the adiabatic approach is developed, which takes into account the slow thermal motion of atoms. The scattering on ripplons is considered in a lowest, nonvanishing order of the perturbation theory.     

Kinetic properties of surface electrons over liquid helium under strong electron-electron interaction

The mobility and lifetime of ground-level electrons are studied experimentally in a two-dimensional electron system at the surface of liquid helium at temperatures of0.4 to1.4 K and charge concentrations of (2.8–12.0) × 10⁸ cm^–2. It is shown that for fairly low temperature and high concentration where the frequency of interelectronic collisions is much higher than that of electron-ripplon ones, the so-called complete control condition is realized in the electron system, i.e., when the average drift velocity of electrons and the effective electron temperature can be introduced. This model is found to describe well the kinetic properties of surface electrons in the range of charge concentrations up to 4×10⁸ cm^–2, where the one-particle approach is no longer applicable. For the value of parameter =e²(n_s)^1/2/T=47 that corresponds to a strong electron-electron interaction, the lifetime is found to increase sharply and the short-range order typical of a liquid state appears in the two-dimensional electron layer.     

Surface study of liquid3He using surface state electrons

We have measured the mobility of surface state electrons (SSE) on liquid³He, 3, aiming to study the elementary surface excitations of the Fermi liquid. A gradual increase of 3 below 300 mK is attributed to the scattering of electrons by ripplons. Ripplons do exist in³He down to 100 mK. We observe an abrupt decrease of 3, due to the transition to the Wigner solid (WS). The dependences of the WS conductivity and mobility on temperature and magnetic field differ from the SSE behavior on liquid⁴He.     

Escape rate of two-dimensional electrons on a liquid helium surface around 1 K

Electron escape from a two-dimensional surface state on liquid helium to three-dimensional free space is studied. A thermal-activation-type temperature dependence of the escape rate is observed at 1.1>T>0.9 K for the first time. The mechanism of electron escape is discussed.     

Investigating surface wave resonances with electrons on helium

Waves on liquid⁴He were excited and detected by capacitively coupling to an electron sheet trapped at the free surface. The standing wave resonances, resulting from the finite size of the sample cell, were measured and their frequencies are in good agreement with theory. The resonant linewidth displays a nonmonotonic dependence on temperature which indicates that it is determined by viscous friction at the watts of the sample cell.     

Alkali dimers on the surface of liquid helium

A recent paper by Ancilottoet al. (Zeitschrift für Physik B, in press), presented calculations of adsorption energies and the geometry of a surface dimple for alkali atoms bound to the surfaces of quantum liquids (⁴He,³He, H₂). Here we present a study of the adsorption of two alkali dimers (Li₂, Na₂) on the surface of liquid helium. The calculations employ a model of an abrupt interface formulated by Ancilotto et al. as well as one using a diffuse interface. Our conclusion its that the dimers are bound to the surface more strongly than their respective monomers. In the case of dimers there is an additional degree of freedom-the orientation of the molecular axis relative to the surface. We study the influence of molecular anisotropy on adsorption by comparing the cases of erect and spinning flat orientations and conclude that the latter is energetically favored.     

Electron-ripplon scattering on the surface of liquid helium

We use an adiabatic development of the electron wave function to calculate the scattering matrix elements for the electron-ripplon interaction. In this treatment the nonadiabatic terms in the total Schrödinger equation are responsible for the scattering. Our calculation shows that the magnitude of the scattering matrix element for this interaction depends critically on the magnitude of the electron wave function at the surface.     

Electronic surface states on liquid helium

Beginning with a microscopically obtained density profile near the free surface of liquid helium an analysis of the electronic surface states, both inside and outside, is carried out. For the potential barrier seen by electron bubbles trapped inside the surface layer we find an upper bound of 38 K, in comparison with experimental values ranging from 25 to 30 K. For outside states we find a binding energy of 9 K and a hydrogenlike spectrum. There are no adjustable parameters in the theory.     

Impedance methods for surface state electrons

A numerical procedure is given to determine the static charge configuration and electrical impedance of a circular pool of electrons on the surface of liquid helium. The response for an ac Corbino probe is obtained for arbitrary frequency. By fitting the results to audiofrequency capacitance-conductance data the local charge density and electric field configuration are found for arbitrary confining potentials. The locations of2D plasma modes are also in excellent agreement with those obtained numerically. Analytic forms are derived for uniform charge density configurations.     

The surface tension meniscus of liquid helium

A technique is described for calculating the shape of the surface tension meniscus at a vertical wall, in the presence of Van der Waals forces. The method of analytic continuation is used to compute a solution of the relevant differential equation. Results (believed accurate to better than 0.5%) are presented for He³ and for He⁴ at a variety of film flow rates. It is found that the shape of the classical meniscus remains unaltered over most of its length, but it is displaced horizontally relative to the wall by a flow dependent amount. The results are contrasted with those from a previous calculation.     

Structure of alkali dimers at the surface of liquid helium

Calculations are presented of the equilibrium configuration (dimple) of a Na₂ or Li₂ molecule absorbed on the surface of liquid³H e or liquid⁴He. The computed aimer binding energies are somewhat greater than those of the monomers. The lowest energy occurs when the molecule lies flat, but the energy in the erect orientation is only 1K higher (implying relatively free rotation). The center of mass lies 4Åabove the liquid surface and the dimple has a depth 3Å. An exceptional case is Li₂ on liquid³H e, for which the surface state is unstable relative to solvation in the bulk.     

Tunneling from electron bubbles beneath the surface of liquid helium

Schoepe and Rayfield have measured the lifetime for escape of electrons from bubbles beneath a liquid He surface. We compute using the tunneling Hamiltonian method of Bardeen. If accepted bubble parameters are assumed, is found to be approximately two orders of magnitude smaller than the measured value. Agreement with experiment can be obtained if the radius is taken to be 50% larger than currently believed. We consider the effects of diffuseness of the bubble boundary, diffuseness of the liquid-vapor interface, and polarizability of the bubble. A discrepancy remains which may be explicable in terms of surface deformation when the bubble is very close to the surface.     

Investigation of quantum systems with surface plasmons and surface state electrons

We report on investigations of thin films of the quantum systems hydrogen and helium both in thermodynamic equilibrium and in metastable states. Information about the film thickness and surface roughness is obtained from the excitation of surface plasmons and mobility measurements of surface state electrons. The equilibrium studies show triple-point wetting for H ₂ on Au substrates, in agreement with earlier results for similar systems. Unexpectedly a distinct hysteretic behavior of the saturated film thickness is found near the triple-point. Superfluid ⁴ He films on as prepared Ag display complete wetting. Investigations of H ₂ films in metastable states prepared by quench-condensation at 1.5K reveal pronounced changes in the film structure upon annealing. These changes set in far below the desorption temperature and are ascribed to surface diffusion.     

Electron escape from the image-potential-induced surface states on liquid helium

Electron escape from the two-dimensional surface state is studied for liquid ⁴He and ³He surfaces. Experimental conditions are established under which proper signals are obtained to give the intrinsic escape rates. The escape rates in the temperature range 1.1 > T > 0.9 K for the ⁴He surface and 0.6 > T > 0.44 K for the ³He surface show the theoretically expected thermalactivation-type temperature dependence. In the present experimental configuration, the measured escape rate at higher electron densities explicitly demonstrates the electron correlation effect. A simple model is presented to account for the correlation effect on the binding energy of the surface electrons.     

Surface state electrons on a hydrogen film. 2. Influence of adsorbed helium films

We have investigated the conductivity of surface state electrons on liquid⁴He films supported by a quench-condensed thin solid hydrogen substrate. A pronounced dip in the ac-conductivity was observed as the He film thickness reached about 10 layers. This phenomenon was studied at different temperatures (range between 1.6 and 2 K), electron densities from 0.9 to 19×10⁸ cm^–2, frequencies between 1 and 100 kHz, and for various amplitudes of the ac driving voltage. Ripplon scattering and a ripplonic polaron are discussed as sources for the conductivity dip.