Equilibrium helium films under the influence of surface roughness

No Heading Equilibrium helium films adsorbed on solid substrates are investigated. Due to their thickness these films are mainly in the retardation regime where the influence of the roughness of the substrates, (x), can be strong enough to be observed. For the definition of (x) we use a simple corrugation model. This model is supported by experimental results using the surface plasmon resonance technique to determine the thickness of helium films grown on different Ag surfaces.PACS numbers: 67.70.+n, 68.15.+e, 68.43.–h, 68.55.–a     

Interfacial friction of submonolayer helium films adsorbed on the surface of graphite

The frictional coupling between an adsorbed helium film and the surface of graphite has been studied using torsional oscillator methods and exfoliated graphite as a substrate, in the temperature range 50mK to 2K. The observed period shift is consistent with the film decoupling from the substrate as the temperature is reduced, and is accompanied by a maximum in dissipation. At coverages below registry and in the incommensurate solid region the data are well described by Debye relations with a thermally activated relaxation time. This would correspond to a vanishing of the interfacial friction for the solid monolayer as T - 0. At coverages between 0.064Ų and 0.08Å-² a double peaked structure in the dissipation is observed. The results relate to the work of Krim et al.¹ who have used a quartz microbalance to study the nanotribology of adsorbed monolayers. In the present work the use of the graphite substrate offers the possibility of studying these effects on a system with a rich and well characterised submonolayer phase diagram.     

Dynamics of helium films

We present quantitative calculations for the static structure and the dynamics of quantum liquid films on a translationally invariant substrate. The excitation spectrum is calculated by solving the equations of motion for time-dependent one- and two-body densities. We find significant corrections to the Feynman spectrum for the phonon-like collective excitations.     

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.     

Some observations with helium films

This appendix contains several comments relevant to the lectures of Roger Bowley.¹ We begin with some introductory remarks on third sound and proceed to utilize third sound to study the stability of flow in helium films. We conclude with a remark about the effective thermal conductivity of a helium film.This is an appendix to the series of lectures delivered by Roger Bowley at the Elba Summer School; much of this material was presented during one of Roger Bowley's lectures.     

Inhomogeneities in thin helium films

We report a study of the inhomogeneities in thin helium films due to the van der Waals potential by a resonant acoustical technique. The van der Waals constant between helium and quartz is estimated to be =65±5 K (layer)³; the model leads to a solid helium layer on the substrate of the order ofH=2.2a ₀ . A comparison is made with data extracted from interferometric acoustical methods and third-sound type experiments.Associated with the Centre National de la Recherche Scientifique.     

Stability of helium and hydrogen films

We use the variational theorem to evaluate the domain of parameter space such thatsome film exists on a given surface. This is accomplished by determining the binding energy variationally for a monolayer film at T=0. The He results are for the most part consistent with those of Cheng, et al., for the domain of wetting films. New results for H₂ are compared with calculated parameters of noble gas adsorption potentials.     

Low-temperature heat capacity of helium films adsorbed on copper

Heat capacity measurements are described for films of pure⁴ He and a 12%He ³ mixture ofHe ³ andHe ⁴He adsorbed on copper, for 0.1<T<1.2 K.He ⁴ heat capacity isotherms show a step-type behavior as a function of coverage for the first two layers, while the mixture isotherms only show the first step. A comparison is made with recent multilayer data for helium films on Vycor published by other authors.Work supported by the National Science Foundation.     

Structure in thin superfluid helium films

Precision measurements of third sound in atomically thin⁴He films on Ne, Ar, and CO₂ substrates reveal a periodic structure not corresponding to whole layers. Treating the He film as an incompressible, continuous fluid, the data indicate that the chemical potential has a contribution proportional to l^–6, where l is the He coverage in layers, which is modulated at intervals of 0.62±0.04 layers and which weakens the van der Waals potential. Alternatively the data indicates the existence in the film of a damped smectic density wave with a 0.54±0.40 layer periodicity.     

X-ray induced electrostatic charging of helium films

It is well known that free electrons can be held onto the free surface of liquid helium through either their own image charges or through the effect of an externally applied electric field. The resultant electrostatic pressure causes films to thin. We have recently measured x-ray reflectivity from static films of isotopic mixtures of helium with an intense x-ray beam in the temperature range between 0.37 K and 1.3 K. Normally, no significant thickness variation with x-ray intensity is expected over a wide range of temperatures when the film is superfluid. We have found that even modest x-ray intensities affect the thickness of films containing only trace amounts of³He. We believe that the effect is due to x-ray produced photoelectrons, which thermalize in the vapor and then reside on the surface, attracted by both the film and a charged substrate. The temperature and concentration dependence is then due to the transport properties of the electrons at the surface. It may be possible to study the 2-D electron gas produced in this way by diffraction techniques.     

The influence of electrostatic fields on films of liquid helium

Prompted by the recent striking experimental results reported by Babkin and Hakonen that appeared to show that liquid helium-II does not wet magnesium fluoride, we have examined the effects that an inhomogeneous electrostatic field has on thin films of liquid helium at temperatures below 0.5K. Our model includes the influence of gravity, surface tension, the electric field and the van der Waals interaction between the helium and its supporting substrate. We show that, an inhomogeneous charge on the substrate can produce effects that mimic the surface profiles between wetted and non-wetted areas. The calculations also indicate that some special precautions may be necessary when studying films of liquid or solid helium on insulators.     

The lifetime of interacting ripplons on the surface of superfluid helium

Ripplons, or quantised surface waves, are known to exist on the surface of superfluid⁴He. We follow the work of previous authors and describe these excitations by quantising the classical expressions for the energy of such surface waves. The resulting quantum mechanical Hamiltonian consists of a term describing free ripplons, together with an additional term (cubic in the ripplon variables) which induces the mutual scattering of ripplons and has the effect of causing any one ripplon to have a finite lifetime. We present here a many body calculation which investigates the lifetimes of ripplons at a temperatureT=0 and the lifetimes of acoustic ripplons at a finite temperature. In these two limits our calculation agrees with separate calculations performed by previous authors carried out at the two limits; however our calculations readily allow a sensible interpolation between these limits. We report hitherto unsuspected divergences in the calculations at finite temperature and we comment on the relevance of such calculations to the results of recent experiments which yield information on the ripplon lifetimes.     

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.     

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.     

Experimental approaches to the wetting transition with helium films

Alkali metal surfaces have been suggested not to be wetted by helium at zero temperature. Several experiments have been realized to check if these surfaces, as well as other weak binding substrates, indeed exhibits this particularly interesting property at any finite temperature.Although works are still in progress, essential results are (i) substrates non wetted by helium films do exist (ii) prewetting jumps from low to high coverage have been observed for weakly wetted ones (iii) the consequences of substrate roughness and chemical impurities are suspected to be important and remain to be assessed. These results are reviewed and discussed. Applications of those substrates for both³He and⁴He isotopes are considered.Unité de recherche de l'Ecole Normale Supérieure et de l'Université Pierre et Mavie Curie, associé au CNRS (URA 18).