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Physical review. B, Condensed matter

Quasi-two-dimensional imperfect Bose gas adsorbed on a surface

E. Cheng, Milton W. Cole

Published Sep 1, 1990• 9 citations
Publisher

Abstract

We study a submonolayer film adsorbed on a substrate surface as a quasi-two-dimensional (2D) imperfect Bose gas. The ground-state energy and the depletion fraction at zero temperature are calculated. It is found that the depletion is independent of the 2D density (in contrast to the 3D case), but is a monotonically increasing function of the substrate potential well depth. Qualitative conclusions are drawn about implications for superfluidity in the case of He on a weak-binding substrate.

DOI
10.1103/physrevb.42.3960

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We study a submonolayer film adsorbed on a substrate surface as a quasi-two-dimensional (2D) imperfect Bose gas. The ground-state energy and the depletion fraction at zero temperature are calculated. It is found that the depletion is independent of the 2D density (in contrast to the 3D case), but is a monotonically increasing function of the substrate potential well depth. Qualitative conclusions are drawn about implications for superfluidity in the case of He on a weak-binding substrate.
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The experimental realization of a thin layer of spin-polarized hydrogen H↓ adsorbed on top of the surface of superfluid (4)He provides one of the best examples of a stable, nearly two-dimensional (2D) quantum Bose gas. We report a theoretical study of this system using quantum Monte Carlo methods in the limit of zero temperature. Using the full Hamiltonian of the system, composed of a superfluid (4)He slab and the adsorbed H↓ layer, we calculate the main properties of its ground state using accurate models for the pair interatomic potentials. Comparing the results for the layer with the ones obtained for a strictly 2D setup, we analyze the departure from the 2D character when the density increases. Only when the coverage is rather small the use of a purely 2D model is justified. The condensate fraction of the layer is significantly larger than in 2D at the same surface density, being as large as 60% at the largest coverage studied.
We have measured the heat capacity of submonolayers of 4He^{4}\mathrm{He}4He adsorbed on Ag films between 1.7 and 3.3 K. Good fits to the results are obtained with a model of a noninteracting two-dimensional Bose gas. The sticking probability for room-temperature 4He^{4}\mathrm{He}4He atoms on cold Ag has been measured as a function of substrate temperature and 4He^{4}\mathrm{He}4He coverage. The sticking probability is 4% at low coverage, and abruptly drops to 1% for coverages above 0.5 monolayer.
We investigate the behavior of the anomalous correlation function in two-dimensional Bose gas. In the local case, we find that this quantity has a finite value in the limit of weak interactions at zero temperature. The effects of the anomalous density on some thermodynamic quantities are also considered. These effects can modify, in particular, the chemical potential, the ground-state energy, the depletion, and the superfluid fraction. Our predictions are in good agreement with recent analytical and numerical calculations. We show also that the anomalous density presents a significant importance compared to the noncondensed one at zero temperature. The single-particle anomalous correlation function is expressed in two-dimensional homogenous Bose gases by using the density-phase fluctuation. We then confirm that the anomalous average accompanies in analogous manner the true condensate at zero temperature, while it does not exist at finite temperature.
The binding energy of a hydrogen atom to the surface of liquid 4He has been calculated to be at least 0.6K by Mantz and Edwards. This means that the properties of adsorbed spin-polarized hydrogen (H↑), a 2D Bose fluid, may soon be observed experimentally. Since 4He is used as a neutral coating for vessels to contain H↑ gas, adsorption onto the 4He surface may enhance the rate of recombination into H2 molecules. For given temperature and density in the gas, the amount of H↑ adsorbed depends strongly on the H↑-H↑ interaction on the 4He surface. We estimate the interaction in a simple approximation, and find that it limits the surface density to not more than 1014 cm-2. Nevertheless this density should be sufficient for a 2D superfluid transition to be observed, under conditions close to those achieved experimentally.