Helium Monolayers Research Articles

Neutron-Scattering Study of the Structure of Adsorbed Helium Monolayers and of the Excitation Spectrum of Few-Atomic-Layer Superfluid Films

Elastic diffraction of neutrons from helium adsorbed on Grafoil shows that the surface monolayer forms as a highly compressed, ordered triangular lattice incommensurate with the structure of the underlying graphite basal planes. Inelastic scattering from thin superfluid films on top of the surface monolayers reveals the existence of bulklike rotons in films containing on average as few as three layers of atoms. (AIP)

Low-density helium monolayers as two-dimensional imperfect gases: An analysis employing the second virial coefficient

The quantum second virial coefficient of two-dimensional systems interacting with a hard-core or Lennard-Jones 6-12 potential are calculated together with the contribution this coefficient makes to the specific heat of such systems. The results are compared with experimental data from low-density ${\mathrm{He}}^{3}$ and ${\mathrm{He}}^{4}$ monolayers adsorbed on graphite. The calculation provides a qualitative and quantitative understandiang of the experimental measurements. In particular it illuminates the manner in which the interaction and the difference in statistics cause the very different specific-heat measurements in the two isotopes. The magnetic susceptibility of low-density ${\mathrm{He}}^{3}$ monolayers is predicted.

Helium Monolayer Films on Graphite

Recent calorimetric studies of helium monolayers adsorbed on basal plane graphite substrates have disclosed two-dimensional gas, liquid and solid phases as well as an ordered epitaxial array believed to be √3 R 30°. Previous failures to observe these phases are ascribed to the heterogeneity of typical adsorbents. The new results suggest several ways in which He films can be used as very sensitive probes of certain properties of solid surfaces.

Low-Temperature Specific Heats of Adsorbed Helium Monolayers in the Mobile Limit

Low-Temperature Specific Heats of Adsorbed Helium Monolayers in the Mobile Limit

On the correlation energy in an adsorbed helium monolayer

The correlation energies in helium monolayers absorbed on argon surfaces are calculated variationally. They are very different from the -15°K implied by experimental data discounting the importance of surface inhomogeneities.

Ordering Transitions in Helium Monolayers

Ordering Transitions in Helium Monolayers

Effects of Lateral Substrate Fields on Helium Monolayers

Effects of Lateral Substrate Fields on Helium Monolayers

Quasiclassical and Quantum Degenerate Helium Monolayers

${\mathrm{He}}^{3}$ and ${\mathrm{He}}^{4}$ adsorbed on graphite have heat capacities qualitatively different from monolayers on other substrates. Both isotopes have quasiclassical two-dimensional gas behavior at low fractional coverage $x$ and $T\ensuremath{\gtrsim}2$\ifmmode^\circ\else\textdegree\fi{}K. At lower $T$ and $0.14l~xl~0.39$, ${\mathrm{He}}^{3}$ shows quantum degeneracy, with Fermi temperatures of several degrees Kelvin. The specific heat per atom of ${\mathrm{He}}^{4}$ at the same coverages rises above $k$ and has pronounced peaks at low $T$.

Two-Dimensional System of Hard-Core Bosons

As a model of a helium monolayer a system of hard-core bosons of mass $m$ and diameter $a$ constrained to motion in two dimensions is considered at absolute zero. In the low-density limit, the ground-state energy per particle and condensate depletion are found to be $\frac{E}{N}=\ensuremath{-}\frac{2\ensuremath{\pi}{\ensuremath{\hbar}}^{2}n}{m\mathrm{ln}n{a}^{2}}$ and ${n}_{0}=n(1+\frac{1}{\mathrm{ln}n{a}^{2}})$, where $n$ is the areal density of the system. The expansion parameter $\ensuremath{-}\frac{1}{\mathrm{ln}n{a}^{2}}$ is approximately equal to unity for real helium monolayers. The variation of the above results with temperature is discussed for a system of finite size.

Liquid and solid monolayers

A discussion of long-range crystalline order, dimensionality, and diffusion suggests the reasons for solidlike heat capacities of helium monolayers having relatively low characteristic temperatures and large interatomic spacings.

Isotherms of Mobile and Localized Ideal Quantum Gases Adsorbed on Crystalline Substrates

A translational band model is applied to the calculation of adsorption isotherms of noninteracting fermions and bosons adsorbed on a crystalline surface. The theory yields analytic expressions for the vapor pressure as a function of temperature and monolayer coverage, in terms of the band parameters of the adsorption system. In the case of fermions, the actual band widths and band gaps can be mapped by a low-temperature isotherm, which will display multiband steps analogous to the multilayer steps of interacting adatoms. The significance of and localization is discussed, and it is argued that the words have physical meanings only in terms of comparisons between the dwell time of an atom on a specific site and a characteristic time of the experiment in question. In the case of adsorption isotherms, the experimental time is related to the vapor pressure, and the band theory offers a criterion for mobility in terms of the energy spectrum of the adsorbed atoms. Numerical estimates indicate that helium monolayers satisfy the criterion for mobility at 4 \ifmmode^\circ\else\textdegree\fi{}K and below, but that Ar and ${\mathrm{N}}_{2}$ monolayers may be localized at 77 \ifmmode^\circ\else\textdegree\fi{}K. The isotherms of all physically adsorbed systems satisfy the criterion for mobility at sufficiently low temperatures. In contrast to the heat capacity, isotherms in the localized and mobile regimes are not qualitatively different. The effects of interactions among the adatoms and of surface inhomogeneities are briefly discussed.

Statistical Mechanics of Monolayers of Bose and Fermi Atoms Adsorbed on Crystalline Surfaces

We have calculated the heat capacity and entropy of Bose and Fermi atoms adsorbed on crystalline surfaces at low temperatures. The treatment is quantum mechanical at the outset, the influence of tunneling of atoms between adsorption sites being discussed in detail. It is shown by general qualitative arguments that the energy spectrum of a low-coverage monolayer contains a low-lying tunneling band of translational surface states. The finite energy width of the tunneling band ensures that the monolayer entropy due to the distribution of particles among the translational states will vanish at 0\ifmmode^\circ\else\textdegree\fi{}K. This entropy is shown to be equivalent to the configuration entropy at relatively high temperatures and therefore demonstrates the manner in which the configuration entropy is removed at 0\ifmmode^\circ\else\textdegree\fi{}K. At higher temperatures, particles become excited to higher bands which may be separated from the tunneling band by an energy gap. Quantum-statistical properties of non-interacting bosons and fermions in a two-band model are analyzed in terms of the number of adsorption sites, the tunneling band width, and the interband energy gap. When the interband gap is larger than the tunneling band width, the monolayer heat capacity displays two distinct peaks, at temperatures $\mathrm{kT}$ characteristic of the interband energy gap and of the tunneling band width. The heat capacity approaches ideal two-dimensional gas behavior at zero interband gap. The systems are studied over a range of other parameters, including the ratios of densities of states in the two bands and the number of atoms adsorbed on the surface. A qualitative discussion is given of the influence of interactions among the adsorbed atoms, and of their modifications by the substrate. The relevance of the theory to current experiments on helium monolayers is discussed.