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
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.
In the one-dimensional (1D) nanopores of FSM-16 (2.8 nm in diameter) and the 3D pores of HMM-2 (2.7 nm, and 5.5 nm in 3D period), the 4 He films adsorbed on these nanopore walls show the properties of the Bose quantum fluid and superfluidity above 1.4 atomic layers at low temperatures. The boundary of the Bose fluid region was determined from the kink (peak) temperature T C of the heat capacity at each coverage n . The phase diagrams obviously show dependence on the 1D and 3D pore connections, respectively. In the 3D nanopores, the coverage (density) dependence of T C is well reproduced by the Bose-Einstein condensation temperature of the 3D ideal gas which is proportional to ( n - n c ) 2/3 , where n c is the onset coverage. In the case of the 1D pores (channels), T C is proportional to ( n - n c ) at 0.1 < T C < 1K. This T C is likely to correspond to the crossover temperature of the 2D ideal gas heat capacity from the constant heat capacity of the Boltzmann gas to the linear in T , with decreasing temperature. At T C , the thermal de Broglie wavelength of the free particle is still shorter than the pore diameter, while the thermal phonon wavelength is estimated to become longer than the diameter below T C , which indicates the 1D phonon state.
We present the results of experiments measuring the film thickness dependence of the sticking probability for H on superfluid {sup 4}He for H atom temperatures of 0.3-5.0 mK. Data is presented for 3 nm to 1 mm thick films on a silver sinter substrate. For the 0.3 mK H atoms, the sticking probability varies from 0.4 for a film 3 nm thick to 6 x 10{sup -3} for films thicker than 100 nm. In the case of the thick films the temperature dependence of the sticking probability is consistent with the observation of pure quantum reflection. Our data are in reasonable agreement with recent theoretical calculations.
The specific heat is calculated for noninteracting Fermi atoms adsorbed into deep potential wells on a close-packed substrate at low temperatures. The atoms have a small, but finite, probability of tunneling to adjacent localized sites, which creates a low-lying energy band. It is shown that in this tight-binding approximation, the band structure is identical with the two-dimensional electronic band structure in graphite, and this is used to calculate the specific heat of the adsorbed particles. For comparison, the specific heat is obtained for a constant density of states. There is a general correspondence between the two cases, with the constant density of states smoothing out the actual specific heat at the lowest temperatures. A short discussion explains how hard-core repulsion between adsorbed particles will affect the surface coverage and the mobility.
We study a submonolayer
4He adsorbed on fluorographene (GF) and on hexagonal boron nitride (hBN) at low coverage. The adsorption potentials have been computed ab initio with a suitable density functional theory including dispersion forces. The properties of the adsorbed
4He atoms have been computed at finite temperature with path integral Monte Carlo and at
T=0K with variational path integral. From both methods we find that the lowest energy state of
4He on GF is a superfluid. Due to the very large corrugation of the adsorption potential this superfluid has a very strong spatial anisotropy, the ratio between the largest and smallest areal density being about 6, the superfluid fraction at the lowest
T is about 55%, and the temperature of the transition to the normal state is in the range 0.5--1 K. Thus, GF offers a platform for studying the properties of a strongly interacting highly anisotropic bosonic superfluid. At a larger coverage
4He has a transition to an ordered commensurate state with occupation of 1/6 of the adsorption sites. This phase is stable up to a transition temperature located between 0.5 and 1 K. The system has a triangular order similar to that of
4He on graphite but each
4He atom is not confined to a single adsorption site and the atom visits also the nearest neighboring sites giving rise to a novel three-lobed density distribution. The lowest energy state of
4He on hBN is an ordered commensurate state with occupation of 1/3 of the adsorption sites and triangular symmetry. A disordered state is present at lower coverage as a metastable state. In the presence of an electric field the corrugation of the adsorption potential is slightly increased but up to a magnitude of 1 V/\AA{} the effect is small and does not change the stability of the phases of
4He on GF and hBN. We have verified that also in the case of graphene such electric field does not modify the stability of the commensurate $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}R{30}^{\ensuremath{\circ}}$ phase.