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arXiv:1208.0842 · Physical Review Letters

Observation of Self-Binding in Monolayer He3

D. Sato, K. Naruse, Tomohiro Matsui, Hiroshi Fukuyama

Published Dec 3, 2012• 34 citations
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Abstract

We report clear experimental signatures of the theoretically unexpected gas-liquid transition in the first three monolayer systems of $^{3}\mathrm{He}$ adsorbed on graphite. The transition is inferred from the linear density dependence of the gamma coefficient of the heat capacity measured in the degenerate region ($2\ensuremath{\le}T\ensuremath{\le}80\text{ }\text{ }\mathrm{mK}$) below a critical liquid density (${\ensuremath{\rho}}_{c0}$). Surprisingly, the measured ${\ensuremath{\rho}}_{c0}$ values ($0.6--0.9\text{ }\text{ }{\mathrm{nm}}^{\ensuremath{-}2}$) are nearly the same for all these layers in spite of their quite different environments. We conclude that the ground state of $^{3}\mathrm{He}$ in strictly two dimensions is not a dilute quantum gas but a self-bound quantum liquid with the lowest density ever found.

DOI
10.1103/physrevlett.109.235306

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We report clear experimental signatures of the theoretically unexpected gas-liquid transition in the first three monolayer systems of 3He^{3}\mathrm{He}3He adsorbed on graphite. The transition is inferred from the linear density dependence of the gamma coefficient of the heat capacity measured in the degenerate region (2\ensuremath≤T\ensuremath≤80  mK2\ensuremath{\le}T\ensuremath{\le}80\text{ }\text{ }\mathrm{mK}2\ensuremath≤T\ensuremath≤80  mK) below a critical liquid density (\ensuremathρc0{\ensuremath{\rho}}_{c0}\ensuremathρc0​). Surprisingly, the measured \ensuremathρc0{\ensuremath{\rho}}_{c0}\ensuremathρc0​ values (0.6−−0.9  nm\ensuremath−20.6--0.9\text{ }\text{ }{\mathrm{nm}}^{\ensuremath{-}2}0.6−−0.9  nm\ensuremath−2) are nearly the same for all these layers in spite of their quite different environments. We conclude that the ground state of 3He^{3}\mathrm{He}3He in strictly two dimensions is not a dilute quantum gas but a self-bound quantum liquid with the lowest density ever found.
At low densities (ρ ≲ 4.2 nm -2 ), measured heat capacities satisfy the C = γT dependence at low T , which is characteristic of the degenerate Fermi liquid.With increasing density effective mass of a 3 He quasiparticle, deduced from γ, shows the divergence up to m * /m = 4.4 ± 0.3 until 4.2 nm -2 .At the lowest densities (0.1 ≲ ρ ≲ 0.7 nm -2 ), we observed the formation of the self-condensed liquid, judging from the γ coefficient smaller than the value of the noninteracting Fermi gas.Its critical density (0.7 nm -2 ) is quantitatively consistent with that of 1 -3 layers on graphite [1], but contradict recent Monte Carlo studies which claims that the potential corrugation play an essential role to stabilize the self-condensed liquid.
The nuclear magnetic susceptibility of 3He^{3}\mathrm{He}3He adsorbed on the surface of graphite, plated with a monolayer of solid 4He^{4}\mathrm{He}4He, has been measured at surface densities less than 0.055 \AA{} $^{\mathrm{\ensuremath{-}}2}$ and at temperatures down to 6 mK. A temperature-independent susceptibility is observed at low temperatures, which is strongly enhanced over the ideal-gas value, due to quasiparticle interactions. The inferred Landau-Fermi-liquid parameters allow a comparison with microscopic theories of interacting Fermi systems.
Superfluid 4He^{4}\mathrm{He}4He films adsorbed on porous Vycor glass have been studied in the low-density limit where the superfluid interparticle spacing is more than an order of magnitude greater than the atomic hard-core diameter. For the lowest transition temperatures observed, the influence of critical fluctuations near Tc{T}_{c}Tc​ is much reduced and a range of crossover to behavior more characteristic of the dilute Bose gas is observed.
Helium atoms or hydrogen molecules are believed to be strongly bound within the interstitial channels (between three carbon nanotubes) within a bundle of many nanotubes. The effects on adsorption of a nonuniform distribution of tubes are evaluated. The energy of a single-particle state is the sum of a discrete transverse energy Et{E}_{t}Et​ (that depends on the radii of neighboring tubes) and a quasicontinuous energy Ez{E}_{z}Ez​ of relatively free motion parallel to the axis of the tubes. At low temperature, the particles occupy the lowest-energy states, the focus of this study. The transverse energy attains a global minimum value (Et=Emin)({E}_{t}={E}_{\mathit{min}})(Et​=Emin​) for radii near Rmin=9.95A˚{R}_{\mathit{min}}=9.95\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}Rmin​=9.95A˚ for H2{\mathrm{H}}_{2}H2​ and 8.48A˚8.48\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}8.48A˚ for 4He^{4}\mathrm{He}4He. The density of states N(E)N(E)N(E) near the lowest energy is found to vary linearly above this threshold value, i.e., N(E)N(E)N(E) is proportional to $(E\ensuremath{-}{E}_{\mathit{min}})$. As a result, there occurs a Bose-Einstein condensation of the molecules into the channel with the lowest transverse energy. The transition is characterized approximately as that of a four-dimensional gas, neglecting the interactions between the adsorbed particles. The phenomenon is observable, in principle, from a singular heat capacity. The existence of this transition depends on the sample having a relatively broad distribution of radii values that include some near Rmin{R}_{\mathit{min}}Rmin​.
The ground-state properties of one-dimensional 3He^{3}\mathrm{He}3He are studied using quantum Monte Carlo methods. The equation of state is calculated in a wide range of physically relevant densities and is well interpolated by a power-series fit. The Luttinger liquid theory is found to describe the long-range properties of the correlation functions. The density dependence of the Luttinger parameter is explicitly found, and interestingly it shows a nonmonotonic behavior. Depending on the density, the static structure factor can be a smooth function of the momentum or might contain a peak of a finite or infinite height. Although no phase transitions are present in the system, we identify a number of physically different regimes, including an ideal Fermi gas, a ``Bose gas.'' a ``super-Tonks-Girardeau'' regime, and a ``quasicrystal.'' The obtained results are applicable to unpolarized, partially, or fully polarized 3He^{3}\mathrm{He}3He.
Quantum Monte Carlo simulations confirm the existence of a bound state of a single He-3 atom at a free superfluid He-4 surface in three dimensions, localized within a ~10-A thick low-density He-4 surface layer, with a binding energy of approximately 4 K with respect to vacuum. As the temperature is raised above ~ 1 K the He-3 atom leaves the surface to dissolve into the superfluid. The situation is entirely different in two dimensions, as the He-3 atom is excluded from the superfluid and no surface bound state exists. Results are also presented for the a He-3 atom binding to nanoscale size He-4 clusters adsorbed on weak substrates, a physical system that may allow for the observation of some of the physics predicted for extended surfaces. It is shown that a He-3 bound state localized at the perimeter of sufficiently small (a few tens of atoms) clusters exists not just on Cs, as previously reported, but on all alkali substrates.