Quasi-2D Liquid ${}^3\mathrm{He}$

Quantum Monte Carlo simulations at zero temperature of an ensemble of ${}^3\mathrm{He}$ atoms adsorbed on Mg and Alkali substrates yield strong evidence of a thermodynamically stable liquid ${}^3\mathrm{He}$ monolayer on all Alkali substrates, with the possible exception of Li. The effective two-dimensional density is $\theta \approx 0.02{\AA }^{-2}$ on Na, making it the lowest density liquid in nature. Its existence is underlain by zero-point atomic motion perpendicular to the substrate, whose effect is softening the short-range repulsion of the helium interatomic potential. The monolayer films should turn superfluid at a temperature $T_c\sim 1\mathrm{mK}$. No liquid film is predicted to form on Mg, or on stronger substrates such as graphite.

Figure 1

Ground state energy per atom $e(\theta )$ computed by DMC calculations for a ${}^3\mathrm{He}$ film adsorbed on different substrates, as a function of coverage $\theta$. The binding energy of a single atom on the given substrate is taken as the reference (zero) value for $e(\theta )$. Open symbols represent a second set of data for the Li substrate, obtained by applying estimates for the finite-size, time step, population control and fixed-node approximation errors. Solid lines are spline interpolations. The line for Li is colored differently, to indicate that the system is borderline for formation of a liquid layer. The data labeled “2D” refer to strictly 2D ${}^3\mathrm{He}$. Results for Cs and Rb substrates are indistinguishable from those on K, within the statistical errors of the calculations. Statistical errors are smaller than the size of the symbols.

Figure 2

${}^3\mathrm{He}$ density profile $n(z)$ (arbitrary units) in the direction perpendicular to the surface, on a Mg, Li, Na and K substrate. The height of the main peak is greater the stronger the substrate (see text). Results shown are for a coverage $\theta =0.03{\AA }^{-2}$.

Figure 3

Reduced pair correlation function $g(R)$ [Eq. (4)], for ${}^3\mathrm{He}$ in 2D (solid line), on a Mg substrate (dashed line) and on a K substrate (dotted line), for a coverage $\theta =0.03{\AA }^{-2}$. On a K substrate, $g(0)$ is finite.