Quantum Monte Carlo simulations confirm the existence of a bound state of a single ${}^3\mathrm{He}$ atom at a free superfluid ${}^4\mathrm{He}$ surface in three dimensions, localized within an $\sim 10$-Å-thick low-density ${}^4\mathrm{He}$ surface layer, with a binding energy of approximately 5 K with respect to vacuum. As the temperature is raised above $\sim 1$ K the ${}^3\mathrm{He}$ atom leaves the surface to dissolve into the superfluid. The situation is entirely different in two dimensions, as the ${}^3\mathrm{He}$ atom is excluded from the superfluid and no surface bound state exists. Results are also presented for a ${}^3\mathrm{He}$ atom binding to nanoscale size ${}^4\mathrm{He}$ 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 ${}^3\mathrm{He}$ 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.

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• Adsorption
• Superfluidity
• Helium-4 superfluids
• Mixtures of 3He & 4He
• Quantum Monte Carlo