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arXiv:2203.01264 · Results in Physics

Bound state of a 3He atom at the interface of crystal and superfluid 4He

Massimo Boninsegni

Published May 14, 2022• 2 citations

Abstract

The bound state of a 3He atom at the interface between coexisting crystalline and superfluid phases of 4He is studied theoretically by means of first principle Quantum Monte Carlo simulations. We consider both the case of a solid/superfluid 4He interface, as well as that of a few solid layers of 4He forming on an attractive substrate. It is observed that the 3He bound state is sharply localized in a well-defined, quasi-2D layer of 4He in the region intermediate between the solid and the liquid. The layer in which the 3He atom resides displays an intriguing interplay of atomic localization and quantum-mechanical exchanges; is not necessarily the first “non-solid” layer, as suggested in previous studies, and it is affected by the attractive strength of the substrate.

DOI: 10.1016/j.rinp.2022.105604

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The bound state of a 3He atom at the interface between coexisting crystalline and superfluid phases of 4He is studied theoretically by means of first principle Quantum Monte Carlo simulations. We consider both the case of a solid/superfluid 4He interface, as well as that of a few solid layers of 4He forming on an attractive substrate. It is observed that the 3He bound state is sharply localized in a well-defined, quasi-2D layer of 4He in the region intermediate between the solid and the liquid. The layer in which the 3He atom resides displays an intriguing interplay of atomic localization and quantum-mechanical exchanges; is not necessarily the first “non-solid” layer, as suggested in previous studies, and it is affected by the attractive strength of the substrate.

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.

The interaction between two 3He atoms is calculated by taking into account the backflow effect of 3He by the 4He in the 3He-4He mixture. The effect contributes solely to the P wave part of the interaction. The repulsive S wave part of the contact interaction contributes to the exchange interaction between the 3He atoms, while the direct one phonon exchange interaction contributes both to the S and P wave attractive interactions. The overall contribution to the attractive interaction is dominated by the P wave part and the superfluidity in the P wave is more predominant than in the S wave for the 5

The interaction between two 3He atoms is calculated by taking into account the backflow effect of 3He by the 4He in the 3He-4He mixture. The effect contributes solely to the P wave part of the interaction. The repulsive S wave part of the contact interaction contributes to the exchange interaction between the 3He atoms, while the direct one phonon exchange interaction contributes both to the S and P wave attractive interactions. The overall contribution to the attractive interaction is dominated by the P wave part and the superfluidity in the P wave is more predominant than in the S wave for the 5

The superfluid response of nanoscale size quasi-2D He-4 droplets adsorbed on a graphite substrate is investigated by computer simulations. It is found that clusters comprising as few as 7 atoms are stable at temperatures lower than < 0.15 K. Clusters of ~20 atoms or less are liquid-like and ~100% superfluid. As the size is increased, the central region crystallizes, forming the commensurate C_1/3 phase, with a surface sliver of superfluidity evolving into a perimetral 1D Luttinger liquid with increasing cluster size. The relevance to quasi-2D molecular spectroscopy and to transverse quantum superfluidity is discussed.

The equation of state of two-dimensional 3He at zero temperature has been calculated using the diffusion Monte Carlo method. By means of a combination of the fixed-node and released-node techniques, it is shown that backflow correlations provide a very accurate equation of state. The results prove unambiguously the non-self-bound character of two-dimensional 3He due to its Fermi statistics. We present solid evidence that the gas phase, predicted for the two-dimensional system, can be extrapolated to the case of 3He adsorbed on a strong substrate such as graphite.