A nuclear spin and spatial symmetry-adapted full quantum method for light particles inside carbon nanotubes: clusters of 3He, 4He, and para-H2.

María Pilar De Lara-Castells,Alexander O Mitrushchenkov

doi:10.1039/d0cp05332e

Abstract

We present a new nuclear spin and spatial symmetry-adapted full quantum method for light fermionic and bosonic particles under cylindrical carbon nanotube confinement. The goal is to address Fermi-Dirac and Bose-Einstein nuclear spin statistics on an equal footing and to deliver excited states with a similar accuracy to that of the ground state, implementing ab initio-derived potential models as well. The method is applied to clusters of up to four (three) 4He atoms and para-H2 molecules (3He atoms) inside a single-walled (1 nm diameter) carbon nanotube. Due to spin symmetry effects, the bound states energy landscape as a function of the angular momentum around the tube axis becomes much more complex and rich as the number of 3He atoms increase compared to the spinless 4He and para-H2 counterparts. Four bosonic 4He and para-H2 particles form pyramidal-like structures which are more compact as the particle mass and the strength of the inter-particle interaction increases. They feature stabilization of the collective rotational motion as bosonic quantum rings bearing persistent rotational motion and superfluid flow. Our results are brought together with two key experimental findings from the group of Jan-Peter Toennies: (1) the congestion of spectral profiles in doped 3He droplets as opposed to the case of 4He droplets (S. Gebenev, J. P. Toennies and A. F. Vilesov, Science, 1998, 279, 2083); (2) the onset of microscopic superfluidity in small doped clusters of para-H2 molecules (S. Grebenev, B. G. Sartakov, J. P. Toennies and A. F. Vilesov, Science, 2000, 289, 1532), but at the reduced dimensionality offered by the confinement inside carbon nanotubes.

Highlights

We present a new nuclear spin and spatial symmetry-adapted full quantum method for light fermionic and bosonic particles under cylindrical carbon nanotube confinement
This work addresses the characterization of multiple quantum particles inside carbon nanotubes and, in particular, in identifying the role of the nuclear spin statistics of the considered particles
It has been motivated by the experimental evidence of microscopic superfluidity in doped 4He (3He) droplets and paraH2 clusters by the group of Professor Jan-Peter Toennies, but at the reduced dimensionality offered by confinement inside carbon nanotubes

Summary

Introduction

We present a new nuclear spin and spatial symmetry-adapted full quantum method for light fermionic and bosonic particles under cylindrical carbon nanotube confinement. The cylindrical confinement provided by carbon nanotubes has offered the possibility of studying the pronounced quantum behaviour of 4He atoms and H2 molecules at reduced dimensionality. The application of orbital-free helium density functional theory to carbon nanotubes immersed in a helium nanodroplet provided theoretical explication that the experimental observations stem from the exceptionally high zero-point energy of 4He as well as its tendency to form 2D layers upon adsorption at low temperatures. These conclusions were further confirmed by applying more accurate ab initio potential modelling along with a wave-function (WF)-based approach.[12]. These studies[12,13,14,15,16,17,18] have highlighted the key role played by the quantum nature of the nuclear degrees of freedom in the confined helium, hydrogen, or deuterium motion

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Results

Conclusion