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arXiv:0804.1297 · Physical Review Letters

Local Superfluidity of Parahydrogen Clusters

Fabio Mezzacapo, Massimo Boninsegni

Published Apr 8, 2008• 71 citations
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Abstract

We study by quantum Monte Carlo simulations the local superfluid response of small (up to 27 molecules) parahydrogen clusters, down to temperatures as low as 0.05 K. We show that at low temperature superfluidity is not confined at the surface of the clusters, as recently claimed by Khairallah et al. [Phys. Rev. Lett. 98, 183401 (2007)10.1103/PhysRevLett.98.183401]. Rather, even clusters with a pronounced shell structure are essentially uniformly superfluid. Superfluidity occurs as a result of long exchange cycles involving all molecules.

DOI
10.1103/physrevlett.100.145301

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We study by quantum Monte Carlo simulations the local superfluid response of small (up to 27 molecules) parahydrogen clusters, down to temperatures as low as 0.05 K. We show that at low temperature superfluidity is not confined at the surface of the clusters, as recently claimed by Khairallah et al. [Phys. Rev. Lett. 98, 183401 (2007)10.1103/PhysRevLett.98.183401]. Rather, even clusters with a pronounced shell structure are essentially uniformly superfluid. Superfluidity occurs as a result of long exchange cycles involving all molecules.
The interplay between magic number stabilities and superfluidity of small parahydrogen clusters with sizes N=5 to 40 and temperatures 0.5 K</=T</=4.5 K is explored with classical and quantum path integral Monte Carlo calculations. Clusters with N<26 and T</=1.5 K have large superfluid fractions even at the stable magic numbers 13, 19, and 23. In larger clusters, superfluidity is quenched especially at the magic numbers 26, 29, 32, and 37 while below 1 K, superfluidity is recovered for the pairs (27,28), (30,31), and (35,36). For all clusters superfluidity is localized at the surface and correlates with long exchange cycles involving loosely bound surface molecules.
The interplay between magic number stabilities and superfluidity of small para-hydrogen clusters with sizes N=5N = 5N=5 to 40 and temperatures $0.5 K \leq T \leq 4.5 $K is explored with classical and quantum Path Integral Monte Carlo calculations. Clusters with N<26N < 26N<26 and T ≤1.5K\leq 1.5 K≤1.5K have large superfluid fractions even at the stable magic numbers 13, 19, and 23. In larger clusters, superfluidity is quenched especially at the magic numbers 23, 26, 29, 32, and 37 while below 1 K, superfluidity is recovered for the pairs (27,28)(27,28)(27,28), (30,31)(30,31)(30,31), and (35,36)(35,36)(35,36). For all clusters superfluidity is localized at the surface and correlates with long exchange cycles involving loosely bound surface molecules.
The low temperature physics of parahydrogen ($p\ensuremath{-}{\mathrm{H}}_{2}$) confined in cylindrical channels of diameter of the order of 1 nm is studied theoretically by quantum Monte Carlo simulations. On varying the attractive strength of the wall of the cylindrical pore, as well as its diameter, the equilibrium phase evolves from a single quasi-one-dimensional (1D) channel along the axis, to a concentric cylindrical shell. It is found that the quasi-1D system retains a strong propensity to crystallization, even though on weakly attractive substrates quantum fluctuations reduce somewhat such a tendency compared to the purely 1D system. No evidence of a topologically protected superfluid phase (in the Luttinger sense) is observed. Implications on the possible existence of a bulk superfluid phase of parahydrogen are discussed.
The low-temperature phase diagram of parahydrogen in one dimension is studied by quantum Monte Carlo simulations, whose results are interpreted within the framework of Luttinger liquid theory. We show that, contrary to what was claimed in a previous study [Phys. Rev. Lett. 85, 2348 (2000)], the equilibrium phase is a crystal. The phase diagram mimics that of parahydrogen in two dimensions, with a single quasicrystaline phase and no quantum phase transition; i.e., it is qualitatively different from that of 4He in one dimension.
We recently presented the first attempt at using an asymmetric top molecule (para-water) to probe the superfluidity of nanoclusters (of para-hydrogen) [ Zeng , T. ; Li , H. ; Roy , P.-N. J. Phys. Chem. Lett. 2013 , 4 , 18 - 22 ]. Unfortunately, para-water could not be used to probe the para-hydrogen superfluid response. We now report a theoretical simulation of sulfur dioxide rotating in para-hydrogen clusters and show that this asymmetric top can serve as a genuine probe of superfluidity. With this probe, we predict that as few as four para-hydrogen molecules are enough to form a superfluid cluster, the smallest superfluid system to date. We also propose the concept of "exchange superfluid fraction" as a more precise measurement. New superfluid scenarios brought about by an asymmetric top dopant and potential experimental measurements are discussed.
Low temperature structural and superfluid properties of 4He^{4}\mathrm{He}4He confined in cylindrical nanopores are theoretically investigated by means of first-principle quantum Monte Carlo (QMC) simulations. We vary the density of 4He^{4}\mathrm{He}4He inside the pore, as well as the pore diameter and the potential describing the interaction of each 4He^{4}\mathrm{He}4He atom with the pore surface. Accordingly, the 4He^{4}\mathrm{He}4He fluid inside the pore forms either a single channel along the axis, or a series of concentric cylindrical shells, with varying degrees of shell overlap. In the limit of pore length greatly exceeding its radius, the 4He^{4}\mathrm{He}4He fluid always displays markedly one-dimensional behavior, with no ``dimensional crossover'' above some specific pore radius and/or as multiple concentric shells form, in contrast to what was recently claimed by other authors [Phys. Rev. B 101, 104505 (2020)]. Indeed, the predicted robustness of one-dimensional physics suggests that this system may offer a broadly viable pathway to the experimental observation of exotic behavior of, e.g., junctions of interacting Tomonaga-Luttinger liquids, in an appropriately designed network of nanopores.