As helium-4 is cooled below 2.17 K it undergoes a phase transition to a fundamentally quantum mechanical state of matter known as a superfluid which supports flow without viscosity. This type of dissipationless transport can be observed by forcing helium to travel through a narrow constriction that the normal liquid could not penetrate. Recent experiments have highlighted the feasibility of fabricating smooth pores with nanometer radii, that approach the truly one-dimensional limit where it is believed that a system of bosons (like helium-4) may have startlingly different behavior than in three dimensions. The one-dimensional system is predicted to have a linear hydrodynamic description known as Luttinger liquid (LL) theory, where no type of long range order can be sustained. In the limit where the pore radius is small, LL theory would predict that helium inside the channel behaves as a sort of quasi-supersolid with all correlations decaying as power-law functions of distance at zero temperature. We have performed large scale quantum Monte Carlo simulations of helium-4 inside nanopores of varying radii at low temperature with realistic helium–helium and helium-pore interactions. The results indicate that helium inside the nanopore forms concentric cylindrical shells surrounding a core that can be described via LL theory and provides insights into the exciting possibility of the experimental detection of this intriguing low-dimensional state of matter.
Low temperature structural and superfluid properties of
4He confined in cylindrical nanopores are theoretically investigated by means of first-principle quantum Monte Carlo (QMC) simulations. We vary the density of
4He inside the pore, as well as the pore diameter and the potential describing the interaction of each
4He atom with the pore surface. Accordingly, the
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 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.
Low dimensional quantum fluids, where one can probe the effects of enhanced thermal and quantum fluctuations on macroscopic quantum wavefunctions, can be experimentally realized through transverse physical confinement of superfluid helium on scales smaller than the coherence length. Reaching this scale is difficult, requiring confinement in single or multiple pores with nanometer radii. Porous silicates such as MCM-41 have a pore radius larger than the coherence length of 4He, and in this work we systematically explore the possibility of pre-plating pores with different elements to reduce the pore size without localizing the confined superfluid. Through a direct solution of the few-body Schrodinger equation combined with quantum Monte Carlo simulations, we explore the behavior of helium confined inside cylindrical nanopores for a range of pre-plating elements, including rare gases and alkali metals. For rare gases, we find that helium remains strongly attracted to the pore walls and any atoms in the core form an incompressible liquid. For alkali metals such as Cs, weak interactions between helium and the pre-plating material prevent localization near the walls and enable delocalization in the pore center. Our results extend previous results for helium wetting on flat two dimensional coated substrates to the curved geometry inside nanopores, and demonstrate that alkali pre-plated nanopores may enable a tunable one-dimensional confined quantum liquid of helium.
One-dimensional bosonic systems, such as helium confined to nanopores, exhibit Luttinger liquid behavior characterized by density waves as collective excitations. We investigate the impact of a scattering potential on a low-dimensional quantum liquid. We consider a microscopic model of ^{4}He inside a perturbed nanopore with a localized constriction and employ quantum Monte Carlo simulations to analyze the density of the core within an effective low-energy framework. Our results reveal the emergence of Friedel oscillations in a bosonic quantum liquid without a Fermi surface. Furthermore, we utilize the Luttinger liquid model to predict experimentally observable signatures of this pinning phenomenon in elastic scattering and via the temperature and pressure dependence of mass transport through the deformed nanopore.
Recent experiments on the flow of helium-4 fluid through nanopores with tunable pore radius provide a platform for studying the quasi-one-dimensional (quasi-1D) superfluid behaviors. In the extreme 1D limit, the helium atoms are localized by disordered small variations in the substrate potential provided by the pore walls. In the limit of wide pore radius, a solid layer of helium-4 is expected to coat the pore walls smoothing out the substrate potential, and superfluidity is observed in the central region. Building on earlier quantum Monte Carlo results, we propose a scenario for this crossover using a shell model of coupled Luttinger liquids. We find that a small-radius pore will always localize the helium atoms, but above a critical radius, a single 1D channel flows through the pore and can be described by Luttinger liquid theory.
We report diffusion Monte Carlo (DMC) and path integral Monte Carlo (PIMC) calculations of the properties of a one-dimensional (1D) Bose quantum fluid. The equation of state, the superfluid fraction ${\ensuremath{\rho}}_{S}/{\ensuremath{\rho}}_{0}$, the one-body density matrix
n(x), the pair distribution function
g(x), and the static structure factor
S(q) are evaluated. The aim is to test Luttinger liquid (LL) predictions for 1D fluids over a wide range of fluid density and LL parameter
K. The 1D Bose fluid examined is a single chain of
4He atoms confined to a line in the center of a narrow nanopore. The atoms cannot exchange positions in the nanopore, the criterion for 1D. The fluid density is varied from the spinodal density where the 1D liquid is unstable to droplet formation to the density of bulk liquid
4He. In this range,
K varies from
K>2 at low density, where a robust superfluid is predicted, to
K<0.5, where fragile 1D superflow and solidlike peaks in
S(q) are predicted. For uniform pore walls, the ${\ensuremath{\rho}}_{S}/{\ensuremath{\rho}}_{0}$ scales as predicted by LL theory. The
n(x) and
g(x) show long range oscillations and decay with
x as predicted by LL theory. The amplitude of the oscillations is large at high density (small
K) and small at low density (large
K). The
K values obtained from different properties agree well verifying the internal structure of LL theory. In the presence of disorder, the ${\ensuremath{\rho}}_{S}/{\ensuremath{\rho}}_{0}$ does not scale as predicted by LL theory. A single
vJ parameter in the LL theory that recovers LL scaling was not found. The one body density matrix (OBDM) in disorder is well predicted by LL theory. The ``dynamical'' superfluid fraction, ${\ensuremath{\rho}}_{S}^{D}/{\ensuremath{\rho}}_{0}$, is determined. The physics of the deviation from LL theory in disorder and the ``dynamical'' ${\ensuremath{\rho}}_{S}^{D}/{\ensuremath{\rho}}_{0}$ are discussed.