In the one-dimensional (1D) nanopores of FSM-16 (2.8 nm in diameter) and the 3D pores of HMM-2 (2.7 nm, and 5.5 nm in 3D period), the 4 He films adsorbed on these nanopore walls show the properties of the Bose quantum fluid and superfluidity above 1.4 atomic layers at low temperatures. The boundary of the Bose fluid region was determined from the kink (peak) temperature T C of the heat capacity at each coverage n . The phase diagrams obviously show dependence on the 1D and 3D pore connections, respectively. In the 3D nanopores, the coverage (density) dependence of T C is well reproduced by the Bose-Einstein condensation temperature of the 3D ideal gas which is proportional to ( n - n c ) 2/3 , where n c is the onset coverage. In the case of the 1D pores (channels), T C is proportional to ( n - n c ) at 0.1 < T C < 1K. This T C is likely to correspond to the crossover temperature of the 2D ideal gas heat capacity from the constant heat capacity of the Boltzmann gas to the linear in T , with decreasing temperature. At T C , the thermal de Broglie wavelength of the free particle is still shorter than the pore diameter, while the thermal phonon wavelength is estimated to become longer than the diameter below T C , which indicates the 1D phonon state.
A theory accounting for the dynamical aspects of the superfluid response of one dimensional (1D) quantum fluids is reported. In long 1D systems, the onset of superfluidity is related to the dynamical suppression of quantum phase slips at low temperatures. The effect of this suppression as a function of frequency and temperature is discussed within the framework of the experimentally relevant momentum response function. Applications of these results to the understanding of the superfluid properties of helium confined in 1D pores with nanometer diameter, dislocations in solid 4He, and ultracold atomic gases are also briefly discussed.
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.
Helium atoms are believed to be strongly bound within the interstitial channels in bundles of carbon nanotubes. In a recent paper [F. Ancilotto et al., Phys. Rev. B 70, 165422 (2004)] inhomogeneity in the size distribution of nanotube radii was shown to make a system of
4He atoms in such an environment effectively a four-dimensional Bose gas, thus permitting a Bose-Einstein condensation (BEC) of the adsorbed atoms into the minimum energy state. This surprising result was obtained for a model of noninteracting atoms in a continuum distribution of (virtually) infinite interstitial channels. Here we investigate how the singular thermal properties of the ideal system and the occurrence of BEC are affected by a more realistic modeling of a bundle of nanotubes where (i) the number of nanotubes is finite and where (ii)
4He atoms adsorbed within the same interstitial channel interact among themselves. Also in this case we observe an anomalous heat capacity close to the ideal condensation temperature, suggesting the persistence of the condensation transition for interacting
4He atoms, which might be experimentally observed.
We present path integral Monte Carlo (PIMC) calculations of the superfluid fraction, ${\ensuremath{\rho}}_{S}/\ensuremath{\rho}$, and the one-body density matrix (OBDM) [Bose-Einstein condensation (BEC)] of liquid
4He confined in nanopores. Liquid
4He in nanopores represents a dense Bose liquid at reduced dimension and in disorder. The goal is to determine the effective dimensions of the liquid in the pores. It is to test whether observed properties, such as a very low onset temperature for superflow,
Tc, can be predicted by a standard, static PIMC ${\ensuremath{\rho}}_{S}/\ensuremath{\rho}$. We simulate a cylinder of liquid of diameter
dL surrounded by 5 \AA{} of inert solid
4He in a nanopore of diameter
d;
d=dL+10A˚. We find a PIMC ${\ensuremath{\rho}}_{S}(T)/\ensuremath{\rho}$ and OBDM that scales as a 1D fluid Luttinger liquid at extremely small liquid pore diameters only,
dL=6A˚. At this
dL, the liquid fills the pore in a 1D line at the center of the pore and there is no PIMC superflow. In the range $8\ensuremath{\le}{d}_{L}\ensuremath{\le}22\phantom{\rule{0.28em}{0ex}}\AA{}$ the PIMC ${\ensuremath{\rho}}_{S}(T)/\ensuremath{\rho}$ scales as a 2D liquid. In this
dL range the liquid fills the pores in 2D-like cylindrical layers. The crossover from no superflow at
d=16A˚ to superflow at $d\ensuremath{\ge}18\phantom{\rule{0.28em}{0ex}}\AA{}$ agrees with experiment. There is a crossover to 3D scaling at larger ${d}_{L}\ensuremath{\simeq}22\phantom{\rule{0.28em}{0ex}}\AA{}$. In the range $8\ensuremath{\le}{d}_{L}\ensuremath{\le}22\phantom{\rule{0.28em}{0ex}}\AA{}$, the
Tc predicted using the Kosterlitz-Thouless 2D scaling criterion of the OBDM agrees well with that obtained from ${\ensuremath{\rho}}_{S}(T)/\ensuremath{\rho}$. These results suggest that the superflow observed in small pore media is standard static superflow with the low
Tc arising from its 2D character. An operational onset temperature,
TBEC, for BEC can be defined as the temperature at which there is a crossover from exponential to algebraic decay in the OBDM. This definition leads to a ${T}_{\mathrm{BEC}}\ensuremath{\ge}{T}_{c}$ as observed in larger pore media.