Superfluidity, BEC, and dimensions of liquid He in nanopores

We present path integral Monte Carlo (PIMC) calculations of the superfluid fraction, ρS/ρ, and the one-body density matrix (OBDM) [Bose-Einstein condensation (BEC)] of liquid He confined in nanopores. Liquid He 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 ρS/ρ. We simulate a cylinder of liquid of diameter dL surrounded by 5 Å of inert solid He in a nanopore of diameter d; d = dL + 10 Å. We find a PIMC ρS(T )/ρ and OBDM that scales as a 1D fluid Luttinger liquid at extremely small liquid pore diameters only, dL = 6 Å. 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 dL 22 Å the PIMC ρS(T )/ρ 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 = 16 Å to superflow at d 18 Å agrees with experiment. There is a crossover to 3D scaling at larger dL 22 Å. In the range 8 dL 22 Å, the Tc predicted using the Kosterlitz-Thouless 2D scaling criterion of the OBDM agrees well with that obtained from ρS(T )/ρ. 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 TBEC Tc as observed in larger pore media.