Frequency and Size Dependences of Superfluidity in Low-Dimensional 4He Fluids

Abstract

We have studied superfluidity of 4He fluids in two- and one-dimensional states. In the 2D state of the 4He films on flat substrate, superfluidity was observed in the normal fluid state above the 2D Kosterlitz-Thouless temperature at high measurement frequencies. The superfluidity in 2D also depends on the system size, e.g. pore diameter of porous glasses and grain size of powder. The 1D state was realized for 4He fluid nanotubes formed in 1D nanopores 1.8–4.7 nm in diameter and about 300 nm in length. Superfluidity in the 1D state was observed by the torsional oscillator experiment. The results are qualitatively well reproduced by the Monte Carlo calculation for a classical XY spin system modeled on the present 4He nanotubes. Although the 1D state is in the normal fluid state at any finite low temperatures due to the 1D phonon fluctuation, the superfluid frequency shift Δf of the oscillator can be observed. Above a temperature, Δf decreases due to another kind of 1D thermal fluctuation of which excitations destroy the phase coherence in the nanotubes. The excitations depend on the tube length as well as the tube diameter.