Observation of superfluidity in two- and one-dimensions

Abstract

Even though there is no long-range-ordered state of a superfluid in dimensions lower than the threedimension (3D) such as bulk 4 He liquid, superfluidity has been observed for flat 4 He films in 2D and recently for nanotubes of 4 He in 1D by the torsional oscillator method. In the 2D state, in addition to the superfluid below the 2D Kosterlitz-Thouless transition temperature T KT , superfluidity is also observed in a normal fluid state above T KT , which depends strongly on the measurement frequency and the system size. In the 1D state of the nanotubes, superfluidity is directly observed as a frequency shift in the torsional oscillator experiment. Some calculations suggest a superfluidity of a 1D Bose fluid with a finite length, where thermal excitations of 2 -phase winding play the main role for superfluid onset of each tube. Dynamics of the 1D superfluidity is also suggested by observing the dissipation in the torsional oscillator experiment.

Driving Force of Molecular/Ionic Superfluid Formation

“…13 It has also been demonstrated that the superfluid onset temperature increases as the diameter of the channel decreases. 14,15 Another peculiar phenomenon is observed when liquid 4 He is added to a small bowl below 2.17 K: a thin invisible film creeps up the inside wall of the bowl and down on the outside. A drop forms from this film and falls off outside the bowl until it is empty, demonstrating that the film behaves like a superfluid confined in a nanochannel (Fig.…”

Quantum Monte Carlo study of the superfluid density in quasi-one-dimensional systems of hard-core bosons: Effect of the suppression of phase slippage

“…For a film, the effective length L eff = z /(n 1 a 2 ) ∼ L z /L x ∼ z / x , i.e., the aspect ratio of the anisotropic lattice, because n 1 = N/ z = N L /(2 z ) and L α ∼ α /a (α = x and z). Experimentally, the aspect ratio L z /L x can be estimated to be 15−50 [4,6,7,11,13,17]. On the other hand, to simulate 4 He atoms filling nanopores, we consider an anisotropic three-dimensional cubic lattice, i.e., a bar, composed of…”

“…To simulate 4 He atoms adsorbed on the inner walls of nanopores [4,6,7,11,13,17], we consider an anisotropic two-dimensional square lattice, i.e., a film, composed of L x × L z sites with L z L x (see Fig. 1).…”

“…, the aspect ratio of the anisotropic lattice, because n 1 = N/ z = N L /(2 z ) and L α ∼ α /a (α = x and z). Experimentally, the aspect ratio L z /L x can be estimated to be 15−50 [4,6,7,11,13,17]. On the other hand, to simulate 4 He atoms filling nanopores, we consider an anisotropic three-dimensional cubic lattice, i.e., a bar, composed of The superfluid density ρ p (T ) in these systems vanishes at finite temperatures in the limit of L z → ∞ because of phase slippage.…”

“…Recently, 4 He atoms confined in straight nanopores have attracted much attention [4][5][6][7][8][9][10][11][12][13][14][15][16][17]. For example, Wada and coworkers studied He atoms adsorbed on the inner walls of one-dimensional pores of porous material, FSM (Folded sheet mesoporous materials)-16 [4][5][6][7]; typical pore length is 200-300 nm and its diameter R can be systematically changed from R = 1.5 nm to 4.7 nm.…”