He3Film Flow: Two-Dimensional Superfluidity

Abstract

3 He film flow has been observed. The maximum flow rate, at 0.7 mK, over a rim 0.9 mm above the 3 He level, was 1.2 mm 3 /h corresponding to an approximate flow velocity of 0.2 mm/sec. A flow rate of 0.2 mm 3 /h ( ~ 0.1 mm/sec) was measured with the rim 14 mm above the level. The transition to superflow occurred at 3.5 ± 0.5 mK for the 0.9-mm film and 2.0 ± 0.5 mK for the 14mm film. This flow is in a regime where the film thickness is less than or comparable to the bulk superfluid 3 He coherence length ( ~ 1000 A at 0.8 mK) and the temperature is higher than the bulk 3 He superfluid transition temperature (1.08 mK) and corresponds, we believe, to a twodimensional superfluid phase of 3 He. PACS numbers: 67.50.-b, 67.70. + nThe superfluid phases of liquid 3 He, discovered a decade ago, have proven a very rich field of physics. 1 Whereas the range of phenomena has been far more extensive than for superfluid liquid 4 He, film flow is one property which was expected to be unique to 4 He. 2 The reason for not expecting film flow in 3 He was that the coherence length is larger than the equilibrium thickness of the 3 He film on a vertical wall at a height of 100 /itm or more above the meniscus of the free surface. This is demonstrated in Fig. 1 which compares film thickness (d), which varies with height (/z), with the coherence length (f), in bulk 3 He at 0, 0.5, and 0.8 mK. The figure is schematic only; the coherence lengths are from BCS theory, 4 and the literature contains many warnings concerning estimates of helif\ 1 \ f \

Andreev bound states in superconducting films and confined superfluid 3 He

“…After detection in 1985 of superfluidity in thin 3 He films formed on vertical walls [70], a number of different techniques was applied to study their properties. A film formed on an elevated substrate [71] was used to measure suppression of the superfluid transition temperature, and flow properties.…”

Directly Detecting the Edge Current in a $p_x + ip_y$ Topological Superfluid

“…3. By adjusting the bulk liquid level, the thickness of the superfluid film on the gyroscope can be controlled from about 30 nm to a few hundred nm [46,47]. To deposit thicker films, voltage can be applied to interdigitated capacitors (IDCs) patterned on the face of the gyroscope.…”

Surface Specific Heat ofHe3and Andreev Bound States

“…Previous experimental work on 3 He in confined ge-ometries, has taken one of two approaches. The first is to investigate 3 He thin layers, for example, films with a free surface for studies of superfluid density [16], flow [17], third sound [18], or in slabs having confinement on two sides, as was the case for a number of NMR experiments [19]. The other method is to determine the effects of surfaces on 3 He constrained in a porous medium, with the corresponding advantage of a larger effective surface area.…”