Long-distance correlation-length effects and hydrodynamics of 4He films in a Corbino geometry

Previous measurements of the superfluid density ρs and specific heat for 4He have identified effects that are manifest at distances much larger than the correlation length ξ3D [1–3]. We report here new measurements of the superfluid density which are designed to explore this phenomenon further. We determine the superfluid fraction ρs/ρ from the resonance of 34 nm films of varying widths 4 ≤ W ≤ 100 µm. The films are formed across a Corbino ring separating two chambers where a thicker 268 nm film is formed. This arrangement is realized using lithography and direct Si-wafer bonding. We identify two effects in the behavior of ρs/ρ : one is hydrodynamic, for which we present an analysis; and the other, a correlation-length effect which manifests as a shift in the transition temperature Tc relative to that of a uniform 34 nm film uninfluenced by proximity effects. We find that one can collapse both ρs/ρ and the quality factor of the resonance onto universal curves by shifting Tc as ∆Tc ∼ W−ν. This new scaling is a surprising result on two counts: it involves a very large length scale W relative to the magnitude of ξ3D; and, the dependence on W is not what is expected from correlation-length finite-size scaling which would predict ∆Tc ∼ W−1/ν .