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

Previous measurements of the superfluid density ρs and specific heat for He4 have identified effects that are manifest at distances much larger than the correlation length ξ3D [Perron, Nat. Phys. 6, 499 (2010)1745-247310.1038/nphys1671; Perron and Gasparini, Phys. Rev. Lett. 109, 035302 (2012)PRLTAO0031-900710.1103/PhysRevLett.109.035302; Perron, Phys. Rev. B 87, 094507 (2013)PRBMDO1098-012110.1103/PhysRevB.87.094507]. We report here 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≤100μm. 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 is 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 ΔTc∼W-ν. This 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 ΔTc∼W-1/ν.