QCM Study on 2D Vortex in Superfluid⁴He and³He-⁴He Mixture Films

Abstract

Abstract. Two-dimensional (2D)4 He fluid films show the Kosterlitz-Thouless (KT) transition where pairing and unpairing of the thermally excited 2D vortices play an important role. However, in the superfluid submonolayer, the vortex parameters (the diffusion constant D, the core diameter a 0 ) have been incompletely estimated for various conditions. Here, we undertake QCM measurements for pure 4 He films (on gold and H2 substrates) and 3 He-4 He mixture films (on gold substrate), and accurately determine the parameter D/a 2 0 by the high frequency dependence of the superfluid onset from 20 to 180 MHz. By the comparison of the results of pure 4 He film on gold and H2 substrates, the vortex diffusion in our study has the largest value D ∼h/m in the quantum limit. The core diameter a 0 is estimated to be the same magnitude as the de Broglie wavelength at TKT between 0.1 and 0.9 K. In terms of 3 He-4 He mixture films, we observe no effect of 3 He on the vortex parameters up to the 3 He coverage of 15.1 µmol/m 2 . IntroductionTwo-dimensional (2D) 4 He fluid films on various substrates show the Kosterlitz-Thouless (KT) superfluid transition [1] where pairing and unpairing of the thermally excited 2D vortices play a major role. Important vortex parameters (the diffusion constant D, the core diameter a 0 ) have been extensively studied on flat and porous substrates by various techniques [2,3, 4]. Most of the researches have been done for the thicker films above the coverage with T KT = 1 K. On the other hand, in the thinner coverage region, there is only a few systematic studies [5,6,7] on the vortex properties, and the important vortex parameters D, a 0 , and even the combination of the two parameters D/a 0 2 are not well determined. In most of the experiments D/a 0 2 is estimated, since D and a 0 are the difficult quantities to be estimated independently. In this paper, we report the accurate determination of the parameter D/a 2 0 in the superfluid submonolayer region by the frequency dependence of the superfluid onset from 20 to 180 MHz by a quartz crystal microbalance (QCM). To study on the 2D vortex under various conditions, the QCM measurements have been done for pure 4 He films on H 2 substrate and 3 He-4 He mixture films on gold substrate, and then both the experiments are compared to the pure 4 He study on gold. H 2 substrate is a weak binding substrate which is prepared by preplating on gold. We can examine substrate dependences, the effects of varying the 4 He-substrate potential strength and smoothing out the surface roughness. In terms of 3 He-4 He mixture films, it is reported that the vortex core size increases nearly linearly with added 3 He to a pure 4 He film in the previous torsional oscillator (TO) study on porous alumina of 50 nm powder [8]. It is interesting of a question as to whether the 3 He effect is reproduced on planar substrate.