Extremely High Frequency Dependence of Two-Dimensional Superfluid Onset

Abstract

We observed the frequency dependence of the superfluid transition of 4 He films adsorbed on planar gold up to a very high frequency of 180 MHz, using the overtone harmonic modes of a quartz crystal microbalance. The superfluid onset was observed at a temperature markedly higher than the KosterlitzThouless (KT) transition temperature, the onset temperature in the low-frequency limit. The observed frequency dependence is surprisingly well reproduced by the dynamic theory close to the high-frequency condition where the vortex diffusion length in a period becomes as small as the vortex core diameter. We also observed that the superfluid vortex parameters depend strongly on the kind of substrate as well as on 4 He film thickness. KEYWORDS: KT transition,4 He film, superfluidity DOI: 10.1143/JPSJ.78.033604The superfluid onset of two-dimensional (2D)4 He films observed using a torsional oscillator at 1.2 kHz 1) was understood in the framework of the Kosterlitz-Thouless (KT) transition, 2) which is completely different from the Ginzburg-Landau (GL)-type phase transition. The KT transition is now a general concept for superconducting films,3) Josephson-junction arrays, 4) and the Bose-Einstein condensation of a 2D atomic Bose gas.5) The KT transition temperature T KT is far below the GL temperature T GL . The KT theory predicts that the observed superfluid onset close to T KT is determined by the pairing/unbinding of superfluid vortices. However, the actual important properties of the vortices, e.g., the vortex core diameter a 0 and the vortex diffusion constant D, have not been obtained precisely even for typical (standard) 2D4 He films. Furthermore, the KT context for the 4 He films would definitely break down under some extreme conditions of the film geometry formed in pores and of the high frequency in the measurement.For 4 He films formed in porous media such as Vycor glasses, Minoguchi and Nagaoka 6) calculated that the superfluid onset temperature becomes higher than T KT and that the onset temperature diverges with a decrease in the pore diameter to the core diameter a 0 . Therefore, the context breaks down for 4 He films formed in nanopores whose diameter is equal to or smaller than a 0 . Recently, superfluidity was observed for 4 He films formed in 1D nanopores larger than 1.8 nm in diameter.7) Its superfluid onset should be considered in another context, because the smallest superfluid tube diameter was estimated to be about 1 nm, which is smaller than a 0 ¼ 2:5 AE 1:2 nm, estimated earlier for the Vycor glasses. 8)According to the dynamic KT theory, 9) the superfluid onset depends on the measuring frequency !=2. The observed superfluid density s is equal to a stiffness at the size of the vortex diffusion length r D ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffi 14D=! p in the period 1=!. At a low frequency limit (i.e., r D ! 1), s shows a universal jump at T KT . At a finite frequency, the superfluid onset occurs at a temperature slightly higher than T KT , where r D becomes equal to the 2D phase coherence leng...

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

“…The onset and dissipation peak temperatures increase with increasing frequency. At 140 MHz on gold substrate, the onset temperature at 0.7 K is about 25 % higher than T KT = 0.561 K. As reported in our previous papers [6,13], the coverage dependence on both gold and H 2 substrates is explained by the KT universal line expected from T KT = πh 2 2k B m 2 σ s , where m is atomic mass of 4 He,h the Planck constant, k B the Boltzmann constant. In terms of the onset coverage, we observe a substrate dependence.…”

“…At extremely high frequencies, the superfluid density will be observed far above T KT up to T GL in terms of the GL theory. In our previous paper [6] on gold substrate, we report that eq. (2) explains the superfluid transition at extremely high frequencies where the diffusion length r D = 14 nm (180 MHz) is only three times larger than a 0 ∼ 4 nm at the lowest measured temperature (70 mK).…”

“…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.…”

Fluid States of Helium Adsorbed in Nanopores

“…Substrate dependence of the vortex parameters is likely to be observed [62]. It will allow to study at the breakdown frequency condition for the present dynamic theory where the fre- …”

“…Although the most important vortex parameters (the diffusion constant D, the core diameter a 0 ) have been experimentally obtained [56][57][58][59][60][61], these have not sufficient accuracies in various conditions even for the typical 2D KT transition. Here, the microscopic vortex parameters are precisely estimated by the dependence of the superfluid onset on the extremely high measurement frequency at the temperatures between 0.05 and 0.9 K [62].…”