4 Kosterlitz-Thouless Transition in He Films Adsorbed to Rough Calcium Fluoride Cite as: AIP Conference Proceedings 850, 267 (2006); https://doi.org/10.1063/1.2354695 Published Online: 01 December 2006 D. R. Luhman, and R. B. Hallock AIP Conference Proceedings 850, 267 (2006); https://doi.org/10.1063/1.2354695 © 2006 American Institute of Physics. 850, 267 Kosterlitz-Thouless Transition in 4He Films Adsorbed to Rough Calcium Fluoride D.R. Luhman and R.B. Hallock Laboratory of Low Temperature Physics, Department of Physics University of Massachusetts, Amherst, USA 01003 Abstract. Previous measurements in our lab have shown that the onset of superfluidity at the KT transition, typically seen as a sharp change in the frequency of a smooth-surface quartz crystal microbalance, becomes less identifiable in the presence of increasing surface roughness or disorder, while the peak in the dissipation is unchanged[l]. Using a series of microbalances coated with increasingly rough CaF2, we have extended our measurements to lower 4 He film coverages and thus lower temperatures. We find at lower 4 He coverages that the presence of disorder on the substrate has a diminished effect on the frequency shift. Keywords: Kosterlitz-Thouless transition, superfluid helium PACS: 68.35.Ct, 64.70.Ja, 67.40.Pm, 68.15.+e INTRODUCTION with porous gold electrodes near the capillary condensation transition, a dissipation peak was observed at the superfluid transition, however, a shift in frequency was not seen. Here we report the results of further observations utilizing a series of QCMs with different surface roughness at lower temperatures and thinner helium films. The superfluid transition in thin helium films has been shown to be well described by the theory of Kosterlitz and Thouless (KT). The onset of superfluidity in static films is abrupt with a discontinuous jump in the areal superfluid density, as. In practice the discontinuous step in as at the onset of superfluidity is slightly rounded due to frequency and velocity effects in the adsorbed film. In addition to the sharp onset of superfluidity there is also a peak in the dissipation at the transition temperature, TKT, that is also characteristic of the superfluid transition in two-dimensional films. A number of experiments have investigated the effect of disorder on the KT transition through the use of three-dimensional multiply connected substrates, such as vycor and packed alumina powder. However there has been little work done on the effect of disorder in quasi-two-dimensional systems. In a previous experimentfl] we used a series of quartz crystal microbalances (QCMs), each with a different surface roughness to investigate the effect of surface roughness (i.e. disorder) on the superfluid transition. Both the shift in frequency and the dissipation were monitored as the helium film thickness was increased at a constant temperature of T = 1.672 K. It was shown that as the surface roughness increases the observed shift in frequency at the transition becomes less well defined and less identifiable with a sharp step in as while the peak in the dissipation remains essentially unchanged. For the roughest substrate a shift in frequency at the transition was barely visible. An earlier experiment on even rougher surfaces did not observe a shift in frequency at the onset of superfluidity. In another experiment, utilizing a QCM EXPERIMENTAL DETAILS The experiment utilized five gold-plated AT-cut QCMs operated in their third harmonic (15 MHz). Four of the crystals were coated with different nominal thicknesses of CaF2, t, to produce differing surface roughness. The surface roughness of CaF2 increases as t increases; the structures increase in size while the porosity stays relatively constant ((j) « 0.64) with increasing t[l]. The remaining crystal was left uncoated. For a particular QCM, the same amount of CaF2 was thermally deposited on each side. The values of t used in the experiment were 30, 60, 90, and 120 nm, covering the same range of CaF2 thicknesses as in Ref. . The crystals, along with a plain glass substrate with third sound generators and Zn bolometers, were mounted in a brass sample can attached to a dilution refrigerator. 4 He was slowly bled in the sample chamber and allowed to equilibrate. The temperature was then brought to T = 0.820 K. The helium film thickness was determined by measuring the speed of third sound in the 4 He film on glass and solving C\ = ((ps)/p)Fd(l + TS/L)2 for the film thickness d. (ps)/p is the effective superfluid fraction in the film, F is the restoring force due to the van der Waals interaction, S is the specific entropy, and L CP850, Low Temperature Physics: 24th International Conference on Low Temperature Physics; edited by Y. Takano, S. P. Hershfield, S. O. Hill, P. J. Hirschfeld, and A. M. Goldman © 2006 American Institute of Physics 0-7354-0347-3/06/$23.00 267 2.0 o o A + X Plain 30 nm 60 nm 90 nm 120 nm 1 1.5 F_oo 0 oo 0 ° oc < 1.00 oQS> 120 n m • _ •++ 0.90 T(K) %> ^fp 0.0 0.95 X A n <foo°.feo ^ 0.5 0.0 + Plain 30 nm 60 nm 90 nm o oo ±£+ 1.0 0.90 o o >o 0.85 1 % ' o ~ , Hi^ ^tk 1 0.95 1.00 c ^ ^ ^ ^ ^ ® 1.05 T(K) FIGURE 1. Frequency data with the background subtracted as a function of T. The large drop in frequency indicates the superfluid transition. Thefilmthickness measured at T = 0.820 K was d = 2J9 layers for these data. FIGURE 2. Frequency data with the background subtracted as a function of T. The large drop in frequency indicates the superfluid transition. Thefilmthickness measured at T = 0.820 K was d = 3.19 layers for these data. is the latent heat. Temperature was scanned upward and the resonant frequency and amplitude of the QCMs were measured using a dc frequency modulation technique. The driving voltage of the QCMs was 1 mV and the sensitivity was 1.77 Hz/layer. thinner helium film thicknesses. This will cause a disordered film thickness that varies greatly with position. We speculate that this disorder in the film thickness itself may lead to suppression in the distinctness of the frequency shift at the KT transition at larger film coverages. RESULTS ACKNOWLEDGMENTS Figures 1 and 2 show frequency data with the background subtracted for d = 2.79 layers and d = 3.19 layers as measured at T = 0.820 K respectively. As the temperature was increased during data collection the film thickness decreased slightly as atoms moved from the film to the vapor. Due to this process, we estimate the thickness of the film at TKT = 0.950 K (Fig. 1) is a few a tenths of a layer thinner than the value measured at T = 0.820 K and near 0.5 layers thinner at TKT = 0.992 K (Fig. 2). In Fig. 1 the general shape and size of the mass coupling at the transition is virtually identical for all the substrates coated with CaF2. The frequency shift on the plain QCM was slightly larger than on the CaF2 substrates but essentially the same shape. For the thicker film data shown in Fig. 2 the substrates with larger values of t show a somewhat broader transition. This broadening is likely a crossover to the behavior seen in the earlier experiment at increased temperature and film thickness where the frequency shift was observed to be less distinct as t increasedfl]. This general behavior is likely due to an increase in helium film thickness. At larger film thicknesses there is additional helium adsorbed to the disordered substrates (e.g. via capillary condensation) than at We thank N. Prokof'ev for productive discussions. This work was supported by the National Science Foundation under grants DMR-0138009 and DMR-0213695 (MRSEC) and also by research trust funds administered by the University of Massachusetts Amherst. 268 REFERENCES 1. D.R. Luhman and R.B. Hallock, Phys. Rev. Lett. 93, 086106 (2004). 2. J. M Kosterlitz and D. J. Thouless, J. Phys. C 6, 1181 (1973). 3. J.E. Berthold, D.J. Bishop, and J.D. Reppy, Phys. Rev. Lett. 39, 348 (1977). 4. V. Kotsubo and G.A. Williams, Phys. Rev. Lett. 53, 691 (1984). 5. J.C. Herrmann and R.B. Hallock, Phys. Rev. B 68, 224510 (2003). 6. R.J. Lazarowick, P. Taborek, and J.E. Rutledge, Bull. Am. Phys. 49, 378 (2004). 7. D. R. Luhman and R. B. Hallock, Phys. Rev. E 70, 051606 (2004). 8. M.J. Lea, P. Fozooni, and P.W. Retz, J. Low Temp. Phys. 54, 303 (1984).