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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[6].
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)[2]. 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[3] and packed alumina powder[4]. 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[5] 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. [1].
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
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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[8].
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).
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