A PRECISION MEASUREMENT OF THE SUPERFLUID DENSITY NEAR THE TRANSITION OF A 2D SUPERFLUID

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A PRECISION MEASUREMENT OF THE

SUPERFLUID DENSITY NEAR THE TRANSITION

OF A 2D SUPERFLUID

D. Bishop, J. Reppy

To cite this version:

JOURNAL DE PHYSIQUE _{Colloque C6, supplPment au no 8, Tome 39, aofit 1978, page C6-339}

A PRECISION MEASUREMENT OF THE SUPERFLUID DENSITY NEAR THE TRANSITION OF A 2D SUPERFLUID D.J. Bishop and J.D. Reppy

D e p a r t m e n t of Physics, C o m e 2 2 University Ithaca, New York 14853, U. S. A .

R6sumb.- Cet article dbcrit l'dtude expdrimentale de la densitd et de la dissipation d'un superfluide dans un milieu P 2 dimensions. En ce qui concerne la densit6 superfluide, les r6sultats confirment le modsle de Kosterlitz-Thouless d'un superfluide 21 2 dimensions. Abstract.- In this paper we report the measurement of the superfluid density and dissipation of a 2 dimensional superfluid. The superfluid density data support the Kosterlitz-Thouless picture of a two dimensional superfluid.

We have studied the transition region of 2d superfluid by measuring the superfluid mass of a 4 ~ e film adsorbed on a mylar substrate using the Andronikashvili torsional oscillator technique. Previous high precision measurements of the superfluid mass of 4 ~ e films adsorbed onto a highly interconnected 3d network (Vycor glass) using both Andronikashvili /I/ and 3rd sound methods yielded the surprising result that the superfluid transition in this system is very similar to that of bulk helium. The superfluid density exponents for the films were found to be near 213 (i.e. that of bulk 'He) and independent of coverage. In an effort to gain some insight into the behaviour of a true 2d superfluid uncomplicated by a highly interconnected geometry we have performed an experiment where the helium film is adsorbed on a substrate of mylar film mounted on a high Q torsional oscillator. The period and amplitude of the oscillator can be used to determine the superfluid mass and dissipation of the 4 ~ e film adsorbed on the substrate. The mylar film consists of a strip 'L 1 cm wide by % 20 m long rolled tightly and inserted into the torsional oscillator with its axis of oscillation the same as that about which the mylar is rolled. The geometrical surface area of the substrate is 0.428 m2. The oscillator has a Q of 'l.

lo5

lo9.

SIDE VlEW OF E X P E R I M E N T Torsion Rod for Vibrot~on Isolation Sample Cell Electrodes to -4 e 0 r 1 v e Cell B

i

Y

+

END VlEW OF CELL B ELECTRODES

SAMPLE C E L L ASSEMBLY

n

t4mil xIcm x 20meter Rolled into a Jelly Roll

Fig. 1 : Sample cell and electrode structure.

The temperature was controlled at each point and the period was allowed to stabilize before a reading was taken. An example of the period and amplitude data taken is shown in figure 2. At the transition two interesting features are seen. The period of the oscillator shows an abrupt drop in a narrow temperature range while the dissipation in the system shows a sharp peak. We interpret our results in terms of the Kosterlitz Thouless theory of a two demensional superfluid

/2,3/.

Data was taken with a fixed amount of 4 ~ e In the Kosterlitz-Thouless.pictarC introduced into the sample cell. The period and superfluidity exists at low temperatures in the amplitude were measured as a function of presence of a population of bound vortex-anti-

temperature. vortex pairs.

T (K)

Fig. 2 : Period and dissipation for a 37.4 p mole/m2 film.

At a suificiently high temperature, a dissociation of a finite fraction of the vortex pairs takes place and superfluidity is destroyed. Kosterlitz /3/, and later Jose, et a1./4/ have shown that for the static case, the superfluid mass drops discontinuously to zero. Further, as has been emphasized by Nelson and Kosterlitz / 5 1 / the ratio of the superfluid mass per unit area, ps, to the transition temperature, TKT, is given by :

This quantity is predicted to be universal, independent of film thickness. In our experiment we can relate the period shift AP to this dis-

continuous superfluid density jump. Our measured values for this ratio give p /T

9 s KT =

3.50 x 10- g / c m 2 ~ = 13 %. Therefore the agreement between theory and experiment is excellent.

In addition to the superfluid density jump, we measure a peak in the superfluid dissipation at the transition. This maximum in the dissipation is due to the depairing of bound vortex pairs at the transition. As the vortices move diffusi- vely over the substrate, energy is dissipated. This dissipation maximum is shown in figure 3 for several different velocities of oscillation. For low velocity runs the height and width of the dissipation peak was independent of the velocity. (Fig. 3, curve a).

by the recent extensions of the Kosterlitz- Thouless static theory to finite frequency /6/.

Fig. 3 : Dissipation for three different cavity velocities.

However, as the drive is increased beyond some critical value, the height and width of the dissipation peak became a function of drive velo- city (Fig. 3-b), c)). We interpret this as the films being driven beyond some critical velocity which aids:the normal mechanism for the production of free vortices which move diffusively/

In conclusion, we have observed both the dissipation and superfluid density of a two dimensional superfluid. The data qualitatively and quantitatively supports the Kosterlitz- Thouless picture of a two dimensional super- 'fluid.

This work has been supported by the National Science Foundation through Grant No. DMR-75- 08624 and through the Cornell Materials Science Center Grant No. DMR-76-81083.

References

/I/ Berthold, J.E., Bishop, D.J. and Reppy, .T.D., Phys. Rev. Lett.

2

/ 2 / Kosterlitz, J.M. and Thouless, D.J., J. Phys. C k (1973) 1181.

/3/ Kosterlitz, J.M., J. Phys.

CL

141 Jose, J., Kadanoff, L.P., Kirkpatrick, S. and Nelson, D.R., Phys. Rev. B c (1977) 1217.

/ 5 / Nelson, D.R. and Kosterlitz, J.M., Phys. Rev. Lett.

39

(1977) 1201.

161 Hubennan, B . A . , Myerson, R.J. and Dontiach, S., Phys. Rev. Lett.

40