Third sound measurements of superfluid 4 He films on multiwall carbon nanotubes below 1K
Emin Menachekanian, John B.S. Abraham, Bob Chen, Vito Iaia, Andrew Li, Gary A. Williams
aa r X i v : . [ c ond - m a t . o t h e r] N ov Third sound measurements of superfluid He films onmultiwall carbon nanotubes below 1 K
Emin Menachekanian, John B.S. Abraham, Bob Chen, Vito Iaia,Andrew Li, and Gary A. Williams
Department of Physics and Astronomy, University of California, Los Angeles, CA 90095E-mail: [email protected]
Abstract.
Third sound is studied for superfluid films of 4He adsorbed on multiwall carbonnanotubes packed into an annular resonator. The third sound is generated with mechanicaloscillation of the cell, and detected with carbon bolometers. A filling curve at temperaturesnear 250 mK shows oscillations in the third sound velocity, with maxima at the completion of the4th and 5th atomic layers. Sharp changes in the Q factor of the third sound are found at partiallayer fillings. Temperature sweeps at a number of fill points show strong broadening effectson the Kosterlitz-Thouless (KT) transition, and rapidly increasing dissipation, in qualitativeagreement with the predictions of Machta and Guyer. At the 4th layer completion there is asudden reduction of the transition temperature T KT , and then a recovery back to linear variationwith temperature, although the slope is considerably smaller than the KT prediction. We have carried out third sound measurements on multiwall carbon nanotubes attemperatures below 1 K, the same tubes used in the 1.3 K measurements of Ref. [1]. The cellgeometry is a little different than those measurements, the tubes (0.75 g) are now lightly packedin a single step into an annular resonator of the type we have used in the past [2], with meandiameter 2.9 cm and thickness 3.2 mm. Fig. 1 shows SEM and TEM photos of the nanotubes,which appear to range in diameter between 10 and 25 nm (larger than the 8-15 nm specified bythe supplier [3]) and lengths between 1-2 µ m. A superconducting coil and permanent magnetassembly is attached to the resonator using thermally insulating thin-wall stainless steel tubes tomechanically vibrate the resonator, exciting the third sound. The resonant modes are detectedfrom the thermal oscillations by current-biased resistance bolometers, whose output goes into aLabView FFT.Fig. 2 shows the third sound speed and Q factor as a function of the helium coverage attemperatures near 250 mK. Strong oscillations in the third sound speed are seen, due to thecompletion of atomic layers, quite similar to those seen in measurements on a highly orientedpyrolitic graphite (HOPG) substrate [4]. We adopt the coverage scale of those authors, takingone layer to be the relative maxima of c at the completion of the fourth and fifth layers,and also using their determination of 0.076 atoms/˚A as the layer coverage above the first two(more dense) layers. Although oscillations in c could not be detected at higher coverages,the observation of maxima in the Q factor at the 5 and 6 layer completions shows this to bea reasonable scale. We were completely unable to detect any signal (due to high dissipation)below 3.18 layers at oscillation levels up to 3.0 V applied to our drive coil, about the maximumwe could sustain before heating of our dilution refrigerator became a problem. The magnitude ofthe third sound speed is reduced from that in Ref. [4] due to multiple scattering effects from our igure 1. SEM (right) and TEM (left) pictures of the multiwall carbon nanotubes c ( m / s ) Number Density (atoms/Å ) Q Film thickness (layers)
Figure 2.
Third sound speed and Q near 250 mK, as a function of the helium coverage.nanotube tangle; we deduce an index of refraction of about 1.7 comparing to their results. Thespeed is only very slightly shifted down with increasing drive, while the Q is more significantlylowered (and has quite a bit of scatter).The Q is initially fairly low when the signal is first observed at 3.18 layers, and thenimmediately increases to a maximum before dropping rapidly to a minimum at 3.37 layers. The c ( m / s ) Q T KT Figure 3.
Temperature sweep at 3.32 layers. . c ( m / s ) Q T KT Figure 4.
Temperature sweep at 3.51 layers.origin of this dissipation is unclear, since at this low temperature there are very few thermalexcitations or vortices. The formation of a gas-liquid interface at the low-density fill of the startof the fourth layer is a possible source of this attenuation, since evaporation due to the thermalcomponent of the third sound would be dissipative. Such interfaces have been predicted for thesecond and higher layers of coverage on flat graphite substrates [5], though it is not entirely clearif this has been observed or not [6, 7]. The sharply curved nanotube substrate differs from theflat substrate, however, and nanotube simulations are only available for single-wall nanotubesand very low coverages [8]. With increasing coverage we find then a climb to a maximum Q near3.5 layers, the minimum of c , showing that the high compressibility of the film at that pointalso plays a role in the Q factor.Fig. 3 shows a temperature sweep carried out at the coverage of 3.32 layers. At lowtemperatures there is a slow decrease of c , with a polynomial fit showing primarily linearand square components in the decrease. Above 520 mK there is a sharp decrease in the Q,and the beginning of a faster drop in c , and we identify this as the onset of the vortex-pair c ( m / s ) Q T KT Figure 5.
Temperature sweep at 3.93 layers. c ( m / s ) Q T KT Figure 6.
Temperature sweep at 4.34 layers. T K T ( m K ) Number density (atoms/Å ) present results, nanotubes Crowell and Reppy, Grafoil Zimmerli and Chan, HOPGFilm thickness (layers)43 5 Figure 7.
Superfluid onset temperatures versus coverage, compared with Refs. [4, 6].Kosterlitz-Thouless transition. The very high dissipation prevents following c to lower values,which is quite different behavior from our previous studies of third sound on alumina powder [2]where we could follow the broadened c to as low as 20% of its initial value. This observationof high dissipation on the cylindrical nanotubes, however, is in qualitative agreement with thepredictions of Guyer and Machta [9] for the KT transition on cylinders, where the driven vortexpairs can counter-rotate around the cylinder, giving attenuation comparable to that on flatsubstrates. They also predict a strong finite-size broadening of the transition due to the finiteratio of the nanotube radius to the vortex core radius, which is apparent from the relativelyslow decrease of the third sound speed above T KT , though due to the loss of signal this cannotbe quantified.Fig. 4 shows a temperature sweep at 3.51 layers, close to the minimum in c . The unusualfeature here is the linear increase of c with temperature. This can only occur if the superfluiddensity increases with temperature, or if the thickness of the film decreases with temperature.The latter possibility seems more likely, since the compressibility of the film is near its maximumhere, and might further change with T . However, it is also possible that internal structuralchanges in the film could lead to an increase in the superfluid density. With this thicker filmthere is an increase in the onset temperature T KT . At coverages just above the minimum in c the low-temperature speed goes back to uniformly decreasing with T , but now the decrease isntirely linear at the lowest temperatures.For coverages near the maximum in c at the fourth layer completion, we find a markeddepression in the superfluid onset temperatures, as shown in Fig. 5 at 3.93 layers, and then afurther increase with higher coverage as in Fig. 6 at 4.34 layers. This is re-entrant superfluidity,as shown in the onset temperatures plotted in Fig. 7: adding coverage at a fixed temperatureof say 600 mK would see superfluidity disappear at 3.8 layers, and then reappear at 4.1 layers.This behavior at the fourth layer completion appears to be unique to the nanotube films, asit is not observed on the Grafoil substrate [6], whose onset temperatures are also plotted onthe same graph. The Graphoil data only shows a relatively constant T KT near the third layercompletion (visible in Fig. 7), and nothing similar at the fourth layer completion. There havebeen simulations [10] predicting a drop in superfluid density at layer completions, from theincreasing atomic repulsion, which would translate to a drop in T KT such as we observe. Theeffect seems to be much stronger on the nanotubes compared to flat substrates.The dashed curve in Fig. 7 shows a linear fit to our onset temperatures (excluding the threepoints near the fourth layer completion), with an onset thickness extrapolating to 2.4 layers,similar to that found in [6] in the third layer. The slope of this curve, however, is only about1/2 of the expected KT universal value, shown as the solid line in the plot for an onset thicknessof three atomic layers as deduced on the HOPG substrate [4]. This is unusual, but it also seemsto be the same result found on the Grafoil substrate [6], where we have plotted the reporteddissipation maximum, which should track T KT . It appears as if only about 1/2 of the atomsthat are being added actually join the superfluid condensate. It is unclear why this occurs:possibilities are that there could be a strong localization of atoms at defects on the substrate,or if gas-liquid phase separation occurs, the gas atoms might not be superfluid, as speculatedin [6]. The HOPG substrate experiment, however, appeared to find results consistent with theuniversal KT line, but unfortunately with only two data points. Our finding in Fig. 2 thatthird sound could not be observed at any temperature below about 3.2 layers brings up thequestion of whether the onset seen in Ref. [4] at 3.4 layers and 0.639 K was an actual KT onset,or simply the same third sound signal loss from high dissipation we observed on approachingthe third-layer completion point.We have found no evidence in our measurements of helium adsorption inside the nanotubes,though that may have occurred. The TEM pictures seem to show a few tubes with what appearto be open ends, but also some of the tubes show closed end caps. If helium did enter it wouldhave been at the very beginning of the fill, due to the strong effects of surface tension. Acknowledgements
We thank William Hubbard and Chris Regan for taking the electron microscope photos at theUCLA NanoSystems Institute. This work was supported in part by the U. S. National ScienceFoundation, Grant No. DMR 0906467.
References [1] Menachekanian E and Williams G 2012
J. Phys. : Conf. Series
Phys. Rev. B [4] Zimmerli G, Mistura G and Chan M H W 1992 Phys. Rev. Lett. J. Low Temp. Phys. Phys. Rev. B Phys. Rev. Lett. Phys. Rev. B (16) 165409[9] Machta J and Guyer R 1989 J. Low Temp. Phys. Phys. Rev. B50