Experiments with Solid Helium

Solid Helium: Searching for Flow


A few years ago it was observed that if a container filled with solid helium was rotated, some of the solid helium appeared to be left behind by the rotation [1]. This led to the interpretation that solid helium might be acting like a "supersolid", as state of matter that had been long-ago predicted [2] but never seen. Although this unusual observation has been confirmed in a number of laboratories, attemps to make the solid flow by squeezing on it directly have shown that it is impossible to create flow by this technique [3]. This observation too has been confirmed [4].

We decided to try to look for flow through helium by a concptiually different approach [5,6]. Rather than squeezinig the lattice of solid helium directly (if you squeeze a porous rock, no water will come out even though the water may fill all the open and connected pores of the rock), we decided to try to inject atoms from the liquid phase. Typically this is not possible beacuse superfuid heliumin direct contact with the solid would cause a hopelessly large heat flux to the sample cell. We created an enviromnent in which porous glass pennetrated the region of our apparatus that was filled with solid helium. In porous glass the freezing pressure of solid helium is well above the normal 25 bars. Thus, by pressurizing the liquid in the porous glass we could attempt to inject helium atoms into the solid that was in contact with the liquid helium held in the porous glass. Figure 1 is a schematic illustration of the apparatus [5,6].

Figure 1: Cell used to study the growth of solid helium from superfluid helium. Helium is admitted to the solid chamber S through capillaries 1 and 2 (heat-sunk only at 4 K) which first lead to liquid reservoirs atop thin porous glass (Vycor) rods V1 and V2. The reservoirs are heated by heaters H1 and H2. Two capacitance strain gages, one on each side of S measure the pressure of solid, while the temperature is measured by carbon thermometer TC. The pressures of the fill lines are measured by pressure transducers P1 and P2 located outside of the cryostat. A third capillary, 3, was heat sunk in several places including the coldest heat exchanger, bypassing the Vycor and was used to initially fill the cell with liquid helium, which was then frozen.

The principle of operation of the appartus is rather simple. One presurizes one of the fill lines, e.g. #1, and looks for a response on the other fill line, #2. Any change in the pressure observed on the other fill line or the cell implies that atoms had to migrate through the experimental cell, which is filled with solid helium. Thus, any change in the pressure in line #2 indicates that mass moved though the solid helium from line #1 to line #2.

Figure 2: An example of a sample of solid helium (Sample BS; ref 6) showing a flow of mass through solid Helium. The pressure in R1, P1, was increased at t $\approx$ 6 minutes, the regulator feeding helium to line 1 was closed at t $\approx$ 30 minutes, and changes in pressure were observed for about 6 hours. Note that dP2/dT was nearly linear for a substantial duration and independent of P1-P2. A change in the pressure of the solid helium in the cell is also recorded on the in situ pressure gauge C1.

The data in figure #2 and other data like it demonstrate that it is apparently possible to transfer atoms through solid helium. The physical mechanism by which this takes place has yet to be fully understood. But, as shown in the next figure, some regions of the solid helium phase diagram do not seem to result in the movement of atoms through the solid. So, if this is the case there must be a transition in properties in the solid that depends on pressure and temperature.

Figure 3: An example of a sample of solid helium that did not show flow. Sample BT was warmed from 400 to 547 mK (from sample BS). The sample at 547 mK did not show flow. In this case the regulator fed atoms into R1 for about 30 minutes, but over 7 hours there was no significant movement of the pressures towards equilibrium. Colder temperatures result in flow; higher temepratueres at nearly the same pressure do not. Samples at temperatures above 600 mK have never shown flow in any of our experiments.

Much more work remains to be done in this extremely active area of current research. The various experiments that have been done in various laboratories sometimes lead to conflicting conclusions. And, various theoretical predictions have been made, but none has been unambiguously confirmed. So, much remains to be learned in this area and we continue our experiments [7, 8, 9, 10].


[1] E. Kim and M. Chan, Nature (London) 427, 225 (2004); Science 305, 1941 (2004).
[2] O. Penrose and L. Onsager, Phys. Rev. 104, 576 (1956); G.V. Chester, Phys. Rev. A 2, 256 (1970).
[3] J. Day and J. Beamish, Nature (London) 450, 853 (2007).
[4] A. Rittner, W. Choi, E.J. Mueller and J.D. Reppy, arXiv:0904.2640.
[5] M.W. Ray and R.B. Hallock, "Observation of Unusual Mass Transport in Solid hcp 4He", Phys. Rev. Lett. 100, 235301 (2008).
[6] M.W. Ray and R.B. Hallock, "Observation of Mass Transport thought Soild 4He", Phys. Rev. B 79, 224302 (2009).
[7] R.B. Hallock, "Experiments with Solid 4He", Physica A 389, 2894 (2010).
[8] M.W. Ray and R.B. Hallock, "Mass Flux and Solid Growth in Solid 4He for 60 mK - 700 mK", Phys. Rev. Lett. 105, 145301 (2010).
[9] M.W. Ray and R.B. Hallock, "Mass Flow through Solid 4He Induced by the Fountain Effect", Phys. Rev. B 84, 144512 (2011).
[10] Ye. Vekhov and R.B. Hallock, "Mass Flux Characteristics in Solid 4He for T > 100 mK: Evidence for Bosonic Luttinger Liquid Behavior", Phys. Rev. Letters 109, 045303 (2012).