The Mystery of "Supersolid" Helium

One of the other ScienceBloggers is prone to complaining in the back-channel forums that we don't have enough bloggers who work in some subfield of biology or another-- we need more left-handed shrew ecologists, or some such. This is, of course, patently ridiculous. What we need is a physics blogger from the condensed matter world, so we'd have somebody to explain what's up with "supersolid" helium:

Superfluidity was discovered in the liquid phase in 1938, when Pjotr Kapitsa - who shared the 1978 Nobel prize for the work - found that liquid helium-4 suddenly behaves as if it has zero viscosity when cooled below a temperature of about 2 K. With no resistance to flow, a superfluid can do bizarre things such as creep up the sides of a vessel containing the material or pass through holes just a few atoms wide. Superconductivity, a similarly dramatic low-temperature phenomenon in which electrical current flows without resistance, is due to the superfluidity of electron pairs. However, in 2004 Moses Chan of Penn State University in the US and his then graduate student Eun-Seong Kim reported evidence for superfluidity in a much more unlikely setting: the atomic lattice of bulk-solid helium-4.

Such a "supersolid" phase of matter would flow through a classical solid as if it were not there. Like superfluidity in a liquid, this weird behaviour is predicted to be a consequence of Bose-Einstein condensation - a phase transition in which all the particles in a system collapse to the same ground state and can therefore no longer be treated as individual entities moving at random. Such quantum degeneracy is possible because helium-4 atoms are bosons, i.e. particles that have integer multiples of spin angular momentum.

I recognize all the words in those paragraphs, but I'm not entirely sure what they mean. Of course, my impression from the rest of the article is that nobody else is entirely sure what's going on, either, so I guess I'm in good company.

The chief evidence for "supersolid" helium is a torsion pendulum experiment done by Moses Chan and his group. Their apparatus consists of a small cylinder suspended from a thin wires, that they can cause to twist back and forth. The cylinder is mostly solid, with a narrow channel near the rim that they can fill with helium. They fill this up with helium, and by varying the temeprature and pressure in the system, they can force that helium into a solid phase, and then continue lowering the temperature until they see the "supersolid" transition.

What they measure is the rotational frequency of the torsion pendulum. The cylinder twists back and forth at a characteristic frequency that depends on both the mass of the cylinder and how it's distributed. The frequency of oscillation when the cylinder is full of He is higher than the frequency when it's empty, for example, because there's more mass toward the outside in the full cylinder.

There's also a difference between the oscillation frequencies for the solid and "supersolid" phases. When the system goes through the "supersolid" transition, some fraction of the atoms in the system begin moving freely through the solid lattice, without friction. This allows them to essentially stop rotating-- while the regular solid atoms turn with the cylinder, the "supersolid" atoms just stay put and let the rest of the solid flow past them.

The effect is a little like the hard-boiled egg trick. If you want to know whether an egg is hard-boiled or not without breaking it open, you can set it on its side on a table, and spin it. A hard-boiled egg will spin happily for a long time, while an uncooked egg will stop spinning relatively quickly because the liquid yolk doesn't rotate with the shell. In the case of the egg, the non-rotating liquid creates drag on the shell that stops the spin quickly. In the case of "supersolid" He, the non-rotating solid is frictionless, so it just smoothly decouples from the motion. The effect looks like a small reduction in the mass of the twisting cylinder.

That's the story, anyway. The problem is, all sorts of quirky results are cropping up. Chan's original experiments showed something like 2% of the atoms moving into the "supersolid" state. Subsequent experiments changing the amount of disorder in the system-- freezing the helium very slowly, to produce nearly perfect crystals, or freezing it very quickly to produce lots of cracks and fissures-- have found that the amount of disorder changes the supersolid fraction dramatically. Increasing the amount of disorder pushes the supersolid fraction as high as 20%, while decreasing it pushes the fraction as low as 0.5%. Existing theories really don't explain this, so something really weird is going on.

(It pains me to have to add that nobody is suggesting that Chan and his colleagues did anything inappropriate. The basic effect that they see has been reproduced by other groups, but the magnitude of that effect varies in an unexpected way with some other parameters. The original interpretation of the results is in question, but the results themselves are solid. Pardon the pun.)

Unfortunately, right here, just where the story starts to get interestingly twisty, is where I decouple from the motion. My condensed matter/ solid state background is not that good, and I really can't follow the intricacies of the debate about what's really going on. the Physics Wold article includes a bunch of speculations from theorists about what's going on, but for all I understand of it, they might as well be saying "Mwah wah mwah mwah WAH wanh," like the adults in a Charlie Brown cartoon.

Which is why we need some good condensed matter physics bloggers here. Somebody needs to explain what's going on here in terms that even an idiot atomic physicist can understand.

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You've hit the high points already in fine style. In the solid state if you remove an electron from a filled band, rather than describing the remaining electrons collectively, it's often easier to keep track of the "hole" left behind, and treat it like an effective particle with charge +e. (We could get into a lengthy debate about what a particle is in this context - a hole is a well-defined excitation of the system with its own quantum numbers, and one can argue that it is just as real as other kinds of particles, though it cannot exist outside the solid. Anyway....) Decades ago people wondered whether the vacancies in crystals of solid 4He could undergo a form of Bose-Einstein condensation and be a weird superfluid.

One signature of this would be some kind of "nonclassical rotational inertia" as you described above. Torsional oscillators (buckets twisting on support rods) have long been the way to study superfluids. In the superfluid state there is no viscosity, and so the fluid becomes decoupled from the walls of the twisting bucket. Once that happens the mass of the torsional oscillator is effectively lower (it's as if the bucket is now empty, in the limit that 100% of the liquid inside is a superfluid).

People looked for this for a long time in solid 4He without finding anything, and I believe that pretty sophisticated theory calculations showed that it was unlikely. In 2004, Moses Chan reported an effect that is real, but it would appear that it is not an intrinsic property of clean, single-crystal 4He with a few vacancies. Rather, amorphous solid 4He at grain boundaries and the interface with the container walls appears to be necessary to see this effect. The difficult question to resolve has been whether there really is a liquid layer that they just can't eliminate. It now appears that there is not a liquid layer in there, but that you need very defect-laden solid to see anything.

I've always been curious about the distinction between supersolid helium and the LOFF (Larkin, Ovchinnikov, Fulde, and Ferrell (sp?)) phase in deconfined quark matter in a neutron star. The latter is indeed "superfluid" and a "solid", but not necessarily a "supersolid"?!?. I asked Moses Chan about this, but he didn't seem to know immediately, but...anyone...?

How many phases of matter are we up to now? I can't keep track. Seems like a new one is found every couple years.

I don't think there is a particular relationship between the FFLO (that's the acronym I learned, anyway) state and the supersolid in 4He. In particular, the FFLO state is relevant for paired fermions that have internal quantum numbers (e.g. spin) and different populations of the species (e.g. there's a Zeeman splitting between spin up and spin down, such that there are more spin down fermions around). For 4He, the individual particles are bosons. There has been a lot of talk about observing the FFLO state in ultracold trapped Fermions, though. My faculty colleague Randy Hulet has been working in this area, as has Wolfgang Ketterle's MIT group.

I'll just add a few explanatory words to what Doug said above, to try to give an intuitive feel for what might be happening.

A (crystalline) solid is a rigid lattice of particles that keep a fixed distance between particles throughout the entire sample. Many believe that Chan crystallized a whole set of domains of solids, each with different orientations. At the interfaces, though, the helium can't decide which crystal to join, so there's a small liquid phase at every interface. Of course, at low temperatures, this liquid phase becomes superfluid, and the interfaces extend through the whole sample, so this superfluid that exists at the boundaries of the solid domains is free to move through the sample.

This explains why the annealing work you mentioned changes the supersolid fraction. If you cool quickly, you get lots of domains (just as in any crystal) and thus a high supersolid fraction. Annealing or cooling slowly drastically suppresses supersolidity as the domains get larger and thus the size of the interfaces goes down.

Doug: There are actually a couple of CM bloggers out there - I touched on this topic very briefly here: [URL] and the Incoherent Ponderer had a great, lengthy post about it here: [URL]

I saw your post, but I hadn't seen Ponderer's. I don't regularly read that blog, so it may have been buried in the Mixed States overflow when Steve Hsu barfed out a million or so old posts into the RSS feed. That is a nice explanation, thanks.

Valerie: How many phases of matter are we up to now? I can't keep track. Seems like a new one is found every couple years.

Quite a few. Solid, liquid, gas, plasma, BEC/supefluid, maybe "supersolid"... I'm not sure whether things like neutron stars count as a different phase of matter or not, though I'm sure somebody's claimed it. Quark-gluon plasma/ liquid/ whatever it is they have at RHIC.

"Phase" is a sloppily used term, that's for sure.

I've followed this through excellent articles in Physics Today, Physics World, Science News, and Discover, such as:

Physics Today, April 2004
"Evidence reported for a "supersolid" phase of helium-4"
The most likely explanation for a sharp drop in rotational inertia in crystalline 4He is the onset of superfluid behavior."

Levi, Barbara Goss
American Center for Physics, One Physics Ellipse, College Park, Maryland 20740-3842
Physics Today, Volume 57, Issue 4, pp. 21-22 (2004).
Publication Date:
solid helium, torsion, oscillators, superfluidity, superfluid helium-4, quantum solids
Bibliographic Code:

Jacob - The concern was that there is fluid at those interfaces. I think that there are still some stalwarts who hope that the highly disordered boundaries are more like a glass than a liquid, and that therefore this is still some sort of supersolidity. I haven't looked carefully at this.

Valerie - part of the issue is that the term "phase" is used sloppily. From the theory perspective, a phase transition (which must occur between at least two distinct phases) involves the change in some "order parameter" across the transition. For example, you can define an order parameter based on the density of particles such that the parameter is zero in the gas phase and nonzero in the liquid phase. In that sense, there are many many phases just in solids - magnetically ordered phases (ferromagnets, antiferromagnets, spin liquids), electronically ordered phases (Fermi liquid, superconductivity, charge density wave), etc. These aren't as dramatic as solid/liquid/gas/plasma, but in the thermodynamic sense, they are real phases.

Yes, there is a theory according to which non-classical rotational inertia (NCRI) actually results from superfluid liquid 4He located between the 4He crystallites. But, the thickness of the liquid helium film with superfluid temperature around 200 mK (the temperature which correspond to supersolid transition in Kim and Chan experiments) should be 0.03 nm (approx 0.1 of monolayer). This means that enormous surface arias are necessary to explain NCRI experiments. This would require the solid 4He crystallites to have the grains size of 10 nm which is not possible. Recently Chan et al. carried out new torsional oscillator measurements but in this case they measured very high quality single 4He crystals with a low 3He concentration (1 ppb). They found the same "supersolid" effect indicating that grain boundaries are not the responsible mechanism.

The interesting thing is that except for the torsional oscillator experiments, other experimental techniques (i.e. neutrons, thermal conductivity, the second sound measurements, X-rays) did not confirm the supersolid behavior. However the group led by Prof. Goodkind (UCSD) studied the propagation of longitudinal ultrasound through solid 4He - when they added as little as a few parts per million of 3He, they observed a sudden increase in the velocity and dissipation of the sound waves near 200 mK. They interpreted this as being due to a thermodynamic phase change - possibly a Bose-Einstein condensate. Our (University of Alberta) recent transverse ultrasound measurements in 4He single crystals did not give a clear answer as well. All of the 11 crystals we measured showed some dislocation effects but there is nothing unusual in it. We were able to increase the dislocation/defects density in our crystals but this did not produce any other effects or evidence for a supersolid state at low temperatures. In one as grown crystal we observed a very large increase in attenuation and a corresponding decrease in the velocity around T = 95 mK (supersolid transition?). So the only clear thing in this subject is that nothing is clear ;-)