## Supersolidity and disorder

It is not often that one attends a colloquium in the Physics department and gets to hear about grain boundaries, dislocations, wetting, grain boundary grooving and coarsening. However, today was one such rare day when I got hear about all those things and more.

I have written about Prof. Sebastian Balibar and his work on liquid and solid helium in an earlier avatar of this blog. I have also written about resistance free flow in solid helium a couple of times: here and here for example. Today, I got to hear Prof. Balibar on the role of disorder (defects) in promoting such resistance free flow in solid helium. Here are my notes from the talk — with one disclaimer: I am going to skip the details of the theoretical background to the problem of Bose-Einstein condensation in solids, and their role in superplasticity that Prof. Balibar described in great detail in the early part of the talk simply because of my unfamiliarity with the issues; my understanding of the area is far too patchy to attempt a summary.

Prof. Balibar began his talk by defining supersolid as a solid which is superfluid; of course, this is a bit paradoxical since solids are defined as bodies with transverse elasticity (non-zero shear modulus) as a consequence of atomic localization; on the other hand, superfluids are quantum fluids with zero viscosity (which is a consequence of Bose-Einstein condesnation), and hence, atoms are undistinguishable and delocalised.

Prof. Balibar then described some experiments carried out by Kim and Chan which showed the existence of such a superfluid property in solid 4He (the fraction of solid that had such a property being calculated as 1% or so), while no such effect was observed in 3He. After describing some of the theoretical studies (Penrose and Onsager [1956], Andreev and Lifshitz [1969], Reatto and Chester [1969], Imry and Schwartz [1975], Leggett [1970], Prokofev, Svistunav, and Boninsegni etal [2005-2006], Clark and Coperley [2006], Cazorla and Boronat [2006] and several others) which made conflicting predictions about the possibility of the existence or non-existence of such an effect, Prof. Balibar described some experiments carried out in own group and that of others which indicate the importance of defects and disorder in promoting such an effect.

Rittner and Reppy (from Cornell, and in the years 2006 and 2007) reported on a couple of their experiments which proved beyond doubt the role of defects (more specifically, grain boundaries) in promoting such an effect: (a) as the samples are annealed, the supersolidity disappears; and, (b) if the solid He sample is prepared by fast quench (resulting in very small grain sizes), the magnitude of the effect increases dramatically; for example, the fraction of solid that behaved like a superfluid could be as high as 20%.

The experiments carried out by Prof. Balibar and his co-workers also seemed to support Rittner and Reppy, initially. However, closer inspection of the results (which involves all the stuff I mentioned in the first paragraph — grain boundary grooves, coarsening in helium polycrystals, wetting at the grain boundaries and the channels that form at the meeting points of grain boundaries and glass walls of the container) have convinced Prof. Balibar and his colleagues that that is not the complete story. Apparently (and, it was anticipated by Prof. Pierre De Gennes shortly before his passing away), dislocations also play a crucial role.

Finally, before ending the post, Prof. Balibar was careful to mention that though he thinks that supersolidity can be explained using such mechanisms that involve defects, there has been at least one experiment to indicate a bump in the specific heat in these samples at around the same temperature where supersolidity is seen indicating that the involvement of a phase transition which gives rise to supersolidity is far from ruled out.

For those of you who are interested in knowing more about this problem, here are the references that Prof. Balibar listed for his talk:

Superfluidity of grain boundaries and supersolid behaviour

When two communicating vessels are filled to a different height with liquid, the two levels equilibrate because the liquid can flow. We have looked for such equilibration with solid 4He. For crystals with no grain boundaries, we see no flow of mass, whereas for crystals containing several grain boundaries, we detect a mass flow. Our results suggest that the transport of mass is due to the superfluidity of grain boundaries.

Supersolidity and the thermodynamics of solid helium

The specific heat of solid helium in the temperature range below about 1.2 K has been found to contain a term varying as T 7, in addition to the usual T 3 contribution always found in a crystalline dielectric solid. It has been proposed by Anderson, Brinkman and Huse, (Science 310, 1164 (2005)) that the existence of this T 7 term supports their theory of supersolidity. However, in this paper we show that corrections to the phonon specific heat arising from phonon dispersion are much larger than expected based on simple order of magnitude estimates and, as a consequence, it is very unlikely that the existence of this T 7 term can be considered as evidence for supersolidity.

Wetting properties of grain boundaries in solid 4He

We have observed boundaries between hcp 4He crystal grains in equilibrium with liquid 4He. We have found that, when emerging at the liquid-solid interface, a grain boundary makes a groove whose dihedral angle 2$\theta$ is nonzero. This measurement shows that grain boundaries are not completely wet by the liquid phase, in agreement with recent Monte Carlo simulations. Depending on the value of $\theta$, the contact line of a grain boundary with a solid wall may be wet by the liquid. In this case, the line is a thin channel with a curved triangular cross section, whose measured width agrees with predictions from a simple model. We discuss these measurements in the context of grain boundary premelting and for a future understanding of the possible supersolidity of solid 4He.

Supersolidity and disorder (Topical Review)

A solid is called ‘supersolid’ if it exhibits superfluid properties. Supersolidity is a paradoxical phenomenon whose understanding has become a major challenge since 2004, when Kim and Chan first observed what could be mass superflow through solid helium 4. In this review, we describe how successive experiments indicated that what was observed in helium 4 was not intrinsic properties of the crystalline state as originally proposed 35 years before. Disorder coming from how the solid is grown (dislocations, grain boundaries and other interfaces, liquid or glassy regions, impurities…) was shown to play an essential role. However, one does not know yet which type of disorder is involved or by which mechanism it leads to the observed properties. Furthermore, all the experimental features probably cannot be explained by a common mechanism. Recent measurements of the shear modulus of helium 4 crystals could even be explained without the need of any superfluidity. In fact, many theoretical predictions need to be checked experimentally, so the whole issue is far from understood. Even some crucial experiments would need to be repeated more systematically. The present review of the experimental observations and theoretical scenarios raises a series of questions which call for answers.

Have fun!

### One Response to “Supersolidity and disorder”

1. Flow in solid Helium: an update (and some superconductivity news to go with it) « Entertaining Research Says:

[…] American Physical Society meeting, the interpretation of which seems to be in disagreement with the “disorders promote superflow” thesis advanced by Balibar and others that we discussed recently: Oddly, although most physicists […]