Solids and Supersolids

“Whether a supersolid phase of matter has indeed been observed in recent solid helium experiments1,2,3,4,5 is still an open question”. This is how one would start a seminar, or a research article on the subject of supersolid helium, addressing an audience of fellow physicists, who would listen patiently, quietly and attentively, waiting for the next transparency to show up on the screen (at which point dozing off is quite accepted… but, I digress).

Friends and acquaintances (non-physicists… normal people) who ask me about my research, or are curious to know what a supersolid is (after reading about it in the newspaper or on the internet), are typically much less patient. “What the heck is a supersolid anyway ?”, “What’s so super about it ?” are their reasonable and obvious questions. And for me, it’s downhill from there. I am soon asked whether I am making stuff up, if I even know what I am talking about, then on to if I have ever considered doing actual work for a living… I find myself praying for the arrival of the pizza delivery guy, to pull myself out of that predicament.
I am in good company, though. Explaining in “layman terms” the main aspects and goals of their work has always been one of the biggest challenges that scientists face, one with plausibly serious, far-reaching repercussions in terms of societal appreciation and overall enthusiasm toward science, and of course its funding. There are many complex reasons for this, not the least the fact that this stuff just isn’t all that easy to explain (alas, most laymen just don’t know much physics…).
In the case of the (hypothetical) supersolid phase of matter the situation is even funnier, because a considerable degree of confusion and bewilderment as to what exactly it should be, exists even among those of us who spend a sizeable portion of our waking time trying to understand matter, and its properties.
Taking advantage of the splendid impunity granted by blogosphere, I am going to take a stab at this.

Looking at physics textbooks, or research articles, one encounters formal definitions of the supersolid phase of matter, filled with such jargon as “simultaneous diagonal and off-diagonal long-range order”. Mathematically rigorous as they are, these definitions scarcely help even a specialist gain any kind of intuitive understanding.
If solid helium indeed undergoes a phase transition into a supersolid phase at low temperature, as proposed some forty years ago and as some recent experiments seem to indicate, how does it change macroscopically ? Does it get softer ? Stiffer ? More transparent ? Would one be able to tell a regular solid from a supersolid just by looking at it ?

Supersolid stands for superfluid solid. Let us begin with the easy part, which is the solid. We are all clear as to what a “solid” is. It has several properties that distinguish it from a liquid or a gas. It is not a gas because it is condensed, i.e., it stays together and does not fill all of the available volume (the way a gas would). It is not a liquid because it is “stiff”, or, more precisely, it offers resistance to shear.
The “superfluid” part is trickier. A superfluid is something capable of flowing without dissipation. I’ll get to what this means in a moment, but first I should mention that the only known (naturally occurring) substance to display this behavior is helium, in its liquid phase, and at very low temperature (below 2.2 K, i.e., -270.8 oC or -455.5 oF for the most abundant isotope of helium, namely 4He…. I’ll spare you a popular local joke about these temperatures and Winter in Alberta…).
When in its superfluid phase, liquid helium displays a behavior unlike that of a conventional liquid. Imagine filling a long pipe with it, and then establishing flow by means of a pump, connected to the two ends of the pipe, as one could do with water. Now we switch off the pump; while the flow would soon cease, if water or any other conventional fluid filled the pipe, the helium liquid would continue to flow, pretty much indefinitely, as if it had no viscosity (such a persistent flow has indeed been observed in a number of experiments equivalent to the one described here).

All right, now comes the big question: how can the two apparently antithetical behaviors of a solid and of a superfluid be combined into a single phase ? This is where much of the confusion arises. What would supersolid helium do, that solid helium does not ? Would it flow like a liquid, even persistently so, all while being a solid ? Experiments carried out at University of Alberta show that it does not. Indeed, for the most part supersolid helium will look and feel like a regular solid [0]. Any experiment aimed at exposing its “super” character, will be, to a greater or lesser degree, indirect. Indeed, one such experiment is precisely the torsional oscillator measurement which first yielded evidence of a possible supersolid transition in 4He.

Another possible experiment that would tell a normal solid and a supersolid apart, and perhaps illustrate cogently the different behavior of the two solid phases, is the following. Consider again a pipe, and this time let us begin by assuming that it is filled with water, right at the freezing temperature where liquid water coexist with ice. Suppose that water is frozen in a section of the pipe, clogging it (middle part of the figure below), while liquid water occupies the rest of the pipe [1].

As we know from experience, one would not be able to make water flow through the pipe (for example, in the direction shown by the arrows), due to the presence of ice (solid water) clogging the frozen section of the pipe. The same would be true of superfluid helium, which could not flow through the same section of the pipe, if it were filled with normal solid helium. But, if instead of normal solid helium, supersolid helium were present in the pipe, then flow of superfluid helium would occur. In other words, whereas water cannot flow through ice, a superfluid would instead manage to flow through a supersolid made of the same elementary constituents (atoms or molecules).

There have already been experiments aimed at observing the very behavior described above, which would definitively prove the existence of a supersolid phase of helium; their interpretation has proven somewhat ambiguous, especially with respect to the possible role of defects in the solid. Other similar experiments are ongoing, or planned.
In these experiments, like in the one described above, the supersolid would manifest itself as “porous” to flow, unlike a normal solid, not due to an actual greater porosity of the supersolid compared to the normal solid, but rather because of a fundamentally quantum mechanical effect, namely the exchange of indistinguishable particles.
In simple terms, it works like this: both superfluid and supersolid helium are made of the same helium atoms. These are relatively light atoms (only hydrogen atoms are lighter), which means that quantum-mechanical effects are important at the low temperatures at which these experiments are carried out, much more so than for heavier atoms or molecules. When two helium atoms are brought in the vicinity of one another, their fundamental indistinguishability translates in their capability of exchanging, essentially trading place with one another. These exchange processes need not be restricted to just two atoms; several such atoms can be involved in an exchange cycle, similar to a merry-go-round, and in a superfluid (and supersolid), very long such cycles occur, to which a finite fraction of all the particles in the system participate.
The “porosity” of supersolid helium, that one ought to observe in an experiment such as the one sketched above, arises essentially from exchanges. That is, helium atoms in the superfluid phase, flowing toward the frozen blockage (left part of the figure), can essentially “emerge” on the right side through a process of exchanges with atoms in the supersolid. All the while, the (super)solid itself does not move, but the superfluid keeps flowing through the pipe. The indistinguishability of the atoms in the superfluid and the supersolid is a crucial ingredient. If in the above experimental setup, the superfluid and supersolid were made of different atoms [2], then flow of the superfluid through the frozen, supersolid section would not take place.

Notes
[0] It should be mentioned for completeness that there is experimental evidence that resistance to shear of solid helium changes somewhat in the range of temperature where supersolid behavior has been reported. The connection between this aspect and superflow is not clear at this time.
[1] The frozen section is assumed to be of macroscopic length (e.g., visible by naked eye). Different quantum-mechanical effects unrelated to supersolidity, e.g., tunnelling of the superfluid across the frozen section, could also occur if the length of the frozen section of the pipe were to become very small, say of the order of several atomic diameters, even if the material in the frozen section were other than helium.
[2] For example, the superfluid and supersolid could be made of different isotopes of Helium, namely 3He and 4He. These are two different types of helium atoms, which have the same electronic configuration and thus chemical properties, but different nuclear masses.

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