“O, that this too too solid flesh would melt, Thaw, and resolve itself into a dew!”
Here Hamlet contemplates a “phase transition” decades before the advent of classical thermodynamics and centuries before quantum mechanics. Shakespeare, ever the prescient observer, builds the metaphor for physical transformation by analogy with changes in a macroscopic collection of molecules he had witnessed — water which changes from solid to liquid to vapor as temperature increases.
Fast forward almost exactly five hundred years since “Hamlet” was first performed at the Globe to the year 2004 and the Penn State University laboratory of physicist Moses Chan, where temperatures can be lowered to 0.2 Kelvin (0.2 above absolute zero), and pressures on a quantum crystal of helium-4 can be increased to 25 times that of earth’s atmosphere at sea level. What may be emerging is a new phase of matter — a “supersolid” both crystalline and superfluid. At issue is the nature of “solid.”
Said Chan, “We thought a crystalline solid is something we all understand — rigid, reliable, stay-put. Our data is indicating, ‘no, not quite’ if the temperature is low enough.”
“We thought a crystalline solid is something we all understand — rigid, reliable, stay-put.”
Theoretical solid-state physicists (Andreev, Lifshitz, Chester, and Leggett) have been envisioning supersolidity since the early 1970s.
“I think theoretical physicists would say what we have seen is not impossible, but the probability of seeing a sufficiently large signature is very small. So in that sense we have exceeded the expectations of theoretical physicists,” said Chan.
David Ceperley, a theoretical solid-state physicist at the University of Illinois at Urbanna, said, “We thought the probability was low because in a solid we think of atoms as localized at the sites. Push on one side of a lattice of atoms in a solid and the atoms should just stay where they are and not move. But then there were these theories that a supersolid phase should exist. There have been searches since the ‘70s that till 2004 have come up with nothing.”
Chan did not find supersolidity by chance. He said, “A colleague at UCSD [University of California at San Diego, John Goodkind, had done some ultrasound measurements over the years, and he saw something rather unusual. The signature he found, while complicated, suggested a phase transition takes place in solid helium near 0.2 Kelvin. John Goodkind’s findings said to me, ‘There’s something funny here; maybe we should take a look.’”
The KITP has instituted a singular, new kind of program—Rapid Response—to address breaking developments in science. Inaugural participants include Moses Chan (l), Phil Anderson, and David Ceperley.
Photo by Nell Campbell.
Chan decided to employ a technique developed by his PhD mentor, Cornell University physicist John Reppy, in the 1970s. That approach enabled Chan to measure directly the non-classical rotational inertia (signature of a supersolid) that Ceperley’s Illinois colleague and 2003 Physics Nobel laureate Tony Leggett had specifically calculated.
What the experiments say about supersolidity and what the theorists thought are not, however, in complete agreement.
Such a confusing picture proved perfect for initiating a new kind of effort at the Kavli Institute for Theoretical Physics at the University of California at Santa Barbara — Rapid Response. Initially supported through Kavli Institute funding, the Rapid Response program aims to address breakthroughs such as Chan’s in a timescale of months, instead of the customary one to two years.
Address how? By bringing together, from around the globe, some 30 aficionados of supersolidity to tackle intensely the issues associated with “The Supersolid State of Matter” (Feb. 6 to 17, 2006). Chan and Ceperley orchestrated the Rapid Response.
The first exciting development of the two-week mini-program — and there were at least two developments that have, according to Ceperley, “changed the nature of the discussion” — was the announcement of confirmation by three other experimental groups of Chan’s discovery. All three groups were represented at the Rapid Response program: John Reppy from Cornell University; Keiya Shirahama of Keio University, Japan; and Minoru Kubota of the University of Tokyo. That was an important milestone for supersolidity because it dispelled for theorists the specter of experimental non-reproducibility and therefore hesitancy about pursuit of theoretical understanding.
The fact of the KITP Rapid Response seems to have speeded up the process of experimental confirmation because the experimentalists pushed to complete confirming experiments in order to report and discuss their findings at the KITP mini-program that brought together a more exotic type of attendee to KITP programs — experimentalists — with the staple participants — theorists.
Take that old fixture of ‘50s house parties, the Lazy Susan tray, and load it with perfectly smooth ball bearings, instead of nuts or mints. Now put a saucer on top of the ball bearings and rotate the Lazy Susan. If the ball bearings and saucer were to behave like a supersolid, the saucer, despite the moving Susan, would not move.
So what is supersolidity? A deep physics explanation, as opposed to a visually analogous explanation (via Lazy Susan laden with ball bearings topped by a plate), requires understanding of the difference between two overriding types of quantum entities — the boson and the fermion (see Fermion vs Boson).
“Large defects in the crystal seem to be important to the phenomenon.”
A supersolid refers to a different phase of matter exemplified in Chan’s experiments by a system of helium-4 atoms. The operative word here may be “system” because it looks like a very small amount of something else — leading to defects in the perfect crystalline structure of a solid’s lattice — may be key.
In helium-4 the atoms are bosons, in contrast to helium-3 in which the atoms are fermions. The nucleus of helium-4, about 99.99986% of the helium on earth, contains two protons and two neutrons. Cooled to below 2.17 Kelvin, helium-4 becomes a superfluid, whose properties differ from those of an ordinary liquid. When, for instance, cooled helium-4 is kept in an open vessel, a thin film climbs the vessel’s sides and flows over the vessel lip. Because of the lack of viscosity (friction between the atoms of the vessel and the atoms of the fluid), a superfluid set in motion in the vessel will rotate forever.
What Chan did in his lab was to take liquid helium-4 into its solid state by increasing the pressure in order to get within the solid component of the system superfluid behavior. Essentially the solid contains a superfluid and that combination is the new state of matter — supersolidity.
The main outlines of the theory for supersolidity, before the Chan experiments and the Rapid Response to them, hypothesize that, within the solid, holes or vacancies — places where atoms aren’t — would behave like a gas of particles, which itself could form a condensate and behave like a superfluid. But the simple picture sketched by those theoretical speculations doesn’t quite stack up with Chan’s experimental results.
In the new KITP auditorium, William Mullin (l), Mark Robbins, and John Toner, participate in the Rapid Response workshop on supersolidity.
Photo by Nell Campbell.
To begin with, said Ceperley, “Moses measured the heat capacity of solid helium much more accurately.” Chan’s experiments going on at Penn State, while the Rapid Responders were meeting in Santa Barbara, revealed an unusual measurement of thermodynamic response.
“Whenever there is some new phenomenon happening,” said Chan, “physicists usually like to think about how it corresponds to the energetics of the situation. We put a certain amount of heat into the system to see how much the temperature will rise. If the system can absorb a lot of energy without raising the temperature, then the system has a large heat capacity. Over the history of physics, we have learned how to use this information to tell us what is going on in the system. If solid helium were to behave like a typical solid, then the heat capacity would increase as the third power of the temperature. But,” said Chan, “we are seeing at the very low temperature, where we see the superfluid response, a deviation from the third power dependence on temperature below 0.2 Kelvin.”
The big question is whether a phase transition to supersolidity is occurring around 0.2 Kelvin. During the Rapid Response program, findings issuing from Chan’s lab failed to detect a peak or bump in the heat capacity curve that would signal the transition. The findings mystified Ceperley, and led at least one prominent theorist participating in the Rapid Response program, Princeton Nobel laureate Phil Anderson, to speculate that the transition occurs at absolute zero.
Written soon after the Rapid Response program ended, the first draft of this article reported no bump. Six weeks later, the bump expected by theorists may be emerging from the ongoing experiments in Chan’s lab. “We are doing more measurements to nail this down," He said.
In addition to experimental confirmation for the phenomenon of supersolidity, the other key development emerging from the Rapid Responders’ consideration of the experimental evidence for supersolidity is that how the crystal is grown appears to be important.
According to Ceperley, “Large defects in the crystal seem to be important to the phenomenon. This thing is at more than 25 atmospheres pressure, and the holes — voids in the crystal which we had theorized would give rise to supersolidity — would have collapsed under that pressure.”
Since the Rapid Responders reason, there are strong theoretical hints that supersolidity cannot happen in a perfect crystal, there is a very strong likelihood that defects are key. So what kinds of defects might be in play if defects understood as “holes,” very roughly analogous to “holes” in the conventional semiconductor paradigm, can’t withstand the pressure?
Well, there is something called “zero point vacancy” or quantum mechanical vacancy. Ultimately related to the uncertainty principle, zero point vacancy means that, to a very minute extent, since a thing’s location cannot be pinpointed, it may not be there. The probability that a thing is not completely there depends on several things, but especially mass, so that the lighter a thing (an atom of helium is quite light), the more likely it isn’t there. Theoretically, this vacancy can go around and form a big loop such that when the system containing it is measured, it would appear that its mass is not there. And that mass that is both there and not may be the signature of the supersolid’s superfluidity.
Said Ceperley, “If supersolidity turns out to have something to do with defects, then helium-4 will provide a simple system to understand how quantum defects work because there are defects in things like metals such as copper, which are really complicated because they have all sorts of impurities. So there is possible long-term impact of this research on metallurgy.”
Said Chan, “Another very curious thing we have seen in our experiments is that when we mix a very little helium-3 (a fraction of a part per million) into helium-4, it has a very great deal of influence on what we see. There is some indication that the supersolid response becomes very small the less the helium-3 (less than one part per billion). Our theoretical friends say, ‘Well, maybe helium-3 as impurity is the source for causing the defect in the system or that this impurity has a great deal of influence on the phenomenon.'
“This work may have materials science implications,” said Chan, “but perhaps most importantly when we try to understand this phenomenon that is very counterintuitive — such that a fraction of a solid can flow with no friction — then we will understand what we mean by a solid because all the things we talk about, in terms of defects, are in all other solids.”
The NSF has provided funding for Chan’s research since 1979. Ceperley, an expert at numerical simulations, is also affiliated with the National Supercomputing Center at Illinois.
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Click to play or watch at the following links (1) Elimination of the Supersolid State Through Crystal Annealing by John Reppy from Cornell University; (2) Observation of NCRI in Bulk Solid 4He Confined to a Cylindrical Cavity by Keiya Shirahama of Keio University; and (3) 3D Superfluid made of 4He Monolayer under Rotation and Supersolid Study by Minoru Kubota of the University of Tokyo