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Condensed-matter physics

Defects and perfect flows

The discovery that parts of a solid helium crystal could flow through other parts without friction ignited physicists' interest. Independent experiments confirm this unusual superflow, but its origin remains mysterious.

In 2004, Kim and Chan reported the spectacular, and controversial, observation of superfluidity — flow without resistance from frictional forces — in crystalline helium1,2. This remarkable finding has now been confirmed3,4,5,6. But the latest experiments indicate that, rather than being an intrinsic property of a perfect quantum solid, superflows owe their existence to macroscopic defects or extended disorder in the structure of solid helium.

Essentially, Kim and Chan observed that a small fraction (around 1%) of the solid 4He mass decoupled from the rest of the solid below a critical temperature, TC, of around 0.2 K. This component, denoted the superfluid fraction, ρs, could flow (or remain at rest) without friction inside the solid. The piquancy of the discovery lay in its extending the concept of superfluidity to all three phases of matter: gases, liquids and solids. Before 2004, superflows had been observed only in fluids. These systems include paired electrons in solids, the root cause of superconductivity (discovered in 1911); 4He atoms in the liquid state (1938); and paired 3He atoms in liquid 3He (1972). The possibility that superflow could occur in a lattice whose atoms have long-range positional order — a crystal — seemed remote.

In three new measurements3,4,5, the rotational moment of inertia of solid 4He is determined in a rotating apparatus known as a torsional oscillator. The decoupling of the superfluid component appears as a reduced moment below TC, at which point a fraction of the solid ceases to oscillate with the rest. Writing in Physical Review Letters, Kim and Chan3 confirm their earlier observation1 that the magnitude of ρs varies from sample to sample of solid 4He (Fig. 1). In the same journal, Rittner and Reppy4 find that ρs can be substantially reduced, even to zero, if the solid sample is annealed; that is, if it is warmed and then re-cooled to below TC. Shirahama and co-workers5 have reported similarly that the supersolid fraction can be halved — but not eliminated entirely — by annealing. The implication of all these experiments is that superfluid decoupling depends on imperfections in the solid helium, as these would vary between samples and would be modified by annealing.

Figure 1: Supersolid component.

The superfluid fraction in crystalline 4He in the low-temperature limit, as a function of pressure, from Kim and Chan's data1,3. Crystals grown at constant pressure and temperature (2006 data)3 show somewhat less variation in the supersolid fraction than do those grown at constant volume (2004 data)1. The fraction also does not decrease sharply with increasing pressure, as would be expected if the phenomenon were the result of quantum-mechanical exchange processes in a perfect crystal. The solid line is a guide to the eye.

Soon after Kim and Chan's initial discovery1,2, efforts were made to observe superflow directly by pressing solid helium against a barrier containing small pores7. The superfluid component should have flowed immediately through the fine pores, but no superflow was observed. This year, however, Sasaki and colleagues6 have observed bulk superflow. Again, it is not seen in all samples, but only in those that have a large, observable boundary between two grains (regions of distinct crystallographic orientations) extending across the sample. Superflow seems to occur along, or close to, these grain boundaries.

To understand the significance of these results3,4,5,6, one must first know that there are two prevalent pictures of superfluidity. The first of these focuses on the quantum-mechanical exchange, or tunnelling, of atoms between lattice sites. At low temperature, the de Broglie wavelength of 4He atoms — a quantum-mechanical measure of a particle's extent in space —is long and covers many sites. A long wavelength enables long-range exchange of atoms between lattice sites. If the exchanges extend right across the sample, superfluidity occurs.

The second picture is based on the phenomenon of Bose–Einstein condensation. Any number of the particles known as bosons, which possess integer spin, may occupy a single quantum state. If, at low temperature, a macroscopic fraction of bosons condenses into a single state, a long-range coherence is brought to the system that makes superfluidity possible. In liquid 4He, the classic superfluid, Bose–Einstein condensation is known to occur below the critical temperature for superfluidity in this system, 2.17 K. As the temperature approaches absolute zero — where ρs is 100% — the condensed fraction is around 7%.

Early theoretical discussions8,9,10 of possible superflow in solid 4He involved quantum tunnelling through ground-state vacancies (these are lattice sites that are vacant at absolute zero), as well as Bose–Einstein condensation and quantum exchanges within the lattice. The predicted10 superfluid fraction within the lattice was of the order 0.01%. Unfortunately, however, ground-state vacancies have not been observed in solid 4He. Thermally activated vacancies are found — but at temperatures above TC that are irrelevant to the establishment of superfluidity. Recent calculations11 also find that individual vacancies are not stable in the ground state of crystalline 4He. The vacancies instead coalesce or migrate to a surface; this is the mechanism by which thermal vacancies leave a classical crystal when it is cooled.

Calculations have also shown that there is no long-range coherence, and so no Bose–Einstein condensation, in a perfect crystal of 4He, essentially because condensation requires double occupancy of a lattice site12,13. In real crystals, the condensate fraction is observed in neutron-scattering experiments14 to be 0.2±0.6% — that is, compatible with zero — at a temperature of 0.08 K. Similarly, long-range quantum exchanges within crystalline 4He are too infrequent to explain the high ρs observed15. As seen in solid 3He, quantum exchange rates decrease dramatically as a solid is compressed under pressure. If the superfluid fraction arises from exchanges of particles between lattice sites, ρs should decrease by orders of magnitude under increasing pressure. But Kim and Chan3 find ρs to be largely independent of pressure (Fig. 1). Superflow in crystalline 4He thus does not seem to be a phenomenon of the perfect bulk solid11,12,13,15, or to involve individual point defects (vacancies) that are in equilibrium at absolute zero.

Given the recently discovered dependence of ρs on sample annealing3,4,5, and the correlation of superflow with grain boundaries6, supersolidity seems to hinge on macroscopic, long-range defects such as grain boundaries or amorphous channels in the helium crystal. But at the same time, a superfluid density of the same magnitude is observed1 in helium confined in a nanoporous medium such as Vycor. It is difficult to imagine that extended defects could be the same in helium thus confined and in bulk helium. The situation is far from clear: revealing the secrets of this latest superfluid is very much a work in progress.


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