Cooled to temperatures just above absolute zero, solid helium starts to behave very oddly. But its 'supersolid' behaviour might just be the result of imperfections that change the bulk properties of the crystal.
In 2004, Eun-Seong Kim and Moses Chan placed a sample of solid helium, 4He, in a torsional oscillator at a temperature of about 0.1 kelvin, and allowed it to twist a little. What they observed1,2 ensured that the properties of solid helium would become a hot topic. A portion of the solid seemed to detach itself and flow through the rest without encountering any frictional resistance — a 'supersolid' seemed to have formed.
On page 853 of this issue3, Day and Beamish report changes in a material property known as the shear modulus — which measures a solid's rigidity, or resistance to elastic deformation — in solid helium. The changes closely mirror the results of the torsional-oscillator experiments. Two possibilities immediately suggest themselves: first, that the onset of supersolidity might strongly affect solid helium's elastic properties; or second, and rather more prosaically, that changes in the solid's elasticity might have mimicked the effects of supersolid behaviour in the previous measurements.
Helium is the noblest of elements: the interactions between even its own atoms are so weak that it solidifies only under intense pressure. If this pressure is reduced to below about 25 atmospheres at absolute zero, the quantum-mechanical fluctuations of the atoms' positions become so large that the solid melts, becoming a 'quantum liquid'. No crystalline solid is perfect — there are always some vacancies in the crystal lattice where atoms are missing — and in 1969 Alexander Andreev and Ilya Lifshitz4 proposed that helium's large quantum fluctuations might, at zero temperature, stabilize a dilute gas of vacancies within the solid. Atoms of the prevalent isotope 4He are bosons (they have zero spin), and so vacancies in solid 4He can also be thought of as bosons. The vacancies can thus condense to form an exotic phase known as a Bose–Einstein condensate that suffuses the solid. This 'supersolid' phase would share some properties with a superfluid — namely, frictionless flow — but at the same time have a non-zero shear modulus, a defining characteristic of a solid.
Until Kim and Chan, however, no one had had much luck in finding experimental evidence for supersolidity. Their torsional oscillator was a rather simple piece of apparatus. They attached a 'bob' containing the helium sample to the end of a torsion rod. A torque applied to the bob caused it to twist and rotate back and forth, with an oscillation period set by the ratio of the bob's moment of inertia (a measure of the amount and distribution of mass being rotated) to the torsional stiffness of the rod. If some of the material in the sample stops participating in this rotation, the moment of inertia of the bob decreases, and the period drops. This is precisely what happens with liquid 4He, which is a well-known superfluid: as the temperature is reduced below that at which the superfluid forms, the superfluid component stops rotating and the oscillator's period drops. Kim and Chan's same result1,2 with solid 4He has now been reproduced in at least four other laboratories.
A supersolid can exhibit other anomalies, for instance in the speed at which sound passes through it. Sound speed depends on the shear modulus of the solid, as well as the density of the superfluid component. To assess why the solid behaves in the way it does, it is thus important to measure the shear modulus independently of the superfluid density. This is precisely what Day and Beamish have now done with solid helium.
Again, the authors' experiment3 is conceptually simple. They placed solid 4He between two parallel plates, known as piezoelectric shear transducers. They moved one plate, the driving transducer, in a direction parallel to the second plate. The solid helium transmits the resulting elastic shear stress between the plates, and this is measured by the second transducer. Day and Beamish find3 that the shear modulus of helium rises by up to 10% as the temperature is reduced from 0.2 to 0.02 kelvin. More significantly, the temperature dependence of this large increase in shear modulus closely tracks the changes in period in the torsional-oscillator experiments.
When these results were first presented at a small workshop on the supersolid state of matter in Minnesota in late July 2007, the reaction of some of us in the audience was that the large change in the shear modulus might be the primary phenomenon, and the much smaller change in the period of the torsional oscillator a related side effect. The various torsional-oscillator experiments are now being re-examined, to estimate the shear stresses and strains that occur within and between the various parts of the assemblies, and to ask if changes in shear stiffness of the helium might cause the observed changes in the oscillation period5.
So what might be the root cause of the observed effects? It has long been known that a solid's strength and shear modulus are not set solely by the intrinsic nature of a perfect crystalline solid, but also depend strongly on defects such as dislocations and grain boundaries. The same seems to be true for the torsional-oscillator experiments: the results depend on the quality of the crystal, with the largest effects seen in the most defective samples.
Day and Beamish3 explain their results very plausibly as the behaviour of dislocations and trace 3He impurities in the solid 4He: when dislocations can move in response to a shear stress, they relax the stress and so lower the shear modulus. Impurities of 3He are thought to bind weakly to dislocations in solid 4He at low temperatures and so restrict their motion. As the temperature is increased, the trace 3He atoms unbind from the dislocations, allowing the dislocations to move more freely. The observed dependence of the shear modulus on the concentration of 3He is consistent with this idea. This is not to say that supersolidity must have no role: careful simulations6 and modelling7 find superfluid flow along dislocation lines in solid 4He.
It seems clear now that both the earlier torsional-oscillator experiments1,2 and Day and Beamish's new experiment3 are probing the quantum-mechanical behaviour of structural defects in imperfect helium crystals. But a thorough understanding of the measured effects remains elusive. Are we studying supersolidity, the quantum properties of dislocations, both — or perhaps something else entirely?
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Journal of Physics: Condensed Matter (2008)