A supersolid is a spatially ordered material (that is, a solid or crystal) with superfluid properties. Superfluidity is a special quantum state of matter in which a substance flows with zero viscosity (or resistance to flow). Liquid helium-4 has long been known (since the work of Peter Kapitza, John F. Allen, and Don Misener, published in 1938 the Journal Nature 141, 74 and 75) to exhibit this property when it is cooled below a characteristic transition temperature called the lambda point T_{lambda}. Also superfluidity is observed when superconductors are cooled below a critical temperature T_{c}. However, before the recent observation of supersolid-like behavior in solid helium-4, superfluidity was considered to only be a property of electron fluids, such as in superconductors, gases, such as dilute alkali gases, or liquids, such as liquid helium-4 or liquid helium-3 at very low temperature.

Superfluidity in helium arose from the normal liquid by a second-order phase transition ("lambda transition"). In a dilute gas of Bose particles it comes about by a phase transition that belongs to the universality class of the spherical model. In thin liquid helium films it arises from the normal liquid by a Kosterlitz-Thouless transition.

In the case of helium-4, it has been conjectured since 1970 that it might be possible to create a supersolid. Several experiments looking for this state over the years failed to see it. However, in 2004 physicists Moses Chan and Eun-Seong Kim at Pennsylvania State University observed phenomena that were interpreted as supersolid behavior. Specifically they called what they saw NCRI--Non-Classical Rotational Inertia: in other words, an unusual decoupling of the solid helium from a container's walls which could not be explained by classical models, but which was consistent with a superfluid-like decoupling of a small percentage of the atoms from the rest of the atoms in the container. If such an interpretation is correct, it would signify the discovery of a new quantum phase of matter.

In most theories of this state, it is supposed that vacancies, empty sites normally occupied by particles in an ideal crystal, exist even at the absolute zero of temperature. These vacancies are caused by zero-point energy, which also causes them to be mobile—they move from site to site as waves. Vacancies are bosons and so, if such clouds of vacancies can exist at very low temperature then, a Bose-Einstein condensation of vacancies could occur at a few tenths of a kelvin in temperature. A coherent flow of vacancies is equivalent to a “superflow” (frictionless flow) of particles in the opposite direction. Despite the presence of the gas of vacancies, the ordered structure of a crystal is maintained, although with less than one particle on each lattice site on average.

The experiment of Kim and Chan looked for superflow by means of a “torsional oscillator.” Picture a record turntable that is attached tightly to a springy spindle in the center. Instead of rotating at constant speed, the turntable is started off by a small twist clockwise and then let go. The spring causes it to spin back counterclockwise for a small angle, then clockwise, and then counterclockwise, and so on, a bit analogous to a swinging pendulum. Now glue a thin hollow donut centered on the turntable with solid helium-4 inside. The rate of oscillation of the turntable and donut depend on the amount of solid moving with it. If there is frictionless superfluid inside, then the mass moving with the donut is less and the twisting motion will occur at a faster rate. In this way one can measure the amount of superfluid existing at various temperatures. Kim and Chan found that up to about 2% of the material in the donut was superfluid. Similar experiments in other laboratories have confirmed these results. A mysterious feature, not in agreement with the old theories, is that the transition continues to occur at high pressures.

Prior to 2007, many theorists performed calculations indicating that vacancies cannot exist at zero temperature in solid helium-4. While not all theorists are in perfect agreement in this, it seems more doubtful that what the experiments are seeing is the supersolid state. Indeed further experimentation, including that by Kim and Chan, also throws some doubt on the existence of a true supersolid. One experiment finds that, as one repeatedly warms and then slowly cools the sample the effect disappears. What such “annealing” does is to remove flaws in the crystal structure. Further, most samples of helium-4 have a small amount of the other helium isotope, helium-3, mixed in. When some of this is removed, the superfluid transition occurs at a lower temperature. These experimental results lead on to the possibility that the superflow is involved with actual fluid moving along imperfections in the crystal rather than a property of the perfect crystal.

Experimental and theoretical work continues in hopes of finally settling the question of the existence of a supersolid.

Recently a real supersolid transition has been discovered. M. Kubota et al.from University of Tokyo, Japan reported first real 3D Supersolid transition from the vortex fluid state proposed by P.W. Anderson.

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