Abstract
A 'supersolid' is a quantum solid in which a fraction of the mass is superfluid. As a remarkable consequence, it is rigid, but part of its mass is able to flow owing to quantum physical processes. This paradoxical state of matter was considered as a theoretical possibility as early as 1969, but its existence was discovered only in 2004, in 4He. Since then, intense experimental and theoretical efforts have been made to explain the origins of this exotic state of matter. It now seems that its physical interpretation is more complicated than originally thought.
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References
Leggett, A. J. A 'superglass' state in solid 4-He. J. Club Condens. Matter Phys. <http://www.condmatjournalclub.org/wp-content/uploads/2009/04/jccm_april09_032.pdf> (2009).
Kim, E. & Chan, M. H. W. Probable observation of a supersolid helium phase. Nature 427, 225–227 (2004). This paper reported the first observation of anomalous rotation properties in solid 4He.
Kim, E. & Chan, M. H. W. Observation of superflow in solid helium. Science 305, 1941–1944 (2004).
Rittner, A. S. & Reppy, J. Observation of classical rotational inertia and nonclassical supersolid signals in solid 4He below 250 mK. Phys. Rev. Lett. 97, 165301 (2006).
Rittner, A. S. & Reppy, J. Disorder and the supersolid state of solid 4He. Phys. Rev. Lett. 98, 175302 (2007).
Kondo, M., Takada, S., Shibayama, Y. & Shirahama, K. Observation of non-classical rotational inertia in bulk solid 4He. J. Low Temp. Phys. 148, 695–699 (2007).
Aoki, Y., Graves, J. C. & Kojima, H. Oscillation frequency dependence of non-classical rotation inertia of solid 4He. Phys. Rev. Lett. 99, 015301 (2007).
Penzev, A. Yasuta, Y. & Kubota, M. AC vortex-dependent torsional oscillation response and onset temperature T 0 in solid 4He. Phys. Rev. Lett. 101, 065301 (2008).
Hunt, B. et al. Evidence for a superglass state in solid 4He. Science 324, 632–636 (2009).
Day, J. & Beamish, J. Low-temperature shear modulus changes in solid 4He and connection to supersolidity. Nature 450, 853–856 (2007). The paper reported the first observation of a stiffening linked to the appearance of supersolidity.
Day, J., Syshchenko, O. & Beamish, J. D. Intrinsic and dislocation-induced elastic behavior of solid helium. Phys. Rev. B 79, 214524 (2009).
Mukharsky, Yu., Penzev, A. & Varoquaux, E. Low-frequency acoustics in solid 4He at low temperature. Phys. Rev. B 80, 140504 (2009).
Rojas, X., Pantalei, C., Maris, H. J. & Balibar, S. Acoustic properties of solid 4He in the limit of zero impurity. J. Low Temp. Phys. 158, 478–484 (2009).
Lin, X., Clark, A. C. & Chan, M. H. W. Heat capacity signature of the supersolid transition. Nature 449, 1025–1028 (2007).
Lin, X., Clark, A. C., Cheng, Z. G. & Chan, M. H. W. Heat capacity peak in solid 4He: effects of disorder and 3He impurities. Phys. Rev. Lett. 102, 125302 (2009). This paper presents the most recent measurements of a heat capacity peak signalling that the supersolid transition is a true phase transition.
Prokof'ev, N. What makes a crystal supersolid? Adv. Phys. 56, 381–402 (2007). This is a recent review on the theory of supersolidity, including results from numerical simulations.
Ceperley, D. M. & Bernu, B. Ring exchanges and the supersolid phase of 4He. Phys. Rev. Lett. 93, 155303 (2004).
Anderson, P. W. Two new vortex liquids. Nature Phys. 3, 160–162 (2007).
Anderson, P. W. Bose fluids above T c: incompressible vortex fluids and 'supersolidity'. Phys. Rev. Lett. 100, 215301 (2008). In this paper, Anderson argues that supersolidity is an intrinsic property of quantum crystals that exists even in the absence of disorder.
Anderson, P. W. A. Gross–Pitaevskii treatment for supersolid helium. Science 324, 631–632 (2009).
Balibar, S. & Caupin, F. Supersolidity and disorder. J. Phys. Condens. Matter 20, 173201 (2008). This is a recent review on the whole field of supersolidity, with emphasis on experimental results.
Galli, D. E. & Reatto, L. Solid 4He and the supersolid phase: from theoretical speculation to the discovery of a new state of matter? A review of the past and present status of research. J. Phys. Soc. Jpn 77, 111010 (2008).
Thouless, D. J. The flow of a dense superfluid. Ann. Phys. 52, 403–427 (1969).
Andreev, A. F. & Lifshitz, I. M. Quantum theory of defects in crystals. Sov. Phys. JETP 29, 1107–1113 (1969).
Leggett, A. J. Can a solid be superfluid? Phys. Rev. Lett. 25, 1543–1546 (1970).
Meisel, F. Supersolid 4He: an overview of past searches and future possibilities. Physica B 178, 121–128 (1992).
Boninsegni, M. et al. Fate of vacancy-induced supersolidity in 4He. Phys. Rev. Lett. 97, 080401 (2006).
Boninsegni, M. et al. Luttinger liquid in the core of screw dislocation in helium-4. Phys. Rev. Lett. 99, 035301 (2007).
Pollet, L. et al. Superfluidity of grain boundaries in solid 4He. Phys. Rev. Lett. 98, 135301 (2007).
Clark, A. C., West, J. T. & Chan, M. H. W. Nonclassical rotational inertia in helium crystals. Phys. Rev. Lett. 99, 135302 (2007).
Sasaki, S., Ishiguro, R., Caupin, F., Maris, H. J. & Balibar, S. Superfluidity of grain boundaries and supersolid behaviour. Science 313, 1098–1100 (2006).
Sasaki, S., Caupin, F. & Balibar, S. Wetting properties of grain boundaries in solid 4He. Phys. Rev. Lett. 99, 205302 (2007).
Ray, M. W. & Hallock, R. B. Observation of unusual mass transport in solid hcp 4He. Phys. Rev. Lett. 100, 235301 (2008).
Sasaki, S., Caupin, F. & Balibar, S. Optical observations of disorder in solid helium-4. J. Low Temp. Phys. 153, 43–76 (2008).
Balibar, S. & Caupin, F. Comment on “Observation of unusual mass transport in solid hcp 4He”. Phys. Rev. Lett. 101, 189601 (2008).
Kim, E. et al. Effect of 3He impurities on the nonclassical response to oscillation of solid 4He. Phys. Rev. Lett. 100, 065301 (2008).
Iwasa, I. & Suzuki, H. Sound velocity and attenuation in hcp 4He crystals containing 3He impurities. J. Phys. Soc. Jpn 49, 1722–1730 (1980).
Paalanen, M. A., Bishop, D. J. & Dail, H. W. Dislocation motion in hcp 4He. Phys. Rev. Lett. 46, 664–667 (1981).
Nussinov, Z., Balatsky, A. V., Graf, M. J. & Trugman, S. A. Origin of the decrease in the torsional-oscillator period of solid 4He. Phys. Rev. B 76, 014530 (2007).
Yoo, C. D. & Dorsey, A. T. Theory of viscoelastic behavior of solid 4He. Phys. Rev. B 79, 100504 (2009).
West, J. T., Syshchenko, O., Beamish, J. D. & Chan, M. H. W. Role of shear modulus and statistics in the supersolidity of helium. Nature Phys. 5, 598–601 (2009).
Rittner, A. S. C. & Reppy, J. D. Probing the upper limit of nonclassical rotational inertia in solid helium-4. Phys. Rev. Lett. 101, 155301 (2008).
Reppy, J. D. Is supersolid superfluid? Supersolids Banff 2009 <http://www.phys.ualberta.ca/supersolids/talks/> (2009).
Balatsky, A. V., Graf, M. J., Nussinov, Z. & Trugman, S. A. Entropy of solid 4He: the possible role of a dislocation-induced glass. Phys. Rev. B 75, 094201 (2007).
Balibar, S., Alles, H. & Parshin, A. Y. The surface of helium crystals. Rev. Mod. Phys. 77, 317–370 (2005).
Ruutu, J. P. et al. Facet growth of helium-4 crystals at mK temperatures. Phys. Rev. Lett. 76, 4187–4190 (1996).
Pantalei, C., Rojas, X., Edwards, D. O., Maris, H. J. & Balibar, S. How to prepare an ideal helium-4 crystal. J. Low Temp. Phys. doi: 10.1007/s10909-010-0159-6 (in the press).
Aleinikava, D., Dedits, E., Kuklov, A. B. & Schmeltzer, D. Mechanical and superfluid properties of dislocations in solid 4He. Phys. Rev. B (submitted); preprint at <http://arxiv.org/abs/0812.0983> (2008).
Allen, J. F. & Misener, A. D. Flow of liquid helium II. Nature 141, 75 (1938).
Kapitza, P. Viscosity of liquid helium below the λ point. Nature 141, 74 (1938).
Balibar, S. The discovery of superfluidity. J. Low Temp. Phys. 146, 441–470 (2007).
Allen, J. F. & Jones, H. New phenomena connected with heat flow in helium II. Nature 141, 243–244 (1938).
London, F. The λ phenomenon of liquid helium and the Bose–Einstein degeneracy. Nature 141, 643–644 (1938).
Tisza, L. Transport phenomena in helium II. Nature 141, 913 (1938).
Penrose, O. On the quantum mechanics of helium II. Phil. Mag. 42, 1373–1377 (1951).
Kamerlingh Onnes, H. The resistance of pure mercury at helium temperatures. Commun. Phys. Lab. Univ. Leiden 120b (1911); The disappearance of the resistivity of mercury. Commun. Phys. Lab. Univ. Leiden 122b (1911); On the sudden change in the rate at which the resistance of mercury disappears. Commun. Phys. Lab. Univ. Leiden 124c (1911).
Bardeen, J., Cooper, L. N. & Schrieffer, J. R. Theory of superconductivity. Phys. Rev. 106, 162–164 (1957).
Bardeen, J., Cooper, L. N. & Schrieffer, J. R. Microscopic theory of superconductivity. Phys. Rev. 108, 1175–1204 (1957).
Osheroff, D. D., Richardson, R. C. & Lee, D. M. Evidence for a new phase in solid 3He. Phys. Rev. Lett. 28, 885–888 (1972).
Osheroff, D. D., Gully, W. J. & Richardson, R. C. New magnetic phenomena in liquid 3He below 3 mK. Phys. Rev. Lett. 29, 920–923 (1972).
Anderson, M. H., Ensher, J. R., Matthews, M. R., Wieman, C. E. & Cornell, E. Observation of Bose–Einstein condensation in a dilute atomic vapour. Science 269, 198–201 (1995).
Davis, K. B. et al. Bose–Einstein condensation in a gas of sodium atoms. Phys. Rev. Lett. 75, 3969–3973 (1995).
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I acknowledge support from the Agence Nationale de la Recherche (grant BLAN07.1.215296).
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Balibar, S. The enigma of supersolidity. Nature 464, 176–182 (2010). https://doi.org/10.1038/nature08913
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DOI: https://doi.org/10.1038/nature08913