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# Probable observation of a supersolid helium phase

## Abstract

When liquid 4He is cooled below 2.176 K, it undergoes a phase transition—Bose–Einstein condensation—and becomes a superfluid with zero viscosity1. Once in such a state, it can flow without dissipation even through pores of atomic dimensions. Although it is intuitive to associate superflow only with the liquid phase2, it has been proposed theoretically3,4,5 that superflow can also occur in the solid phase of 4He. Owing to quantum mechanical fluctuations, delocalized vacancies and defects are expected to be present in crystalline solid 4He, even in the limit of zero temperature. These zero-point vacancies can in principle allow the appearance of superfluidity in the solid3,4. However, in spite of many attempts6, such a ‘supersolid’ phase has yet to be observed in bulk solid 4He. Here we report torsional oscillator measurements on solid helium confined in a porous medium, a configuration that is likely to be more heavily populated with vacancies than bulk helium. We find an abrupt drop in the rotational inertia5 of the confined solid below a certain critical temperature. The most likely interpretation of the inertia drop is entry into the supersolid phase. If confirmed, our results show that all three states of matter—gas7, liquid1 and solid—can undergo Bose–Einstein condensation.

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## References

1. Kapitza, P. Viscosity of liquid helium below the λ-point. Nature 141, 74 (1938)

2. Penrose, O. & Onsager, L. Bose-Einstein condensation and liquid helium. Phys. Rev. 104, 576–584 (1956)

3. Andreev, A. F. & Lifshitz, I. M. Quantum theory of defects in crystals. Sov. Phys. JETP 29, 1107–1113 (1969)

4. Chester, G. V. Speculations on Bose-Einstein condensation and quantum crystals. Phys. Rev. A 2, 256–258 (1970)

5. Leggett, A. J. Can a solid be “superfluid”? Phys. Rev. Lett. 25, 1543–1546 (1970)

6. Meisel, M. W. Supersolid 4He—An overview of past searches and future possibilities. Physica B 178, 121–128 (1992)

7. Anderson, M. H., Ensher, J. R., Matthews, M. R., Wieman, C. E. & Cornell, E. A. Observation of Bose-Einstein condensation in a dilute atomic vapour. Science 269, 198–201 (1995)

8. Bishop, D. J., Paalanen, M. A. & Reppy, J. D. Search for superfluidity in hcp 4He. Phys. Rev. B 24, 2844–2845 (1981)

9. Levitz, P., Ehret, G., Sinha, S. K. & Drake, J. M. Porous Vycor glass—the micro structure as probed by electron-microscopy, direct energy-transfer, small-angle scattering, and molecular adsorption. J. Chem. Phys. 95, 6151–6161 (1991)

10. Brewer, D. F., Cao, L., Girit, C. & Reppy, J. D. 4He transition in a restricted geometry below and above the bulk solidification pressure. Physica B 107, 583–584 (1981)

11. Cao, L., Brewer, D. F., Girit, C., Smith, E. N. & Reppy, J. D. Flow and torsional oscillator measurements on liquid helium in restricted geometries under pressure. Phys. Rev. B 33, 106–117 (1986)

12. Beamish, J. R., Hikata, A., Tell, L. & Elbaum, C. Solidification and superfluidity of 4He in porous Vycor glass. Phys. Rev. Lett. 50, 425–428 (1983)

13. Molz, E. B. & Beamish, J. R. Freezing and melting of helium in different porous media. J. Low-Temp. Phys. 101, 1055–1077 (1995)

14. Adams, E. D., Uhlig, K., Tang, Y. H. & Haas, G. E. Solidification and superfluidity of 4He in confined geometries. Phys. Rev. Lett. 52, 2249–2252 (1984)

15. Bittner, D. N. & Adams, E. D. Solidification of helium in confined geometries. J. Low-Temp. Phys. 97, 519–535 (1994)

16. Chan, M. H. W., Yanof, A. W. & Reppy, J. D. Superfluidity of thin 4He films. Phys. Rev. Lett. 32, 1347–1350 (1974)

17. Mehl, J. B. & Zimmermann, W. Jr Flow of superfluid helium in a porous medium. Phys. Rev. 167, 214–229 (1968)

18. Berthold, J. E., Bishop, D. J. & Reppy, J. D. Superfluid transition of 4He films adsorbed on porous Vycor glass. Phys. Rev. Lett. 39, 348–352 (1977)

19. Huang, K. Statistical Mechanics 2nd edn, 293 (Wiley & Son, New York, 1967)

20. Palaanen, M. A., Bishop, D. J. & Dail, H. W. Dislocation motion in hcp 4He. Phys. Rev. Lett. 46, 664–667 (1981)

21. Csáthy, G. A. & Chan, M. H. W. Effect of 3He on submonolayer superfluidity. Phys. Rev. Lett. 87, 045301 (2001)

## Acknowledgements

We acknowledge discussions with J. Banavar, J. Beamish, V. Crespi, J. Goodkind, J. Jain, A. Leggett and J. Reppy. This work was supported by the Condensed Matter Physics Program of the National Science Foundation.

## Author information

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Correspondence to M. H. W. Chan.

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### Competing interests

The authors declare that they have no competing financial interests.

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Kim, E., Chan, M. Probable observation of a supersolid helium phase. Nature 427, 225–227 (2004). https://doi.org/10.1038/nature02220

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• DOI: https://doi.org/10.1038/nature02220

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