Journal of Low Temperature Physics

, Volume 171, Issue 3–4, pp 315–321 | Cite as

Effects of a 3He impurity on the Elastic Anomalies of 4He at T=0



Effects on the elastic constants of a system formed from 4He atoms with a 3He impurity concentration of 0.14 % are investigated in a range of densities varying from 0.029 to 0.035 Å−3. A model wave function of the shadow class is used to compute elastic constants and quantities defined through relations satisfied by them. The linear compressibility assumes the isotropic character expected for an hcp crystal with a constant value of the structure axis ratio c/a. This is in contrast with bulk 4He where an anisotropic behavior is observed.


Elastic constants 3He impurities Supersolidity 



The authors acknowledge financial support from the Brazilian agencies FAPESP, and CAPES. Part of the computations were performed at the CENAPAD high-performance computing facility at Universidade Estadual de Campinas and at the laboratory of scientific computation of Universidade Federal de Goiás.


  1. 1.
    E. Kim, M.H.W. Chan, Nature 427(6971), 225 (2004). doi: 10.1038/nature02220 ADSCrossRefGoogle Scholar
  2. 2.
  3. 3.
    J. Day, J. Beamish, Nature 450(7171), 853 (2007). doi: 10.1038/nature06383 ADSCrossRefGoogle Scholar
  4. 4.
    D.Y. Kim, J.T. West, T.A. Engstrom, N. Mulders, M.H.W. Chan, Phys. Rev. B 85, 024533 (2012). doi: 10.1103/PhysRevB.85.024533 ADSCrossRefGoogle Scholar
  5. 5.
    A.D. Fefferman, X. Rojas, A. Haziot, S. Balibar, J.T. West, M.H.W. Chan, Phys. Rev. B 85, 094103 (2012). doi: 10.1103/PhysRevB.85.094103 ADSCrossRefGoogle Scholar
  6. 6.
    J.R. Beamish, A.D. Fefferman, A. Haziot, X. Rojas, S. Balibar, Phys. Rev. B 85, 180501 (2012). doi: 10.1103/PhysRevB.85.180501 ADSCrossRefGoogle Scholar
  7. 7.
    S. Vitiello, K. Runge, M.H. Kalos, Phys. Rev. Lett. 60(19), 1970 (1988). doi: 10.1103/PhysRevLett.60.1970 ADSCrossRefGoogle Scholar
  8. 8.
    T. MacFarland, S.A. Vitiello, L. Reatto, G.V. Chester, M.H. Kalos, Phys. Rev. B 50, 13577 (1994) ADSCrossRefGoogle Scholar
  9. 9.
    B. Chaudhuri, F. Pederiva, G.V. Chester, Phys. Rev. B 60, 3271 (1999). doi: 10.1103/PhysRevB.60.3271 ADSCrossRefGoogle Scholar
  10. 10.
    R.A. Aziz, V.P.S. Nain, J.S. Carley, W.L. Taylor, G.T. McConville, J. Chem. Phys. 70(9), 4330 (1979). doi: 10.1063/1.438007 ADSCrossRefGoogle Scholar
  11. 11.
    S. Ujevic, S.A. Vitiello, Phys. Rev. B, Condens. Matter Mater. Phys. 71(22), 224518 (2005). ADSCrossRefGoogle Scholar
  12. 12.
    D. Ceperley, G.V. Chester, M.H. Kalos, Phys. Rev. B 16(7), 3081 (1977). doi: 10.1103/PhysRevB.16.3081 ADSCrossRefGoogle Scholar
  13. 13.
    R. Pessoa, S.A. Vitiello, M. de Koning, Phys. Rev. Lett. 104(8), 085301 (2010). doi: 10.1103/PhysRevLett.104.085301 ADSCrossRefGoogle Scholar
  14. 14.
    R. Pessoa, M. de Koning, S.A. Vitiello, arXiv:1203.0456v1 [cond-mat] (2012)
  15. 15.
    J. Beamish, J. Low Temp. Phys. 168(3–4), 1–27 (2012). doi: 10.1007/s10909-012-0621-8 Google Scholar
  16. 16.
    M. Born, K. Huang, Dynamical Theory of Crystal Lattices. International Series of Monographs on Physics (Oxford University Press, London, 1998). Google Scholar
  17. 17.
    J.P. Franck, R. Wanner, Phys. Rev. Lett. 25(6), 345 (1970). doi: 10.1103/PhysRevLett.25.345 ADSCrossRefGoogle Scholar
  18. 18.
    C. Cazorla, Y. Lutsyshyn, J. Boronat, Phys. Rev. B 85, 024101 (2012). doi: 10.1103/PhysRevB.85.024101 ADSCrossRefGoogle Scholar
  19. 19.
    P. Loubeyre, R. LeToullec, J.P. Pinceaux, H.K. Mao, J. Hu, R.J. Hemley, Phys. Rev. Lett. 71, 2272 (1993). doi: 10.1103/PhysRevLett.71.2272 ADSCrossRefGoogle Scholar
  20. 20.
    A. Hüller, W. Götze, H. Schmidt, Z. Phys. A, Hadrons Nucl. 231, 173 (1970). doi: 10.1007/BF01392508 CrossRefGoogle Scholar
  21. 21.
    S. Ujevic, S.A. Vitiello, J. Chem. Phys. 119(16), 8482 (2003). ADSCrossRefGoogle Scholar
  22. 22.
    R. Rota, J. Boronat, Phys. Rev. Lett. 108, 045308 (2012). doi: 10.1103/PhysRevLett.108.045308 ADSCrossRefGoogle Scholar
  23. 23.
    Y. Lutsyshyn, C. Cazorla, G.E. Astrakharchik, J. Boronat, Phys. Rev. B 82(18), 180506 (2010). doi: 10.1007/s10909-012-0739-8 ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Instituto de FísicaUniversidade Federal de Goiás (UFG)GoiâniaBrazil
  2. 2.Instituto de Física Gleb WataghinUniversidade Estadual de Campinas—UNICAMPCampinasBrazil

Personalised recommendations