Skip to main content
SpringerLink
Log in

Elementary Excitations, Spectral Weights and Experimental Signatures of a Supersolid and a Fulde-Ferrell-Larkin-Ovchinnikov State

  • Published:
Journal of Low Temperature Physics Aims and scope Submit manuscript

Abstract

We construct a Ginsburg Landau (GL) theory to study the phases of liquid, solid, superfluid, especially a possible supersolid and phase transitions among these phases in a unified framework. In this GL, we put the two competing orders between the solid component and the superfluid component on the same footing. We only introduce two parameters: v which is the repulsive interaction between the normal component and the local superfluid mode and g which is a periodically changing chemical potential for the local superfluid mode. The microscopic origins of v and g are given. By using this GL action, we study the superfluid to supersolid transition, normal solid to the supersolid transition and analyze the conditions for the existence of the supersolid. The non-classical rotational inertial (NCRI) in the SS state is calculated and found to be isotropic in bcc and fcc lattice, but weakly anisotropic in hcp lattice. We study the elementary low energy excitation inside a supersolid. We find that there are one upper branch and one lower branch longitudinal “supersolidon” modes inside the SS, while the transverse modes in the SS stay the same as those inside the NS. We also determine the corresponding spectral weights of the two branches. We work out the experimental signatures of these elementary excitations in Debye-Waller factor, density-density correlation, vortex loop interaction and specific heat. The estimated excess entropy due to vacancies seems consistent with data measured in the specific experiment in Helium 4. Detecting the two supersolidon modes by various equilibrium and thermodynamic experiments such as X-ray scattering, neutron scattering, acoustic wave attenuation and heat capacity can prove or disapprove the existence of a supersolid in Helium 4. A toy model of supersolid wavefunction is analyzed. The difference and similarities with lattice supersolid are clearly demonstrated. Elementary excitations inside a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state of superfluid are also discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. C.N. Yang, Rev. Mod. Phys. 34, 694 (1962)

    Article  ADS  Google Scholar 

  2. A. Andreev, I. Lifshitz, Sov. Phys. JETP 29, 1107 (1969)

    ADS  Google Scholar 

  3. G.V. Chester, Phys. Rev. A 2, 256 (1970)

    Article  ADS  Google Scholar 

  4. A.J. Leggett, Phys. Rev. Lett. 25, 1543 (1970)

    Article  ADS  Google Scholar 

  5. W.M. Saslow, Phys. Rev. Lett. 36, 1151–1154 (1976)

    Article  ADS  Google Scholar 

  6. F. Dalfovo, S. Giorgini, L.P. Pitaevskii, S. Stringari, Rev. Mod. Phys. 71, 463–512 (1999)

    Article  ADS  Google Scholar 

  7. A.J. Leggett, Rev. Mod. Phys. 73, 307–356 (2001)

    Article  ADS  Google Scholar 

  8. E. Kim, M.H.W. Chan, Nature 427, 225–227 (2004)

    Article  ADS  Google Scholar 

  9. E. Kim, M.H.W. Chan, Science 305, 1941–1944 (2004)

    Article  ADS  Google Scholar 

  10. A. Clark, M. Chan, J. Low Temp. Phys. 138, 853 (2005)

    Article  ADS  Google Scholar 

  11. E. Kim, M.H.W. Chan, Phys. Rev. Lett. 97, 115302 (2006)

    Article  ADS  Google Scholar 

  12. A.C. Clark, X. Lin, M.H.W. Chan, cond-mat/0610240

  13. A.S.C. Rittner, J.D. Reppy, Phys. Rev. Lett. 97, 165301 (2006)

    Article  ADS  Google Scholar 

  14. J. Day, T. Herman, J. Beamish, Phys. Rev. Lett. 95, 035301 (2005)

    Article  ADS  Google Scholar 

  15. I.A. Todoshchenko, H. Alles, J. Bueno, H.J. Junes, A.Ya. Parshin, V. Tsepelin, Phys. Rev. Lett. 97, 165302 (2006)

    Article  ADS  Google Scholar 

  16. D.M. Ceperley, B. Bernu, Phys. Rev. Lett. 93, 155303 (2004)

    Article  ADS  Google Scholar 

  17. N. Prokof’ev, B. Svistunov, Phys. Rev. Lett. 94, 155302 (2005)

    Article  ADS  Google Scholar 

  18. D.E. Galli, M. Rossi, L. Reatto, Phys. Rev. B 71, 140506(R) (2005)

    Article  ADS  Google Scholar 

  19. E. Burovski, E. Kozik, A. Kuklov, N. Prokof’ev, B. Svistunov, Phys. Rev. Lett. 94, 165301 (2005)

    Article  ADS  Google Scholar 

  20. M. Boninsegni, A.B. Kuklov, L. Pollet, N.V. Prokof’ev, B.V. Svistunov, M. Troyer, Phys. Rev. Lett. 97, 080401 (2006)

    Article  ADS  Google Scholar 

  21. W.M. Saslow, Phys. Rev. B 71, 092502 (2005)

    Article  ADS  Google Scholar 

  22. N. Kumar, cond-mat/0507553

  23. G. Baskaran, cond-mat/0505160

  24. X. Dai, M. Ma, F.-C. Zhang, Phys. Rev. B 72, 132504 (2005)

    Article  ADS  Google Scholar 

  25. A.T. Dorsey, P.M. Goldbart, J. Toner, Phys. Rev. Lett. 96, 055301 (2006)

    Article  ADS  Google Scholar 

  26. P.W. Anderson, W.F. Brinkman, D.A. Huse, Science 310, 1164–1166 (2005)

    Article  ADS  Google Scholar 

  27. J. Ye, Phys. Rev. Lett. 97, 125302 (2006)

    Article  ADS  Google Scholar 

  28. J. Ye, Europhys. Lett. 82, 16001 (2008)

    Article  Google Scholar 

  29. G.S. Jeon, J. Ye, Phys. Rev. B 71, 035348 (2005)

    Article  ADS  Google Scholar 

  30. P. Nozieres, J. Low. Temp. Phys. 137, 45 (2004)

    Article  ADS  Google Scholar 

  31. G. Ahlers, Phys. Rev. A 3, 696–716 (1971)

    Article  ADS  Google Scholar 

  32. D.S. Greywall, G. Ahlers, Phys. Rev. A 7, 2145–2162 (1973)

    Article  ADS  Google Scholar 

  33. P.M. Chaikin, T.C. Lubensky, Principles of Condensed Matter Physics (Cambridge University Press, Cambridge, 1995)

    Google Scholar 

  34. J. Ye, L. Jiang, Phys. Rev. Lett. 98, 236802 (2007)

    Article  ADS  Google Scholar 

  35. J. Ye, Phys. Rev. Lett. 97, 236803 (2006)

    Article  ADS  Google Scholar 

  36. J. Ye, Ann. Phys. 323, 580–630 (2008)

    Article  MATH  ADS  Google Scholar 

  37. B.A. Fraass, P.R. Granfors, R.O. Simmons, Phys. Rev. B 39, 124–131 (1989)

    Article  ADS  Google Scholar 

  38. C.A. Burns, E.D. Isaacs, Phys. Rev. B 55, 5767–5771 (1997)

    Article  ADS  Google Scholar 

  39. M.P.A. Fisher, P.B. Weichman, G. Grinstein, D.S. Fisher, Phys. Rev. B 40, 546 (1989)

    Article  ADS  Google Scholar 

  40. F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Köhl, T. Esslinger, Nature 450, 268–271 (2007)

    Article  ADS  Google Scholar 

  41. Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, J. Reichel, Nature 450, 272–276 (2007)

    Article  ADS  Google Scholar 

  42. L. Jiang, J. Ye, J. Zhang, T.C. Zhang, C.L. Zhang, arXiv:0912.1982

  43. J. Kasprzak et al., Nature 443, 409–414 (2006)

    Article  ADS  Google Scholar 

  44. H. Deng et al., Phys. Rev. Lett. 99, 126403 (2007)

    Article  ADS  Google Scholar 

  45. R. Balili et al., Science 316, 1007–1010 (2007)

    Article  ADS  Google Scholar 

  46. J.E. Hoffman et al., Science 295, 466 (2002)

    Article  ADS  Google Scholar 

  47. S.R. White, D.J. Scalapino, Phys. Rev. Lett. 80, 1272 (1998)

    Article  ADS  Google Scholar 

  48. M.A. De Moura, T.C. Lubensky, Y. Imry, A. Aharony, Phys. Rev. B 13, 2176 (1976)

    Article  ADS  Google Scholar 

  49. D. Bergman, B. Halperin, Phys. Rev. B 13, 2145 (1976)

    Article  ADS  Google Scholar 

  50. W. Saslow, Phys. Rev. B 15, 173 (1977)

    Article  ADS  Google Scholar 

  51. M. Liu, Phys. Rev. B 18, 1165 (1978)

    Article  ADS  Google Scholar 

  52. M. Bijlsma, H. Stoof, Phys. Rev. B 56, 14631 (1997)

    Article  ADS  Google Scholar 

  53. R.H. Crepeau et al., Phys. Rev. A 3, 1162 (1971)

    Article  ADS  Google Scholar 

  54. D.S. Greywall, Phys. Rev. A 3, 2106 (1971)

    Article  ADS  Google Scholar 

  55. D.G. Henshaw, A.D.B. Woods, Phys. Rev. 121, 1266–1274 (1961)

    Article  ADS  Google Scholar 

  56. P.E. Sokol, in Bose-Einstein Condensation, ed. by A. Griffin, D.W. Snoke, S. Stringari (Cambridge University Press, Cambridge, 1995), p. 51

    Google Scholar 

  57. J.M. Goodkind, Phys. Rev. Lett. 89, 095301 (2002)

    Article  ADS  Google Scholar 

  58. G. Lengua, J.M. Goodkind, J. Low Temp. Phys. 79, 251 (1990)

    Article  ADS  Google Scholar 

  59. C.A. Burns, J.M. Goodkind, J. Low Temp. Phys. 95, 695 (1994)

    Article  ADS  Google Scholar 

  60. P.C. Martin, O. Parodi, P.S. Pershan, Phys. Rev. A 6, 2401 (1972)

    Article  ADS  Google Scholar 

  61. J. Ye, J. Low Temp. Phys. 158(5), 882 (2010)

    Article  ADS  Google Scholar 

  62. K.S. Liu, M.E. Fisher, J. Low Temp. Phys. 10, 655 (1973)

    Article  ADS  Google Scholar 

  63. X. Lin, A.C. Clark, M.H.W. Chan, Nature 06228 (2007)

  64. A.V. Balatsky, M.J. Graf, Z. Nussinov, S.A. Trugman, Phys. Rev. B 75, 094201 (2007)

    Article  ADS  Google Scholar 

  65. J. Ye, T. Shi, L. Jiang, Phys. Rev. Lett. 103, 177401 (2009)

    Article  ADS  Google Scholar 

  66. T. Shi, L. Jiang, J. Ye, arXiv:0904.1429 (to appear in Phys. Rev. B)

  67. J. Ye, T. Shi, L. Jiang, arXiv:0802.1065

  68. A.H. Castro Neto, Phys. Rev. Lett. 86, 4382 (2001)

    Article  ADS  Google Scholar 

  69. J. Ye, Nucl. Phys. B 805(3), 418–440 (2008)

    Article  ADS  Google Scholar 

  70. Y. Chen, J. Ye, cond-mat/0612009 (updated version on May 3, 2010)

  71. J. Ye, J.M. Zhang, W.M. Liu, K. Zhang, Y. Li, W. Zhang, arXiv:1001.3230

  72. P.A. Crowell, J.D. Reppy, Phys. Rev. Lett. 70, 3291–3294 (1993)

    Article  ADS  Google Scholar 

  73. P.A. Crowell, J.D. Reppy, Phys. Rev. B 53, 2701–2718 (1996)

    Article  ADS  Google Scholar 

  74. G. Murthy, D. Arovas, A. Auerbach, Phys. Rev. B 55, 3104 (1997)

    Article  ADS  Google Scholar 

  75. P. Fulde, R.A. Ferrell, Phys. Rev. 135, A550–A563 (1964)

    Article  ADS  Google Scholar 

  76. A.I. Larkin, Y.N. Ovchinnikov, Sov. Phys. JETP 20, 762 (1965)

    MathSciNet  Google Scholar 

  77. G. Murthy, R. Shankar, J. Phys. Condens. Matter 7, 9155 (1995)

    Article  ADS  Google Scholar 

  78. R. Casalbuoni, G. Nardulli, Rev. Mod. Phys. 76, 263 (2004)

    Article  ADS  Google Scholar 

  79. L. Jiang, J. Ye, Phys. Rev. B 76, 184104 (2007)

    Article  ADS  Google Scholar 

  80. D.T. Son, M.A. Stephanov, Phys. Rev. A 74, 013614 (2006)

    Article  ADS  Google Scholar 

  81. C.-D. Yoo, A.T. Dorsey, arXiv:1001.0621

  82. J. Zaanen, Z. Nussinov, S.I. Mukhin, Ann. Phys. 310, 181–260 (2004)

    Article  MATH  ADS  Google Scholar 

  83. G.C. Batrounil et al., Phys. Rev. Lett. 74, 2527 (1995)

    Article  ADS  Google Scholar 

  84. G.C. Batrounil et al., Phys. Rev. Lett. 84, 1599 (2000)

    Article  ADS  Google Scholar 

  85. P. Sengupta et al., Phys. Rev. Lett. 94, 207202 (2005)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Capital Normal University, Beijing, 100048, China

    Jinwu Ye

  2. Department of Physics, The Pennsylvania State University, University Park, PA, 16802, USA

    Jinwu Ye

Authors
  1. Jinwu Ye
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jinwu Ye.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ye, J. Elementary Excitations, Spectral Weights and Experimental Signatures of a Supersolid and a Fulde-Ferrell-Larkin-Ovchinnikov State. J Low Temp Phys 160, 71–111 (2010). https://doi.org/10.1007/s10909-010-0184-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10909-010-0184-5

Keywords

Search

Navigation