Advertisement

Journal of Low Temperature Physics

, Volume 121, Issue 5–6, pp 357–366 | Cite as

Vortices Observed and to be Observed

  • G. E. Volovik
Article

Abstract

Linear defects are generic in continuous media. In quantum systems they appear as topological line defects which are associated with a circulating persistent current. In relativistic quantum vacuum they are known as cosmic strings, in superconductors as quantized flux lines, and in superfluids and low-density atomic Bose-Einstein condensates as quantized vortex lines. We discuss unconventional vortices in unconventional superfluids and superconductors, which have been observed or have to be observed, such as continuous singly and doubly quantized vortices in 3 He-A and chiral Bose condensates; half-quantum vortices (Alice strings) in 3 He-A and in nonchiral Bose condensates; Abrikosov vortices with fractional magnetic flux in chiral and d-wave superconductors; vortex sheets in 3 He-A and chiral superconductors; the nexus—combined object formed by vortices and monopoles. Some properties of vortices related to the fermionic quasiparticles living in the vortex core are also discussed.

Keywords

Vortex Vortex Core Cosmic String Vortex Line Flux Line 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. 1.
    M. Bartkowiak, S. W. J. Daley, S. N. Fisher, A. M. Guenault, G. N. Plenderleith, R. P. Haley, G. R. Pickett, & P. Skyba, Thermodynamics of the A-B phase transition and the geometry of the A-phase gap nodes in superfluid 3He at low temperatures, Phys. Rev. Lett. 833462–3465 (1999).Google Scholar
  2. 2.
    B. Revaz, J.-Y. Genoud, A. Junod, K. Meumaier, A. Erb, & E. Walker, Phys. Rev. Lett., 80,3364–3367 (1998).Google Scholar
  3. 3.
    G.E. Volovik & V.P. Mineev, 3He-A vs Bose liquid: Orbital angular momentum and orbital dynamics, Sov.Phys. JETP 54 524–530 (1981).Google Scholar
  4. 4.
    P. Muzikar & D. Rainer, Phys. Rev.B 27,4243 (1983).Google Scholar
  5. 5.
    K. Nagai J. LowTemp. Phys., 55 ,233 (1984).Google Scholar
  6. 6.
    G.E. Volovik, (1993) JETP Lett. 58, 469–473.Google Scholar
  7. 7.
    J.R. Kirtley, C.C. Tsuei, M. Rupp, et al., Phys. Rev. Lett. 76,1336 (1996).Google Scholar
  8. 8.
    V. Geshkenbein, A. Larkin & A. Barone, Phys. Rev.B 36 235 (1987).Google Scholar
  9. 9.
    G.E. Volovik & V.P. Mineev, 1976, JETP Lett. 24,561–563 (1976).Google Scholar
  10. 10.
    G.E. Volovik & V.P. Mineev, Current in superfluid Fermi liquids and the vortex core structure, Sou. Phys. JETP 56, 579–586 (1982).Google Scholar
  11. 11.
    H.B. Nielsen & M. Ninorniya, Absence of neutrinos on a lattice. I-Proof by homotopy theory, Nucl. Phys. B 18520 (1981), [Erratum-Nucl. Phys. B 195, 541 (1982)l; Nucl. Phys. B 193173 (1981).Google Scholar
  12. 12.
    G.E. Volovik, Superfluid analogies of cosmological phenomena., gr-qc/0005091.Google Scholar
  13. 13.
    M. Rice, Nature 396627 (1998)Google Scholar
  14. 14.
    K. Ishida, H. Mukuda, Y. Kitaoka et al, Nature 396658660 (1998).Google Scholar
  15. 15.
    T.L. Ho, Phys. Rev. Lett. 81742 (1998).Google Scholar
  16. 16.
    T. Ohmi & K. Machida Bose-Einstein condensation with internal degrees of freedom in alkali atom gases, J. Phys. Soc. Jpn. 671822 (1998); T. Isoshima, M. Nakahara, T. Ohrni & K. Machida, Creation of persistent current and vortex in a Bose-Einstein condensate of alkali-metal atoms, cond-mat/9908470.Google Scholar
  17. 17.
    L. Onsager, NUOVO Cimento 6Suppl. 2, 249 (1949).Google Scholar
  18. 18.
    R.P. Feynman, Progress in Low Temp. Phys.vol. 1, ed. Gorter, C.G. (North-Holland, Amsterdam, 1955) p. 17–53.Google Scholar
  19. 19.
    N.D. Mermin & T.L. Ho, Circulation and angular momentum in the A phase of superfluid 3He. Phys. Rev. Lett. 36594 (1976).Google Scholar
  20. 20.
    P.W. Anderson & G. Toulouse, Phys. Rev. Lett. 38508 (1977).Google Scholar
  21. 21.
    T.L. Ho, Bose-Einstein condensates with internal degrees of freedom, talk at International Conference on Low Temperature Physics LT-22 (Helsinki, 1999).Google Scholar
  22. 22.
    A. Achucarro & T. Vachaspati, Semilocal and Electroweak Strings, Phys. Rep. 327 347–426 (2000).Google Scholar
  23. 23.
    V. R. Eltsov & M. Krusius, Topological defects in 3He superfluids, in "Topolog-ical Defects and the Non-Equilibrium Dynamics of Symmetry Breaking Phase Transitions", Eds. Y.M. Bunkov and H. Godfrin, Kluwer Academic Publishers, 2000, pp. 325–344.Google Scholar
  24. 24.
    R. Blaauwgeers, V.B. Eltsov, H. Gotz, M. Krusius, J.J. Ruohio, R. Schanen & G.E. Volovik, Double-quantum vortex in superfluid 3He-A, Nature 404,471–473 (2000).Google Scholar
  25. 25.
    T.D.C. Bevan, A. J. Manninen, J.B. Cook, J.R. Hook, H.E. Hall, T. Vachaspati & G.E. Volovik, Nature 386689–692 (1997).Google Scholar
  26. 26.
    V. Ruutu, et al.Critical velocity of vortex nucleation in rotating superfluid 3He-A Phys. Rev. Lett. 795058 (1997).Google Scholar
  27. 27.
    M. Joyce & M. Shaposhnikov, Primordial magnetic fields, right electrons, and the abelian anomaly, Phys. Rev. Lett. 791193 (1997).Google Scholar
  28. 28.
    M. Giovannini & E.M. Shaposhnikov, Phys. Rev.D 572186 (1998).Google Scholar
  29. 29.
    U. Parts, E.V. Thuneberg, G.E. Volovik, J.H. Koivuniemi, V.M.H. Ruutu, M. Heinila, J.M. Karimaki & M. Krusius, Phys. Rev. Lett. 72 3839–3842 (1994); M. Heinila & G.E. Volovik, (1995), Physica,B 210,300–310 (1995).Google Scholar
  30. 30.
    A.S. Schwarz, Nucl. Phys. B 208141 (1982).Google Scholar
  31. 31.
    Z.K. Silagadze, TEV scale gravity, mirror universe, and... dinosaurs, hep ph/0002255; Z.K. Silagadze, Mod. Phys. Lett. A14, 2321–2328 (1999).Google Scholar
  32. 32.
    H.Y. Kee, Y.B. Kim & K. Maki, Half-quantum vortex and drsoliton in SrzRu04, cond-rnat/0005510.Google Scholar
  33. 33.
    G.E. Volovik, Monopoles and fractional vortices in chiral superconductors, Proc. Natl. Acad. Sc. USA 972431–2436 (2000).Google Scholar
  34. 34.
    G.E. Volovik & L.P. Gor'kov, JETP Lett. 39674–677 (1984).Google Scholar
  35. 35.
    M. Sigrist, T.M. Rice & K. Ueda, Phys. Rev. Lett. 63, 1727–1730 (1989)Google Scholar
  36. 36.
    M. Sigrist, D.B. Bailey & R.B. Laughlin, Phys. Rev. Lett. 743249–3252 (1995).Google Scholar
  37. 37.
    G.E. Volovik & L.P. Gor'kov, Superconductivity classes in the heavy fermion systems, Sov. Phys. JETP 61843–854 (1985).Google Scholar
  38. 38.
    E. Shung, T.F. Rosenbaum & M. Sigrist, Phys. Rev. Lett. 80107–1981 (1998).Google Scholar
  39. 39.
    S. Blaha Phys. Rev.Lett. 36874 (1976).Google Scholar
  40. 40.
    G.E. Volovik & V.P. Mineev, Vortices with free ends in superfluid 3He-A, JETP Lett. 23593–596 (1976).Google Scholar
  41. 41.
    J.M. Cornwall, Phys. Rev.D 59125015 (1999).Google Scholar
  42. 42.
    Y. Nambu String-like configurations in the Weinberg-Salam theory, Nucl. Phys. B 130505 (1977).Google Scholar
  43. 43.
    K.P. Marzlin, W. Zhang & B.C. Sanders, Creation of skyrmions in a spinor Bose-Einstein condensate, cond-mat/0003273.Google Scholar
  44. 44.
    U. Leonhardt & G.E. Volovik, How to create Alice string (half-quantum vortex) in a vector BoseEinstein condensate, Pisma ZhETF 7266–70 (2000).Google Scholar
  45. 45.
    M.R. Matthews, B.P. Anderson, P.C. Haljan, D.S. Hall, C.E. Wieman, E.A. Cornell, Phys. Rev. Lett. 832498 (1999).Google Scholar
  46. 46.
    R. Jackiw & C. Rebby, Phys. Rev. Lett. 361116 (1976).Google Scholar
  47. 47.
    C. Caroli, P.G. de Gennes & J. Matricon, Phys. Lett. 9307 (1964).Google Scholar
  48. 48.
    G.E. Volovik, Gapless fermionic excitations on the quantized vortices in super-fluids and superconductors, JETP Lett. 49391–395 (1989).Google Scholar
  49. 49.
    Yu.G. Makhlin & G.E. Volovik, One-dimensional Fermi liquid and symmetry breaking in the vortex core, JETP Lett. 62, 737–744 (1995).Google Scholar
  50. 50.
    S.G. Naculich, Ferrnions destabilize electroweak strings, Phys. Rev. Lett. 75 998–1001 (1995).Google Scholar
  51. 51.
    A. Vishwanath & T. Senthil, Luttinger liquid physics in the superconductor vortex core, cond-mat/0001003.Google Scholar
  52. 52.
    N.B. Kopnin & M.M. Salomaa, Phys. Rev. B449667 (1991).Google Scholar
  53. 53.
    G.E. Volovik, Fermion zero modes on vortices in chiral superconductors, JETP Lett. 70609–614 (1999).Google Scholar
  54. 54.
    N. Read & D. Green, Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect, Phys. Rev. B61 ,10267–10297 (2000).Google Scholar
  55. 55.
    D.A. Ivanov, Non-Abelian statistics of half-quantum vortices in pwave super-conductors, cond-mat/0005069.Google Scholar
  56. 56.
    S. Bravyi & A. Kitaev, Fermionic quantum computation, quant-ph/0003137.Google Scholar
  57. 57.
    J. Goryo, Vortex with fractional quantum numbers in a chiral pwave supercon-ductor, Phys. Rev.B 614222 (2000).Google Scholar
  58. 58.
    K. Ishikawa & T. Matsuyama, Z.Phys. C 3341 (1986); Nuclear PhysicsB 280,532 (1987).Google Scholar
  59. 59.
    G.E. Volovik & V.M. Yakovenko, Fkactional charge, spin and statistics of soli-tons in superfluid 3He film, J. Phys.: Cond. Matter 1,5263 (1989).Google Scholar
  60. 60.
    V.M. Yakovenko, Spin, statistics and charge of solitons in (2+1)-dimensional theories, Fizika (Zagreb) 21suppl. 3, 231 (1989) [cond-mat/9703195].Google Scholar
  61. 61.
    T. Senthil, J.B. Marston & M.P.A. Fisher, Phys. Rev. B 60,4245 (1999).Google Scholar

Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • G. E. Volovik
    • 1
    • 2
  1. 1.Low Temperature LaboratoryHelsinki University of TechnologyHUTFinland
  2. 2.L.D. Landau Institute for Theoretical PhysicsMoscowRussia

Personalised recommendations