JETP Letters

, Volume 104, Issue 3, pp 201–203 | Cite as

Condensation of fermion zero modes in the vortex

  • G. E. Volovik
Condensed Matter


The energy levels of the fermions bound to the vortex are considered for vortices in the superfluid/superconducting systems that contain the symmetry protected plane of zeroes in the gap function in bulk. The Caroli–de Gennes–Matricon branches with different approach zero energy level at p z → 0. The density of states of the bound fermions diverges at zero energy giving rise to the \(\sqrt \Omega \) dependence of the density of states in the polar phase of superfluid 3He rotating with the angular velocity Ω and to the \(\sqrt B \) dependence of the density of states for superconductors in the (d xz + id yz )-wave pairing state.


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  1. 1.
    C. Caroli, P. G. de Gennes, and J. Matricon, Phys. Lett. 9, 307 (1964).ADSCrossRefGoogle Scholar
  2. 2.
    G. E. Volovik, JETP Lett. 70, 609 (1999); condmat/9909426.ADSCrossRefGoogle Scholar
  3. 3.
    G. E. Volovik, The Universe in a Helium Droplet (Clarendon, Oxford, 2003).zbMATHGoogle Scholar
  4. 4.
    N. Read and D. Green, Phys. Rev. B 61, 10267 (2000).ADSCrossRefGoogle Scholar
  5. 5.
    D. A. Ivanov, Phys. Rev. Lett. 86, 268 (2001).ADSCrossRefGoogle Scholar
  6. 6.
    N. B. Kopnin and M. M. Salomaa, Phys. Rev. B 44, 9667 (1991).ADSCrossRefGoogle Scholar
  7. 7.
    G. E. Volovik, JETP Lett. 93, 66 (2011); arXiv:1011.4665.ADSCrossRefGoogle Scholar
  8. 8.
    D. Lee and A. P. Schnyder, Phys. Rev. B 93, 064522 (2016).ADSCrossRefGoogle Scholar
  9. 9.
    T. Mizushima, Ya. Tsutsumi, T. Kawakami, M. Sato, M. Ichioka, and K. Machida, J. Phys. Soc. Jpn. 85, 022001 (2016).ADSCrossRefGoogle Scholar
  10. 10.
    Sh. Kittaka, Y. Shimizu, T. Sakakibara, Y. Haga, E. Yamamoto, Y. Onuki, Y. Tsutsumi, T. Nomoto, H. Ikeda, and K. Machida, J. Phys. Soc. Jpn. 85, 033704 (2016).ADSCrossRefGoogle Scholar
  11. 11.
    S. Autti, V. V. Dmitriev, V. B. Eltsov, J. Makinen, G. E. Volovik, A. N. Yudin, and V. V. Zavjalov, arXiv:1508.02197.Google Scholar
  12. 12.
    V. V. Dmitriev, A. A. Senin, A. A. Soldatov, and A. N. Yudin, Phys. Rev. Lett. 115, 165304 (2015).ADSCrossRefGoogle Scholar
  13. 13.
    G. E. Volovik and L. P. Gor’kov, Sov. Phys. JETP 61, 843 (1985).CrossRefGoogle Scholar
  14. 14.
    M. A. Silaev, JETP Lett. 90, 433 (2009); arXiv:0907.5341.ADSCrossRefGoogle Scholar
  15. 15.
    M. A. Silaev, E. V. Thuneberg, and M. Fogelström, Phys. Rev. Lett. 115, 235301 (2015).ADSCrossRefGoogle Scholar
  16. 16.
    G. E. Volovik, JETP Lett. 58, 469 (1993).ADSGoogle Scholar

Copyright information

© Pleiades Publishing, Inc. 2016

Authors and Affiliations

  1. 1.Low Temperature Laboratory, Department of Applied PhysicsAalto UniversityAALTOFinland
  2. 2.Landau Institute for Theoretical PhysicsChernogolovka, Moscow regionRussia
  3. 3.Nordita, KTH Royal Institute of Technology and Stockholm UniversityStockholmSweden

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