Journal of Low Temperature Physics

, Volume 187, Issue 5–6, pp 340–353 | Cite as

Electron Bubbles in Superfluid \(^3\)He-A: Exploring the Quasiparticle–Ion Interaction

Article

Abstract

When an electron is forced into liquid \(^3\)He, it forms an “electron bubble”, a heavy ion with radius, \(R\simeq 1.5\) nm, and mass, \(M\simeq 100\,m_3\), where \(m_3\) is the mass of a \(^3\)He atom. These negative ions have proven to be powerful local probes of the physical properties of the host quantum fluid, especially the excitation spectra of the superfluid phases. We recently developed a theory for Bogoliubov quasiparticles scattering off electron bubbles embedded in a chiral superfluid that provides a detailed understanding of the spectrum of Weyl Fermions bound to the negative ion, as well as a theory for the forces on moving electron bubbles in superfluid \(^3\)He-A (Shevtsov and Sauls in Phys Rev B 94:064511, 2016). This theory is shown to provide quantitative agreement with measurements reported by the RIKEN group (Ikegami et al. in Science 341(6141):59, 2013) for the drag force and anomalous Hall effect of moving electron bubbles in superfluid \(^3\)He-A. In this report, we discuss the sensitivity of the forces on the moving ion to the effective interaction between normal-state quasiparticles and the ion. We consider models for the quasiparticle–ion (QP–ion) interaction, including the hard-sphere potential, constrained random-phase-shifts, and interactions with short-range repulsion and intermediate-range attraction. Our results show that the transverse force responsible for the anomalous Hall effect is particularly sensitive to the structure of the QP–ion potential and that strong short-range repulsion, captured by the hard-sphere potential, provides an accurate model for computing the forces acting on the moving electron bubble in superfluid \(^{3}\)He-A.

Keywords

Superfluid \(^3\)He Electron bubbles Scattering theory t Matrix Weyl Fermions Broken parity and time-reversal Chirality 

References

  1. 1.
    G.E. Volovik, Sov. Phys. JETP 67, 1804 (1988)Google Scholar
  2. 2.
    G.E. Volovik, JETP Lett. 55(6), 368 (1992)ADSGoogle Scholar
  3. 3.
    M. Stone, R. Roy, Phys. Rev. B 69(18), 184511 (2004)ADSCrossRefGoogle Scholar
  4. 4.
    J.A. Sauls, Phys. Rev. B 84, 214509 (2011)ADSCrossRefGoogle Scholar
  5. 5.
    Y. Tsutsumi, K. Machida, J. Phys. Soc. Jpn. 81(7), 074607 (2012)ADSCrossRefGoogle Scholar
  6. 6.
    Y. Tsutsumi, K. Machida, Phys. Rev. B 85, 100506 (2012)ADSCrossRefGoogle Scholar
  7. 7.
    H. Ikegami, Y. Tsutsumi, K. Kono, Science 341(6141), 59 (2013)ADSCrossRefGoogle Scholar
  8. 8.
    H. Ikegami, S.B. Chung, K. Kono, J. Phys. Soc. Jpn. 82, 124607 (2013)ADSCrossRefGoogle Scholar
  9. 9.
    H. Ikegami, Y. Tsutsumi, K. Kono, J. Phys. Soc. Jpn. 84(4), 044602 (2015)ADSCrossRefGoogle Scholar
  10. 10.
    R.A. Ferrell, Phys. Rev. 108, 167 (1957)ADSCrossRefGoogle Scholar
  11. 11.
    C.G. Kuper, Phys. Rev. 122, 1007 (1961)ADSCrossRefGoogle Scholar
  12. 12.
    A.C. Anderson, M. Kuchnir, J.C. Wheatley, Phys. Rev. 168, 261 (1968)ADSCrossRefGoogle Scholar
  13. 13.
    O. Shevtsov, J.A. Sauls, Phys. Rev. B 94, 064511 (2016)ADSCrossRefGoogle Scholar
  14. 14.
    A.I. Ahonen, J. Kokko, O.V. Lounasmaa, M.A. Paalanen, R.C. Richardson, W. Schoepe, Y. Takano, Phys. Rev. Lett. 37, 511 (1976)ADSCrossRefGoogle Scholar
  15. 15.
    A.I. Ahonen, J. Kokko, M.A. Paalanen, R.C. Richardson, W. Schoepe, Y. Takano, J. Low Temp. Phys. 30(1), 205 (1978)ADSCrossRefGoogle Scholar
  16. 16.
    B.D. Josephson, J. Lekner, Phys. Rev. Lett. 23, 111 (1969)ADSCrossRefGoogle Scholar
  17. 17.
    A.L. Fetter, J. Kurkijärvi, Phys. Rev. B 15, 4272 (1977)ADSCrossRefGoogle Scholar
  18. 18.
    J. Rammer, Quantum Transport Theory (Perseus Books, Reading, 1998)MATHGoogle Scholar
  19. 19.
    A. Messiah, Quantum Mechanics, vol. I (North-Holland, Amsterdam, 1958)MATHGoogle Scholar
  20. 20.
    F. Calogero, Variable Phase Approach to Potential Scattering (Academic Press, New York, 1967)MATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Physics and AstronomyNorthwestern UniversityEvanstonUSA

Personalised recommendations