Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Dynamic interaction between chiral currents and surface waves in topological superfluid

S. Forstner1,2,*, H. Choi3,4,†, G. I. Harris1, A. Sawadsky1, W. P. Bowen1, and C. G. Baker1,‡

  • *Contact author: stefan.forstner@icfo.eu
  • †Contact author: h.choi@kaist.ac.kr
  • ‡Contact author: c.baker3@uq.edu.au

Phys. Rev. Research 8, 033275 – Published 4 September, 2026

DOI: https://doi.org/10.1103/93r1-vqk2

Abstract

Despite extensive experimental efforts over the past two decades, topological superconductivity and Majorana fermions have remained elusive. By shifting focus from superconductors—whose topological nature is often debated—to the well-established p-wave superfluid He3, we propose an experimental approach designed to identify quantum Hall nature of the chiral superfluid He3−A phase. The method exploits the interaction between surface waves and the induced current transverse to varying density of the superfluid. It allows one to quantitatively measure this Hall current and thus to directly evaluate whether the Hall current is quantized or not. As the quantum Hall effect is a hallmark of topological condensed matter, such an experiment would offer direct evidence of nontrivial topology of superfluid He3. With the advent of microscopic superfluid resonators coupled to optical cavities, this proposal is both realistic and promising, potentially opening the door to future experiments ranging from topological acoustics to fault-tolerant quantum computing.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (70)

  1. C.-K. Chiu, J. C. Y. Teo, A. P. Schnyder, and S. Ryu, Classification of topological quantum matter with symmetries, Rev. Mod. Phys. 88, 035005 (2016).
  2. B. A. Bernevig, T. L. Hughes, and S.-C. Zhang, Quantum spin Hall effect and topological phase transition in HgTe quantum wells, Science 314, 1757 (2006).
  3. M. Kono, S. Wiedmann, C. Brune, A. Roth, H. Buhmann, L. W. Molenkamp, X.-L. Qi, and S.-C. Zhang, Quantum spin Hall insulator state in HgTe quantum wells, Science 318, 766 (2007).
  4. A. A. Burkov, Topological semimetals, Nat. Mater. 15, 1145 (2016).
  5. Z. Liu, B. Zhou, Y. Zhang, Z. Wang, H. Weng, D. Prabhakaran, S.-K. Mo, Z. Shen, Z. Fang, X. Dai, Z. Hussain, and Y. Chen, Discovery of a three-dimensional topological Dirac semimetal, Na3Bi, Science 343, 864 (2014).
  6. S.-Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z. Yuan, C.-C. Lee, S.-M. Huang, H. Zheng, J. Ma, D. Sanchez, B. Wang, A. Bansil, F. Chou, P. Shibayev, H. Lin, and M. Z. Hasan, Discovery of a Weyl fermion semimetal and topological Fermi arcs, Science 349, 613 (2015).
  7. X.-L. Qi and S.-C. Zhang, Topological insulators and superconductors, Rev. Mod. Phys. 83, 1057 (2011).
  8. M. Sato and Y. Ando, Topological superconductors: A review, Rep. Prog. Phys. 80, 076501 (2017).
  9. A. Yazdani, F. Oppen, B. Halperin, and A. Yacoby, Hunting for Majoranas, Science 380, eade0850 (2023).
  10. M. Mandal, N. C. Drucker, P. Siriviboon, T. Nguyen, A. Boonkird, T. N. Lamichhane, R. Okabe, A. Chotrattanapituk, and M. Li, Topological superconductors from a materials perspective, Chem. Mater. 35, 6184 (2023).
  11. L. Fu and C. L. Kane, Superconducting proximity effect and Majorana fermions at the surface of a topological insulator, Phys. Rev. Lett. 100, 096407 (2008).
  12. V. Mourik, K. Zuo, S. M. Frolov, S. R. Plissard, E. P. A. M. Bakkers, and L. P. Kouwenhoven, Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices, Science 336, 1003 (2012).
  13. S. Nadj-Perge, I. K. Drozdov, J. Li, H. Chen, S. Jeon, J. Seo, A. H. MacDonald, B. A. Bernevig, and A. Yazdani, Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor, Science 346, 602 (2014).
  14. Q. L. He, L. Pan, A. L. Stern, E. C. Burks, X. Che, G. Yin, J. Wang, B. Lian, Q. Zhou, E. S. Choi, K. Murata, X. Kou, Z. Chen, T. Nie, Q. Shao, Y. Fan, S.-C. Zhang, K. Liu, J. Xia, and K. L. Wang, Chiral Majorana fermion modes in a quantum anomalous Hall insulator–superconductor structure, Science 357, 294 (2017).
  15. R. M. Lutchyn, E. P. A. M. Bakkers, L. P. Kouwenhoven, P. Krogstrup, C. M. Marcus, and Y. Oreg, Majorana zero modes in superconductor–semiconductor heterostructures, Nat. Rev. Mater. 3, 52 (2018).
  16. Microsoft Azure Quantum, M. Aghaee, A. A. Ramirez, Z. Alam, R. Ali, M. Andrzejczuk, A. Antipov, M. Astafev, A. Barzegar, B. Bauer, et al., Interferometric single-shot parity measurement in InAs-Al hybrid devices, Nature (London) 638, 651 (2025).
  17. M. Kayyalha, D. Xiao, R. Zhang, J. Shin, J. Jiang, F. Wang, Y.-F. Zhao, R. Xiao, L. Zhang, K. M. Fijalkowski, P. Mandal, M. Winnerlein, C. Gould, Q. Li, L. W. Molenkamp, M. H. W. Chan, N. Samarth, and C.-Z. Chang, Absence of evidence for chiral Majorana modes in quantum anomalous Hall-superconductor devices, Science 367, 64 (2020).
  18. P. Yu, J. Chen, M. Gomanko, G. Badawy, E. P. A. M. Bakkers, K. Zuo, V. Mourik, and S. M. Frolov, Non-Majorana states yield nearly quantized conductance in proximatized nanowires, Nat. Phys. 17, 482 (2021).
  19. M. Valentini, M. Borovkov, E. Prada, S. Martí-Sánchez, M. Botifoll, A. Hofmann, J. Arbiol, R. Aguado, P. San-Jose, and G. Katsaros, Majorana-like Coulomb spectroscopy in the absence of zero-bias peaks, Nature (London) 612, 442 (2022).
  20. Y. Tanaka, S. Tamura, and J. Cayao, Theory of Majorana zero modes in unconventional superconductors, Prog. Theor. Exp. Phys. 2024, 08C105 (2024).
  21. D. Castelvecchi, Microsoft claims quantum-computing breakthrough—But some physicists are sceptical, Nature (London) 638, 872 (2025).
  22. Y. Aoki, Y. Wada, M. Saitoh, R. Nomura, Y. Okuda, Y. Nagato, M. Yamamoto, S. Higashitani, and K. Nagai, Observation of surface Andreev bound states of superfluid He3 by transverse acoustic impedance measurements, Phys. Rev. Lett. 95, 075301 (2005).
  23. H. Choi, J. P. Davis, J. Pollanen, and W. P. Halperin, Surface specific heat of He3 and Andreev bound states, Phys. Rev. Lett. 96, 125301 (2006).
  24. H. Ikegami, Y. Tsutsumi, and K. Kono, Chiral symmetry breaking in superfluid He3-A, Science 341, 59 (2013).
  25. M. C. Cross, A generalized Ginzburg-Landau approach to the superfluidity of helium 3, J. Low Temp. Phys. 21, 525 (1975).
  26. N. D. Mermin and P. Muzikar, Cooper pairs versus Bose condensed molecules: The ground-state current in superfluid He3-A, Phys. Rev. B 21, 980 (1980).
  27. R. Combescot and T. Dombre, Superfluid current in He3-A at T = 0, Phys. Rev. B 28, 5140 (1983).
  28. V. Ambegaokar, P. G. deGennes, and D. Rainer, Landau-Ginsburg equations for an anisotropic superfluid, Phys. Rev. A 9, 2676 (1974).
  29. J. E. Avron, R. Seiler, and P. G. Zograf, Viscosity of quantum Hall fluids, Phys. Rev. Lett. 75, 697 (1995).
  30. N. Read, Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states and px+ipy paired superfluids, Phys. Rev. B 79, 045308 (2009).
  31. M. Barkeshli, S. B. Chung, and X.-L. Qi, Dissipationless phonon Hall viscosity, Phys. Rev. B 85, 245107 (2012).
  32. S. T. Ramamurthy and T. L. Hughes, Patterns of electromagnetic response in topological semimetals, Phys. Rev. B 92, 085105 (2015).
  33. P. Rao and B. Bradlyn, Hall viscosity in quantum systems with discrete symmetry: Point group and lattice anisotropy, Phys. Rev. X 10, 021005 (2020).
  34. A. M. R. Schechter, R. W. Simmonds, R. E. Packard, and J. C. Davis, Observation of third sound in superfluid He3, Nature (London) 396, 554 (1998).
  35. H. S. Byun, J. Jeong, K. Kim, S. G. Kim, S.-B. Shim, J. Suh, and H. Choi, Measuring angular momentum of px+ipy topological superfluids: A proposal, Phys. Rev. B 98, 024518 (2018).
  36. G. I. Harris, D. L. McAuslan, E. Sheridan, Y. Sachkou, C. Baker, and W. P. Bowen, Laser cooling and control of excitations in superfluid helium, Nat. Phys. 12, 788 (2016).
  37. D. L. McAuslan, G. I. Harris, C. Baker, Y. Sachkou, X. He, E. Sheridan, and W. P. Bowen, Microphotonic forces from superfluid flow, Phys. Rev. X 6, 021012 (2016).
  38. Y. P. Sachkou, C. G. Baker, G. I. Harris, O. R. Stockdale, S. Forstner, M. T. Reeves, X. He, D. L. McAuslan, A. S. Bradley, M. J. Davis, and W. P. Bowen, Coherent vortex dynamics in a strongly interacting superfluid on a silicon chip, Science 366, 1480 (2019).
  39. X. He, G. I. Harris, C. G. Baker, A. Sawadsky, Y. L. Sfendla, Y. P. Sachkou, S. Forstner, and W. P. Bowen, Strong optical coupling through superfluid Brillouin lasing, Nat. Phys. 16 417 (2020).
  40. A. Sawadsky, R. A. Harrison, G. I. Harris, W. W. Wasserman, Y. L. Sfendla, W. P. Bowen, and C. G. Baker, Engineered entropic forces allow ultrastrong dynamical backaction, Sci. Adv. 9, eade3591 (2023).
  41. F. M. Ellis and L. Li, Quantum swirling of superfluid helium films, Phys. Rev. Lett. 71, 1577 (1993).
  42. J. A. Sauls, Surface states, edge currents, and the angular momentum of chiral p-wave superfluids, Phys. Rev. B 84, 214509 (2011).
  43. M. Stone and R. Roy, Edge modes, edge currents, and gauge invariance in px+ipy superfluids and superconductors, Phys. Rev. B 69, 184511 (2004).
  44. K. R. Atkins, Third and fourth sound in liquid helium II, Phys. Rev. 113, 962 (1959).
  45. C. G. Baker, G. I. Harris, D. L. McAuslan, Y. Sachkou, X. He, and W. P. Bowen, Theoretical framework for thin film superfluid optomechanics: Towards the quantum regime, New J. Phys. 18, 123025 (2016).
  46. S. Forstner, Y. Sachkou, M. Woolley, G. I. Harris, X. He, W. P. Bowen, and C. G. Baker, Modelling of vorticity, sound and their interaction in two-dimensional superfluids, New J. Phys. 21, 053029 (2019).
  47. I. Rudnick, H. Kojima, W. Veith, and R. S. Kagiwada, Observation of superfluid-helium persistent current by Doppler-shifted splitting of fourth-sound resonance, Phys. Rev. Lett. 23, 1220 (1969).
  48. F. M. Ellis and H. Luo, Observation of the persistent-current splitting of a third-sound resonator, Phys. Rev. B 39, 2703 (1989).
  49. G. Volovik, An analog of the quantum Hall effect in a superfluid He3 film, Z. Eksp. Teor. Fiz. 94, 123 (1988) [Sov. Phys. JETP 67, 1804 (1988)].
  50. N. Zhelev, T. S. Abhilash, E. N. Smith, R. G. Bennett, X. Rojas, L. Levitin, J. Saunders, and J. M. Parpia, The A-B transition in superfluid helium-3 under confinement in a thin slab geometry, Nat. Commun. 8, 15963 (2017).
  51. L. V. Levitin, R. G. Bennett, A. Casey, B. Cowan, J. Saunders, D. Drung, T. Schurig, and J. M. Parpia, Phase diagram of the topological superfluid He3 confined in a nanoscale slab geometry, Science 340, 841 (2013).
  52. L. V. Levitin, R. G. Bennett, E. V. Surovtsev, J. M. Parpia, B. Cowan, A. J. Casey, and J. Saunders, Surface-induced order parameter distortion in superfluid He3−B measured by nonlinear NMR, Phys. Rev. Lett. 111, 235304 (2013).
  53. A. Vorontsov and J. A. Sauls, Spectrum of third sound cavity modes on superfluid 3, J. Low Temp. Phys. 134, 1001 (2004).
  54. W. W. Wasserman, R. A. Harrison, G. I. Harris, A. Sawadsky, Y. L. Sfendla, W. P. Bowen, and C. G. Baker, Cryogenic and hermetically sealed packaging of photonic chips for optomechanics, Opt. Express 30, 30822 (2022).
  55. V. Almeida, C. Barrios, R. Panepucci, and M. Lipson, All-optical control of light on silicon chip, Nature (London) 431, 1081 (2004).
  56. S. M. Meenehan, J. D. Cohen, G. S. MacCabe, F. Marsili, M. D. Shaw, and O. Painter, Pulsed excitation dynamics of an optomechanical crystal resonator near its quantum ground state of motion, Phys. Rev. X 5, 041002 (2015).
  57. M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Cavity optomechanics, Rev. Mod. Phys. 86, 1391 (2014).
  58. D. Vollhardt and P. Wölfle, The Superfluid Phases of Helium 3 (Taylor & Francis, London, 1990).
  59. Z. Yang, F. Gao, X. Shi, X. Lin, Z. Gao, Y. Chong, and B. Zhang, Topological acoustics, Phys. Rev. Lett. 114, 114301 (2015).
  60. A. Souslov, B. C. van Zuiden, D. Bartolo, and V. Vitelli, Topological sound in active-liquid metamaterials, Nat. Phys. 13, 1091 (2017).
  61. R. Fleury, D. L. Sounas, C. F. Sieck, M. R. Haberman, and A. Alù, Sound isolation and giant linear nonreciprocity in a compact acoustic circulator, Science 343, 516 (2014).
  62. J. T. Mäkinen, V. Dmitriev, J. Nissinen, J. Rysti, G. Volovik, A. Yudin, K. Zhang, and V. Eltsov, Half-quantum vortices and walls bounded by strings in the polar-distorted phases of topological superfluid He3, Nat. Commun. 10, 237 (2019).
  63. G. E. Volovik, The Universe in a Helium Droplet, International Series of Monographs on Physics (Oxford University Press, Oxford, 2009).
  64. C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. Das Sarma, Non-Abelian anyons and topological quantum computation, Rev. Mod. Phys. 80, 1083 (2008).
  65. B. Lian, X.-Q. Sun, A. Vaezi, X.-L. Qi, and S.-C. Zhang, Topological quantum computation based on chiral Majorana fermions, Proc. Natl. Acad. Sci. USA 115, 10938 (2018).
  66. D. A. Ivanov, Non-Abelian statistics of half-quantum vortices in p-wave superconductors, Phys. Rev. Lett. 86, 268 (2001).
  67. S. Das Sarma, M. Freedman, and C. Nayak, Majorana zero modes and topological quantum computation, npj Quantum Inf. 1, 15001 (2015).
  68. C. G. Baker and S. Forstner, Calculation of the interaction between chiral current and surface waves in the A-phase of helium-3, Zenodo, 2024, https://doi.org/10.5281/zenodo.10867829.
  69. M. Iino, M. Suzuki, A. J. Ikushima, and Y. Okuda, Surface tension of liquid He3 down to 0.3 K, J. Low Temp. Phys. 59, 291 (1985).
  70. A. M. R. Schechter, Third sound in superfluid helium-3, Ph.D. thesis, University of California, Berkeley, 1999.

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation