- Physical Review Journals
All JournalsPhysics Magazine

Physical Review B

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

Axion electrodynamics of Weyl superconductors with broken time-reversal symmetry

Vira Shyta1, Jeroen van den Brink1,2, and Flavio S. Nogueira1

PDF

Phys. Rev. B 112, 104517 – Published 30 September, 2025

DOI: https://doi.org/10.1103/5fpw-gc9g

Abstract

The low-energy effective description of Weyl semimetals is defined by the axion electrodynamics, which captures the effects arising due to the presence of nodes of opposite chirality in the electronic structure. Here, we explore the magnetoelectric response of time-reversal breaking (TRB) Weyl superconductors in the London regime. The influence of the axion contribution leads to an increase in the London penetration depth—a behavior that can be anticipated by first considering the photon spectrum of a TRB Weyl semimetal. Moreover, we find that both the Meissner state and the vortex phase feature an interplay between the electric and magnetic fields. This leads to a nonvanishing electromagnetic angular momentum, which we calculate for a number of geometrical configurations.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (50)

  1. F. Wilczek, Two applications of axion electrodynamics, Phys. Rev. Lett. 58, 1799 (1987).
  2. P. Hosur, X. Dai, Z. Fang, and X.-L. Qi, Time-reversal-invariant topological superconductivity in doped Weyl semimetals, Phys. Rev. B 90, 045130 (2014).
  3. S. Ryu, J. E. Moore, and A. W. W. Ludwig, Electromagnetic and gravitational responses and anomalies in topological insulators and superconductors, Phys. Rev. B 85, 045104 (2012).
  4. A. Burkov, Weyl metals, Annu. Rev. Condens. Matter Phys. 9, 359 (2018).
  5. S. L. Adler, Axial-vector vertex in spinor electrodynamics, Phys. Rev. 177, 2426 (1969).
  6. J. S. Bell and R. W. Jackiw, A PCAC puzzle: π0→γγ in σ-model, Nuovo Cimento A 60, 47 (1969).
  7. K. Fujikawa, Path integral for gauge theories with fermions, Phys. Rev. D 21, 2848 (1980).
  8. H. Nielsen and M. Ninomiya, The Adler-Bell-Jackiw anomaly and Weyl fermions in a crystal, Phys. Lett. B 130, 389 (1983).
  9. X.-L. Qi, T. L. Hughes, and S.-C. Zhang, Topological field theory of time-reversal invariant insulators, Phys. Rev. B 78, 195424 (2008).
  10. X.-L. Qi, E. Witten, and S.-C. Zhang, Axion topological field theory of topological superconductors, Phys. Rev. B 87, 134519 (2013).
  11. A. Karch, Electric-magnetic duality and topological insulators, Phys. Rev. Lett. 103, 171601 (2009).
  12. L. Wu, M. Salehi, N. Koirala, J. Moon, S. Oh, and N. P. Armitage, Quantized Faraday and Kerr rotation and axion electrodynamics of a 3D topological insulator, Science 354, 1124 (2016).
  13. V. Dziom, A. Shuvaev, A. Pimenov, G. V. Astakhov, C. Ames, K. Bendias, J. Böttcher, G. Tkachov, E. M. Hankiewicz, C. Brüne, H. Buhmann, and L. W. Molenkamp, Observation of the universal magnetoelectric effect in a 3D topological insulator, Nat. Commun. 8, 15197 (2017).
  14. A. Karch, Surface plasmons and topological insulators, Phys. Rev. B 83, 245432 (2011).
  15. A. Lakhtakia and T. G. Mackay, Electromagnetic scattering by homogeneous, isotropic, dielectric–magnetic sphere with topologically insulating surface states, J. Opt. Soc. Am. B 33, 603 (2016).
  16. J. Schultz, F. S. Nogueira, B. Büchner, J. van den Brink, and A. Lubk, Axion Mie theory of electron energy loss spectroscopy in topological insulators, SciPost Phys. Core 4, 023 (2021).
  17. X.-L. Qi, R. Li, J. Zang, and S.-C. Zhang, Inducing a magnetic monopole with topological surface states, Science 323, 1184 (2009).
  18. F. S. Nogueira and J. van den Brink, Absence of induced magnetic monopoles in Maxwellian magnetoelectrics, Phys. Rev. Res. 4, 013074 (2022).
  19. F. S. Nogueira, Z. Nussinov, and J. van den Brink, Josephson currents induced by the Witten effect, Phys. Rev. Lett. 117, 167002 (2016).
  20. F. S. Nogueira, Z. Nussinov, and J. van den Brink, Fractional angular momentum at topological insulator interfaces, Phys. Rev. Lett. 121, 227001 (2018).
  21. E. Witten, Dyons of charge eθ/2π, Phys. Lett. B 86, 283 (1979).
  22. F. S. Nogueira, Z. Nussinov, and J. van den Brink, Duality of a compact topological superconductor model and the Witten effect, Phys. Rev. D 94, 085003 (2016).
  23. B. Yan and C. Felser, Topological materials: Weyl semimetals, Annu. Rev. Condens. Matter Phys. 8, 337 (2017).
  24. A. G. Grushin, Consequences of a condensed matter realization of Lorentz-violating QED in Weyl semi-metals, Phys. Rev. D 86, 045001 (2012).
  25. E. V. Gorbar, V. A. Miransky, I. A. Shovkovy, and P. O. Sukhachov, Anomalous transport properties of Dirac and Weyl semimetals (Review Article), Low Temp. Phys. 44, 487 (2018).
  26. A. A. Zyuzin and A. A. Burkov, Topological response in Weyl semimetals and the chiral anomaly, Phys. Rev. B 86, 115133 (2012).
  27. D. T. Son and B. Z. Spivak, Chiral anomaly and classical negative magnetoresistance of Weyl metals, Phys. Rev. B 88, 104412 (2013).
  28. C.-X. Liu, P. Ye, and X.-L. Qi, Chiral gauge field and axial anomaly in a Weyl semimetal, Phys. Rev. B 87, 235306 (2013).
  29. S. A. Parameswaran, T. Grover, D. A. Abanin, D. A. Pesin, and A. Vishwanath, Probing the chiral anomaly with nonlocal transport in three-dimensional topological semimetals, Phys. Rev. X 4, 031035 (2014).
  30. M. Z. Hasan, S.-Y. Xu, and G. Bian, Topological insulators, topological superconductors and Weyl fermion semimetals: Discoveries, perspectives and outlooks, Phys. Scr. 2015, 014001 (2015).
  31. N. P. Ong and S. Liang, Experimental signatures of the chiral anomaly in Dirac-Weyl semimetals, Nat. Rev. Phys. 3, 394 (2021).
  32. V. Könye, L. Mertens, C. Morice, D. Chernyavsky, A. G. Moghaddam, J. van Wezel, and J. van den Brink, Anisotropic optics and gravitational lensing of tilted Weyl fermions, Phys. Rev. B 107, L201406 (2023).
  33. P. E. C. Ashby and J. P. Carbotte, Magneto-optical conductivity of Weyl semimetals, Phys. Rev. B 87, 245131 (2013).
  34. R. Côté, R. N. Duchesne, G. D. Duchesne, and O. Trêpanier, Chiral filtration and Faraday rotation in multi-Weyl semimetals, Results Phys. 54, 107064 (2023).
  35. N. Nagaosa, J. Sinova, S. Onoda, A. H. MacDonald, and N. P. Ong, Anomalous Hall effect, Rev. Mod. Phys. 82, 1539 (2010).
  36. A. A. Burkov, Chiral anomaly and transport in Weyl metals, J. Phys.: Condens. Matter 27, 113201 (2015).
  37. D. E. Kharzeev, The chiral magnetic effect and anomaly-induced transport, Prog. Part. Nucl. Phys. 75, 133 (2014).
  38. N. P. Armitage, E. J. Mele, and A. Vishwanath, Weyl and Dirac semimetals in three-dimensional solids, Rev. Mod. Phys. 90, 015001 (2018).
  39. V. Shyta, J. van den Brink, and F. S. Nogueira, Chiral Meissner state in time-reversal invariant Weyl superconductors, Phys. Rev. Res. 6, 013240 (2024).
  40. S. M. Carroll, G. B. Field, and R. Jackiw, Limits on a Lorentz- and parity-violating modification of electrodynamics, Phys. Rev. D 41, 1231 (1990).
  41. Y. Ferreiros and A. Cortijo, Unconventional electromagnetic mode in neutral Weyl semimetals, Phys. Rev. B 93, 195154 (2016).
  42. S. Deser, R. Jackiw, and S. Templeton, Topologically massive gauge theories, Ann. Phys. (NY) 281, 409 (2000).
  43. F. M. D. Pellegrino, M. I. Katsnelson, and M. Polini, Helicons in Weyl semimetals, Phys. Rev. B 92, 201407(R) (2015).
  44. F. London, Superfluids: Macroscopic Theory of Superconductivity, Structure of Matter Series (Wiley, New York, 1950).
  45. R. Becker, G. Heller, and F. Sauter, Über die stromverteilung in einer supraleitenden kugel, Z. Phys. 85, 772 (1933).
  46. A. F. Hildebrandt, Magnetic field of a rotating superconductor, Phys. Rev. Lett. 12, 190 (1964).
  47. C. W. F. Everitt, D. B. DeBra, B. W. Parkinson, J. P. Turneaure, J. W. Conklin, M. I. Heifetz, G. M. Keiser, A. S. Silbergleit, T. Holmes, J. Kolodziejczak, M. Al-Meshari, J. C. Mester, B. Muhlfelder, V. G. Solomonik, K. Stahl, P. W. Worden, W. Bencze, S. Buchman, B. Clarke, A. Al-Jadaan et al., Gravity Probe B: Final results of a space experiment to test general relativity, Phys. Rev. Lett. 106, 221101 (2011).
  48. C. W. F. Everitt, B. Muhlfelder, D. B. DeBra, B. W. Parkinson, J. P. Turneaure, A. S. Silbergleit, E. B. Acworth, M. Adams, R. Adler, W. J. Bencze et al., The Gravity Probe B test of general relativity, Class. Quant. Grav. 32, 224001 (2015).
  49. R. Jackiw and E. J. Weinberg, Self-dual Chern-Simons vortices, Phys. Rev. Lett. 64, 2234 (1990).
  50. J. E. Hirsch, The London moment: What a rotating superconductor reveals about superconductivity, Phys. Scr. 89, 015806 (2014).

Outline

Information

Phys. Rev. B 112, 104517– Published 30 September, 2025
  • Received 20 June 2025
  • Revised 29 August 2025
  • Accepted 16 September 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation