- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Letters

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

Micromotion Area as Proxy for Anomalous Floquet Topological Systems

Luca Asteria1,*, Klaus Sengstock2,3, André Eckardt4, and Christof Weitenberg5,†

  • *Contact author: asteria.luca.6w@kyoto-u.ac.jp
  • †Contact author: christof.weitenberg@tu-dortmund.de
PDF

Phys. Rev. Lett. 137, 153401 – Published 5 October, 2026

DOI: https://doi.org/10.1103/7wl9-5971

Abstract

Driven Floquet systems can realize topological phases with no static counterparts. This so-called anomalous Floquet topology breaks the bulk-boundary correspondence based on the Chern number. The number of edge modes in each band gap is instead determined by another integer index, a winding number, which is calculated from the time evolution operator of the bulk states within one driving period. While topological Chern numbers can be inferred from real-space measurements, it is not straightforward to obtain information about the anomalous Floquet topological phase from bulk measurements. Here we consider two-band models and show that the area enclosed during a Floquet period by an initially localized particle signals the presence of an anomalous phase when it approaches half the unit cell area. In general, we show that for dispersionless dynamics during the micromotion, the enclosed area is quantized and an exact proportionality relation exists between the area and the winding number. Direct detection of anomalous topology in real space could be realized in several quantum simulation platforms, and could be useful for systems with disorder or interactions. Building on the connection between area and winding number, we also show a way to realize arbitrarily high winding numbers.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (42)

  1. M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. 82, 3045 (2010).
  2. A. P. Schnyder, S. Ryu, A. Furusaki, and A. W. W. Ludwig, Phys. Rev. B 78, 195125 (2008).
  3. A. Kitaev, AIP Conf. Proc. 1134, 22 (2009).
  4. S. Ryu, A. P. Schnyder, A. Furusaki, and A. W. W. Ludwig, New J. Phys. 12, 065010 (2010).
  5. A. Eckardt, Rev. Mod. Phys. 89, 011004 (2017).
  6. C. Weitenberg and J. Simonet, Nat. Phys. 17, 1342 (2021).
  7. T. Kitagawa, E. Berg, M. Rudner, and E. Demler, Phys. Rev. B 82, 235114 (2010).
  8. M. S. Rudner, N. H. Lindner, E. Berg, and M. Levin, Phys. Rev. X 3, 031005 (2013).
  9. Á. Gómez-León, Quantum 8, 1522 (2024).
  10. L. J. Maczewsky, J. M. Zeuner, S. Nolte, and A. Szameit, Nat. Commun. 8, 13756 (2017).
  11. S. Mukherjee, A. Spracklen, M. Valiente, E. Andersson, P. Öhberg, N. Goldman, and R. R. Thomson, Nat. Commun. 8, 13918 (2017).
  12. Y.-G. Peng, C.-Z. Qin, D.-G. Zhao, Y.-X. Shen, X.-Y. Xu, M. Bao, H. Jia, and X.-F. Zhu, Nat. Commun. 7, 13368 (2016).
  13. K. Wintersperger, C. Braun, F. N. Ünal, A. Eckardt, M. D. Liberto, N. Goldman, I. Bloch, and M. Aidelsburger, Nat. Phys. 16, 1058 (2020).
  14. C. Braun, R. Saint-Jalm, A. Hesse, J. Arceri, I. Bloch, and M. Aidelsburger, Nat. Phys. 20, 1306 (2024).
  15. F. N. Ünal, B. Seradjeh, and A. Eckardt, Phys. Rev. Lett. 122, 253601 (2019).
  16. M. Aidelsburger, M. Lohse, C. Schweizer, M. Atala, J. T. Barreiro, S. Nascimbène, N. R. Cooper, I. Bloch, and N. Goldman, Nat. Phys. 11, 162 (2015).
  17. T. Chalopin, T. Satoor, A. Evrard, V. Makhalov, J. Dalibard, R. Lopes, and S. Nascimbene, Nat. Phys. 16, 1017 (2020).
  18. R. Bianco and R. Resta, Phys. Rev. B 84, 241106(R) (2011).
  19. See Supplemental Material at http://link.aps.org/supplemental/10.1103/7wl9-5971 for a discussion of upper bounds on the extra terms, a discussion of the wave packet spread as additional diagnostic, and numerical simulations with disorder.
  20. L. Asteria, M. N. Kosch, H. P. Zahn, J. Bracker, A. Eckardt, K. Sengstock, and C. Weitenberg, arXiv:2606.16942.
  21. L. Peralta Gavensky, G. Usaj, and N. Goldman, Phys. Rev. X 15, 031067 (2025).
  22. F. Cardano, A. D’Errico, A. Dauphin, M. Maffei, B. Piccirillo, C. de Lisio, G. De Filippis, V. Cataudella, E. Santamato, L. Marrucci, M. Lewenstein, and P. Massignan, Nat. Commun. 8, 15516 (2017).
  23. M. Maffei, A. Dauphin, F. Cardano, M. Lewenstein, and P. Massignan, New J. Phys. 20, 013023 (2018).
  24. X. Shen, Y.-Q. Zhu, and Z. Li, Phys. Rev. B 106, L180301 (2022).
  25. X. Shen, B. Lu, and Y.-Q. Zhu, Phys. Rev. A 113, 043314 (2026).
  26. D. Vanderbilt, Berry phases and curvatures, in Berry Phases in Electronic Structure Theory: Electric Polarization, Orbital Magnetization and Topological Insulators (Cambridge University Press, Cambridge, England, 2018), p. 117.
  27. M. F. Martínez and F. N. Ünal, Phys. Rev. A 108, 063314 (2023).
  28. A. Quelle, C. Weitenberg, K. Sengstock, and C. M. Smith, New J. Phys. 19, 113010 (2017).
  29. K. Wintersperger, Realization of Floquet topological systems with ultracold atoms in optical honeycomb lattices, Ph.D. thesis, Ludwig-Maximilians-Universität München, 2020.
  30. P. Titum, E. Berg, M. S. Rudner, G. Refael, and N. H. Lindner, Phys. Rev. X 6, 021013 (2016).
  31. A. Hesse, J. Arceri, M. Hornung, C. Braun, and M. Aidelsburger, arXiv:2508.20154.
  32. A. Dutta, E. Sen, J.-H. Zheng, M. Aidelsburger, and W. Hofstetter, Phys. Rev. B 109, L121114 (2024).
  33. L. Zhou and J. Gong, Phys. Rev. B 97, 245430 (2018).
  34. K. Shi, X. Zhang, and W. Zhang, Phys. Rev. A 109, 013324 (2024).
  35. J.-Y. Zhang, C.-R. Yi, L. Zhang, R.-H. Jiao, K.-Y. Shi, H. Yuan, W. Zhang, X.-J. Liu, S. Chen, and J.-W. Pan, Phys. Rev. Lett. 130, 043201 (2023).
  36. M. Aidelsburger, M. Atala, M. Lohse, J. T. Barreiro, B. Paredes, and I. Bloch, Phys. Rev. Lett. 111, 185301 (2013).
  37. R. V. Roell, A. W. Laskar, F. R. Huybrechts, and M. Weitz, Phys. Rev. A 107, 043302 (2023).
  38. S. Mukherjee and M. C. Rechtsman, Science 368, 856 (2020).
  39. D. Vu, Phys. Rev. B 105, 064304 (2022).
  40. J. Yu, R.-X. Zhang, and Z.-D. Song, Nat. Commun. 12, 5985 (2021).
  41. S. Franca, J. van den Brink, and I. C. Fulga, Phys. Rev. B 98, 201114(R) (2018).
  42. B. Huang, V. Novičenko, A. Eckardt, and G. Juzeliūnas, Phys. Rev. B 104, 104312 (2021).

Outline

Information

Phys. Rev. Lett. 137, 153401– Published 5 October, 2026
  • Received 1 April 2026
  • Accepted 14 September 2026
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