- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

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

On-demand positioning of topological states via non-Hermitian defects

Hamidreza Ramezani*

  • *Contact author: hramezani@tarleton.edu
PDF

Phys. Rev. Research 8, 023074 – Published 24 April, 2026

DOI: https://doi.org/10.1103/1sph-n3p8

Abstract

We show that a single non-Hermitian defect embedded in an otherwise Hermitian topological lattice can anomalously relocate an edge state into the bulk without altering the topology. Using one- and two-dimensional models, including the Su-Schrieffer-Heeger chain and honeycomb lattices, we demonstrate that tuning an asymmetric coupling or a local parity-time-symmetric perturbation shifts the edge mode to the defect site, where it becomes strongly localized. In two dimensions, the defect further acts as a momentum-bandpass filter, selectively relocating a narrow subset of edge modes from the continuum of boundary states. This relocation is distinct from the non-Hermitian skin effect, which drives collective bulk accumulation, and from trivial defect-induced modes, which lack topological origin. The effect is robust against disorder and system size, enabling programmable, on-demand positioning of topological states for applications in photonic routing, switching, and robust sensing.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (38)

  1. M. Z. Hasan and C. L. Kane, Colloquium: Topological insulators, Rev. Mod. Phys. 82, 3045 (2010).
  2. X.-L. Qi and S.-C. Zhang, Topological insulators and superconductors, Rev. Mod. Phys. 83, 1057 (2011).
  3. L. Lu, J. D. Joannopoulos, and M. Soljačić, Topological photonics, Nat. Photon. 8, 821 (2014).
  4. T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, Topological photonics, Rev. Mod. Phys. 91, 015006 (2019).
  5. N. Goldman, J. C. Budich, and P. Zoller, Topological quantum matter with ultracold gases in optical lattices, Nat. Phys. 12, 639 (2016).
  6. Z. Yang, F. Gao, X. Shi, X. Lin, Z. Gao, Y. Chong, and B. Zhang, Topological acoustics, Phys. Rev. Lett. 114, 114301 (2015).
  7. Y.-G. Peng, C.-Z. Qin, D.-G. Zhao, Y.-X. Shen, X.-Y. Xu, M. Bao, H. Jia, and X.-F. Zhu, Experimental demonstration of anomalous Floquet topological insulator for sound, Nat. Commun. 7, 13368 (2016).
  8. J. Ferdous, C. Yuce, A. Alù, and H. Ramezani, Observation of robust zero-energy extended states, Phys. Rev. Appl. 19, L061002 (2023).
  9. C. L. Kane and T. C. Lubensky, Topological boundary modes in isostatic lattices, Nat. Phys. 10, 39 (2014).
  10. S. D. Huber, Topological mechanics, Nat. Phys. 12, 621 (2016).
  11. C. H. Lee, S. Imhof, C. Berger, F. Bayer, J. Brehm, L. W. Molenkamp, T. Kiessling, and R. Thomale, Topolectrical circuits, Commun. Phys. 1, 39 (2018).
  12. D. Leykam, K. Y. Bliokh, C. Huang, Y. Chong, and F. Nori, Edge modes, degeneracies, and topological numbers in non-Hermitian systems, Phys. Rev. Lett. 118, 040401 (2017).
  13. S. Yao and Z. Wang, Edge states and topological invariants of non-Hermitian systems, Phys. Rev. Lett. 121, 086803 (2018).
  14. N. Okuma, K. Kawabata, K. Shiozaki, and M. Sato, Topological origin of non-Hermitian skin effects, Phys. Rev. Lett. 124, 086801 (2020).
  15. S. Longhi, Non-Hermitian gauged topological laser arrays, Annalen der Physik, Ann. Phys. 530, 1800023 (2018).
  16. W. Zhu, W. X. Teo, L. Li, and J. Gong, Delocalization of topological edge states, Phys. Rev. B 103, 195414 (2021).
  17. C. Yuce and H. Ramezani, Non-Hermitian skin effect in two dimensional continuous systems, Phys. Scr. 98, 015005 (2023).
  18. J. Qian, J. Li, S.-Y. Zhu, J. You, and Y.-P. Wang, Probing pt-symmetry breaking of non-Hermitian topological photonic states via strong photon-magnon coupling, Phys. Rev. Lett. 132, 156901 (2024).
  19. S. Hamanaka, T. Yoshida, and K. Kawabata, Non-Hermitian topology in Hermitian topological matter, Phys. Rev. Lett. 133, 266604 (2024).
  20. L. Xiong, Q. Zhang, X. Feng, Y. Leng, M. Pi, S. Tong, and C. Qiu, Tracking intrinsic non-Hermitian skin effects in lossy lattices, Phys. Rev. B 110, L140305 (2024).
  21. C. Yuce and H. Ramezani, Strong edge burst with bipolar non-Hermitian skin effect, Phys. Rev. B 109, 214301 (2024).
  22. L. Jin, P. Wang, and Z. Song, Su-Schrieffer-Heeger chain with one pair of PT-symmetric defects, Sci. Rep. 7, 5903 (2017).
  23. H. Zhao, P. Miao, M. H. Teimourpour, S. Malzard, R. El-Ganainy, H. Schomerus, and L. Feng, Topological hybrid silicon microlasers, Nat. Commun. 9, 981 (2018).
  24. Z. O. Turker and C. Yuce, Open and closed boundaries in non-Hermitian topological systems, Phys. Rev. A 99, 022127 (2019).
  25. F. Mostafavi, C. Yuce, O. S. Maganã-Loaiza, H. Schomerus, and H. Ramezani, Robust localized zero-energy modes from locally embedded PT-symmetric defects, Phys. Rev. Res. 2, 032057 (2020).
  26. N. Lazarides and G. P. Tsironis, Topological split-ring resonator based metamaterials with PT symmetry relying on gain and loss, Phys. Rev. B 102, 064306 (2020).
  27. S. Garmon and K. Noba, Reservoir-assisted symmetry breaking and coalesced zero-energy modes in an open PT-symmetric Su-Schrieffer-Heeger model, Phys. Rev. A 104, 062215 (2021).
  28. A. Sivan and M. Orenstein, Topology of multiple cross-linked Su-Schrieffer-Heeger chains, Phys. Rev. A 106, 022216 (2022).
  29. L. Xiao, K. Wang, D. Qu, H. Gao, Q. Lin, Z. Bian, X. Zhan, and P. Xue, Non-Hermitian physics in photonic systems, Photonics Insights 4, R09 (2025).
  30. H. Cao and J. Wiersig, Dielectric microcavities: Model systems for wave chaos and non-Hermitian physics, Rev. Mod. Phys. 87, 61 (2015).
  31. P. St-Jean, V. Goblot, E. Galopin, A. Lemaître, T. Ozawa, L. Le Gratiet, I. Sagnes, J. Bloch, and A. Amo, Lasing in topological edge states of a one-dimensional lattice, Nat. Photon. 11, 651 (2017).
  32. M. Parto, S. Wittek, H. Hodaei, G. Harari, M. A. Bandres, J. Ren, M. C. Rechtsman, M. Segev, D. N. Christodoulides, and M. Khajavikhan, Edge-mode lasing in 1D topological active arrays, Phys. Rev. Lett. 120, 113901 (2018).
  33. Y. Ota, R. Katsumi, K. Watanabe, S. Iwamoto, and Y. Arakawa, Topological photonic crystal nanocavity laser, Commun. Phys. 1, 86 (2018).
  34. M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, Photonic Floquet topological insulators, Nature (London) 496, 196 (2013).
  35. J. M. Zeuner, M. C. Rechtsman, Y. Plotnik, Y. Lumer, S. Nolte, M. S. Rudner, M. Segev, and A. Szameit, Observation of a topological transition in the bulk of a non-Hermitian system, Phys. Rev. Lett. 115, 040402 (2015).
  36. F. Zangeneh-Nejad and R. Fleury, Topological Fano resonances, Phys. Rev. Lett. 122, 014301 (2019).
  37. S. Puri, J. Ferdous, A. Shakeri, A. Basiri, M. Dubois, and H. Ramezani, Tunable non-Hermitian acoustic filter, Phys. Rev. Appl. 16, 014012 (2021).
  38. M. Kohmoto and Y. Hasegawa, Zero modes and edge states of the honeycomb lattice, Phys. Rev. B 76, 205402 (2007).

Outline

Information

Phys. Rev. Research 8, 023074– Published 24 April, 2026
  • Received 13 October 2025
  • Accepted 2 April 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