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

Multiple physical quantities sensors based on non-Hermitian topological systems with an impurity

J. J. Wang1, Yubin Zhang1, Xiaomin Zhang1, and X. X. Yi2,3,*

  • *Contact author: yixx@nenu.edu.cn

Phys. Rev. Research 7, 033133 – Published 8 August, 2025

DOI: https://doi.org/10.1103/h9b6-md2f

Abstract

Spectra of non-Hermitian systems with skin effects are sensitive to the boundary conditions. In this work, we introduce a system composed of an impurity and a nonreciprocal Su-Schrieffer-Heeger (SSH) chain with odd number of lattice sites. The shift in the energy of the zero mode can be dramatically changed by adding two vanishingly small couplings between the impurity and two ends of the chain. Here, we propose a multiple physical quantities sensor with exponential-power-law amplification mechanism. Sensitivity of the proposed sensor exhibits an exponential scaling with SSH chain size and a power-law scaling with frequency of the impurity. This system is designed for detecting two small physical quantities, i.e., the impurity-chain coupling strengths. If and only if these two physical quantities exist simultaneously, the energy of zero mode will obviously change. Moreover, sensitivity is also robust against on-site disorder or dissipation of the impurity. Sufficiently strong disorder will change the localization of the eigenstate, and this leads to device failure. We also show the parameter range of the proposed sensor, and this range accurately corresponds to a nontrivial spectral winding number. The single physical quantity sensors suffered from repeated construction and low utilization rate. Thus, our findings pave a basic way toward sensors that couple multiple physical quantities to the boundary of the non-Hermitian topological chain.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (52)

  1. C. L. Degen, F. Reinhard, and P. Cappellaro, Quantum sensing, Rev. Mod. Phys. 89, 035002 (2017).
  2. M. V. Berry, Physics of non-Hermitian degeneracies, Czech. J. Phys. 54, 1039 (2004).
  3. W. D. Heiss, The physics of exceptional points, J. Phys. A: Math. Theor. 45, 444016 (2012).
  4. S. Lin, Y. Liang, J. Zhang, M. K. Chen, and D. P. Tsai, Controllable flatbands via non-Hermiticity, Appl. Phys. Lett. 123, 221103 (2023).
  5. R. Kononchuk, J. Cai, F. Ellis, R. Thevamaran, and T. Kottos, Exceptional-point-based accelerometers with enhanced signal-to-noise ratio, Nature (London) 607, 697 (2022).
  6. H. Hodaei, A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, Enhanced sensitivity at higher-order exceptional points, Nature (London) 548, 187 (2017).
  7. W. Chen, Şahin Kaya Özdemir, G. Zhao, J. Wiersig, and L. Yang, Exceptional points enhance sensing in an optical microcavity, Nature (London) 548, 192 (2017).
  8. J. Wiersig, Enhancing the sensitivity of frequency and energy splitting detection by using exceptional points: Application to microcavity sensors for single-particle detection, Phys. Rev. Lett. 112, 203901 (2014).
  9. T. E. Lee, Anomalous edge state in a non-Hermitian lattice, Phys. Rev. Lett. 116, 133903 (2016).
  10. D. Leykam, K. Y. Bliokh, C. Huang, Y. D. Chong, and F. Nori, Edge modes, degeneracies, and topological numbers in non-Hermitian systems, Phys. Rev. Lett. 118, 040401 (2017).
  11. Z. Gong, Y. Ashida, K. Kawabata, K. Takasan, S. Higashikawa, and M. Ueda, Topological phases of non-Hermitian systems, Phys. Rev. X 8, 031079 (2018).
  12. T. Liu, Y.-R. Zhang, Q. Ai, Z. Gong, K. Kawabata, M. Ueda, and F. Nori, Second-order topological phases in non-Hermitian systems, Phys. Rev. Lett. 122, 076801 (2019).
  13. H. Shen, B. Zhen, and L. Fu, Topological band theory for non-Hermitian Hamiltonians, Phys. Rev. Lett. 120, 146402 (2018).
  14. F. K. Kunst, E. Edvardsson, J. C. Budich, and E. J. Bergholtz, Biorthogonal bulk-boundary correspondence in non-Hermitian systems, Phys. Rev. Lett. 121, 026808 (2018).
  15. K. Yokomizo and S. Murakami, Non-Bloch band theory of non-Hermitian systems, Phys. Rev. Lett. 123, 066404 (2019).
  16. S. Yao and Z. Wang, Edge states and topological invariants of non-Hermitian systems, Phys. Rev. Lett. 121, 086803 (2018).
  17. S. Yao, F. Song, and Z. Wang, Non-Hermitian Chern bands, Phys. Rev. Lett. 121, 136802 (2018).
  18. F. Song, S. Yao, and Z. Wang, Non-Hermitian skin effect and chiral damping in open quantum systems, Phys. Rev. Lett. 123, 170401 (2019).
  19. F. Song, S. Yao, and Z. Wang, Non-Hermitian topological invariants in real space, Phys. Rev. Lett. 123, 246801 (2019).
  20. Z. Yang, K. Zhang, C. Fang, and J. Hu, Non-Hermitian bulk-boundary correspondence and auxiliary generalized Brillouin zone theory, Phys. Rev. Lett. 125, 226402 (2020).
  21. K. Zhang, Z. Yang, and C. Fang, Correspondence between winding numbers and skin modes in non-Hermitian systems, Phys. Rev. Lett. 125, 126402 (2020).
  22. Y. Yi and Z. Yang, Non-Hermitian skin modes induced by on-site dissipations and chiral tunneling effect, Phys. Rev. Lett. 125, 186802 (2020).
  23. N. Okuma, K. Kawabata, K. Shiozaki, and M. Sato, Topological origin of non-Hermitian skin effects, Phys. Rev. Lett. 124, 086801 (2020).
  24. D. S. Borgnia, A. J. Kruchkov, and R.-J. Slager, Non-Hermitian boundary modes and topology, Phys. Rev. Lett. 124, 056802 (2020).
  25. L. Li, C. H. Lee, and J. Gong, Topological switch for non-Hermitian skin effect in cold-atom systems with loss, Phys. Rev. Lett. 124, 250402 (2020).
  26. C. H. Lee, L. Li, and J. Gong, Hybrid higher-order skin-topological modes in nonreciprocal systems, Phys. Rev. Lett. 123, 016805 (2019).
  27. L. Li, C. H. Lee, S. Mu, and J. Gong, Critical non-Hermitian skin effect, Nat. Commun. 11, 5491 (2020).
  28. S. Liu, R. Shao, S. Ma, L. Zhang, O. You, H. Wu, Y. J. Xiang, T. J. Cui, and S. Zhang, Non-Hermitian skin effect in a non-Hermitian electrical circuit, Research 2021, 5608038 (2021).
  29. T. Hofmann, T. Helbig, F. Schindler, N. Salgo, M. Brzezińska, M. Greiter, T. Kiessling, D. Wolf, A. Vollhardt, A. Kabaši, C. H. Lee, A. Bilušić, R. Thomale, and T. Neupert, Reciprocal skin effect and its realization in a topolectrical circuit, Phys. Rev. Res. 2, 023265 (2020).
  30. L. Xiao, T. Deng, K. Wang, G. Zhu, Z. Wang, W. Yi, and P. Xue, Non-Hermitian bulk-boundary correspondence in quantum dynamics, Nat. Phys. 16, 761 (2020).
  31. J. C. Budich and E. J. Bergholtz, Non-Hermitian topological sensors, Phys. Rev. Lett. 125, 180403 (2020).
  32. A. McDonald and A. A. Clerk, Exponentially-enhanced quantum sensing with non-Hermitian lattice dynamics, Nat. Commun. 11, 5382 (2020).
  33. F. Koch and J. C. Budich, Quantum non-Hermitian topological sensors, Phys. Rev. Res. 4, 013113 (2022).
  34. M. Parto, C. Leefmans, J. Williams, R. M. Gray, and A. Marandi, Enhanced sensitivity via non-Hermitian topology, Light Sci. Appl. 14, 6 (2025).
  35. H. Yuan, W. Zhang, Z. Zhou, W. Wang, N. Pan, Y. Feng, H. Sun, and X. Zhang, Non-Hermitian topolectrical circuit sensor with high sensitivity, Adv. Sci. 10, 2301128 (2023).
  36. L. Li, C. H. Lee, and J. Gong, Impurity induced scale-free localization, Commun. Phys. 4, 42 (2021).
  37. K. Yokomizo and S. Murakami, Scaling rule for the critical non-Hermitian skin effect, Phys. Rev. B 104, 165117 (2021).
  38. C.-X. Guo, C.-H. Liu, X.-M. Zhao, Y. Liu, and S. Chen, Exact solution of non-Hermitian systems with generalized boundary conditions: Size-dependent boundary effect and fragility of the skin effect, Phys. Rev. Lett. 127, 116801 (2021).
  39. Y. Liu, Y. Zeng, L. Li, and S. Chen, Exact solution of the single impurity problem in nonreciprocal lattices: Impurity-induced size-dependent non-Hermitian skin effect, Phys. Rev. B 104, 085401 (2021).
  40. Y. Liu and S. Chen, Diagnosis of bulk phase diagram of nonreciprocal topological lattices by impurity modes, Phys. Rev. B 102, 075404 (2020).
  41. F. Roccati, Non-Hermitian skin effect as an impurity problem, Phys. Rev. A 104, 022215 (2021).
  42. J. Lu, W.-Y. Shan, H.-Z. Lu, and S.-Q. Shen, Non-magnetic impurities and in-gap bound states in topological insulators, New J. Phys. 13, 103016 (2011).
  43. R.-J. Slager, L. Rademaker, J. Zaanen, and L. Balents, Impurity-bound states and Green’s function zeros as local signatures of topology, Phys. Rev. B 92, 085126 (2015).
  44. P. Molignini, O. Arandes, and E. J. Bergholtz, Anomalous skin effects in disordered systems with a single non-Hermitian impurity, Phys. Rev. Res. 5, 033058 (2023).
  45. X. Wang, T. Liu, A. F. Kockum, H.-R. Li, and F. Nori, Tunable chiral bound states with giant atoms, Phys. Rev. Lett. 126, 043602 (2021).
  46. W. Cheng, Z. Wang, and Yu-xi Liu, Boundary effect and dressed states of a giant atom in a topological waveguide, Phys. Rev. A 106, 033522 (2022).
  47. J. J. Wang, Fude Li, and X. X. Yi, Giant atom induced zero modes and localization in the nonreciprocal Su-Schrieffer-Heeger chain, J. Phys. A: Math. Theor. 56, 455306 (2023).
  48. J. J. Wang, F. Li, and W. Cheng, Anomalous behavior of the non-Hermitian topological system with an asymmetric coupling impurity, Entropy 27, 78 (2025).
  49. D. C. Brody, Biorthogonal quantum mechanics, J. Phys. A: Math. Theor. 47, 035305 (2014).
  50. M. M. Sternheimt and J. F. Walker, Non-Hermitian Hamiltonians, decaying states, and perturbation theory, Phys. Rev. C 6, 114 (1972).
  51. P. W. Anderson, Absence of diffusion in certain random lattices, Phys. Rev. 109, 1492 (1958).
  52. S. Weimann, M. Kremer, Y. Plotnik, Y. Lumer, S. Nolte, K. G. Makris, M. Segev, M. C. Rechtsman, and A. Szameit, Topologically protected bound states in photonic parity-time-symmetric crystals, Nat. Mater. 16, 433 (2017).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation