Skip to main content
SpringerLink
Log in

Topological circuit of a versatile non-Hermitian quantum system

  • Article
  • Published:
Science China Physics, Mechanics & Astronomy Aims and scope Submit manuscript

Abstract

We propose an resistors, inductors and capacitors (RLC) electrical circuit to theoretically analyze and fully simulate a new type of non-Hermitian Su-Schrieffer-Heeger (SSH) model with complex hoppings. We formulate its construction and investigate its properties by taking advantage of the circuit’s versatility. Rich physical properties can be identified in this system from the normal modes of oscillation of the RLC circuit, including the highly tunable bulk-edge correspondence between topological winding numbers and edge states and the non-Hermitian skin phenomenon originating from a novel complex energy plane topology. The present study is able to show the wide and appealing topological physics inherent to electric circuits, which is readily generalizable to a plenty of both Hermitian and non-Hermitian nontrivial systems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. W. P. Su, J. R. Schrieffer, and A. J. Heeger, Phys. Rev. B 22, 2099 (1980).

    Article  ADS  Google Scholar 

  2. C. H. Lee, and R. Thomale, Phys. Rev. B 99, 201103 (2019), arXiv: 1809.02125.

    Article  ADS  Google Scholar 

  3. S. Yao, and Z. Wang, Phys. Rev. Lett. 121, 086803 (2018), arXiv: 1803.01876.

    Article  ADS  Google Scholar 

  4. J. M. Zeuner, M. C. Rechtsman, Y. Plotnik, Y. Lumer, S. Nolte, M. S. Rudner, M. Segev, and A. Szameit, Phys. Rev. Lett. 115, 040402 (2015).

    Article  ADS  Google Scholar 

  5. S. Weimann, M. Kremer, Y. Plotnik, Y. Lumer, S. Nolte, K. G. Makris, M. Segev, M. C. Rechtsman, and A. Szameit, Nat. Mater. 16, 433 (2017).

    Article  ADS  Google Scholar 

  6. H. Schomerus, Opt. Lett. 38, 1912 (2013), arXiv: 1301.0777.

    Article  ADS  Google Scholar 

  7. C. Poli, M. Bellec, U. Kuhl, F. Mortessagne, and H. Schomerus, Nat. Commun. 6, 6710 (2015), arXiv: 1407.3703.

    Article  ADS  Google Scholar 

  8. G. Alicata, F. Bagarello, F. Gargano, and S. Spagnolo, J. Math. Phys. 59, 042112 (2018), arXiv: 1804.03968.

    Article  ADS  MathSciNet  Google Scholar 

  9. H. Jiang, L. J. Lang, C. Yang, S. L. Zhu, and S. Chen, Phys. Rev. B 100, 054301 (2019), arXiv: 1901.09399.

    Article  ADS  Google Scholar 

  10. W. Zhang, D. Zou, Q. Pei, W. He, J. Bao, H. Sun, and X. Zhang, Phys. Rev. Lett. 126, 146802 (2021), arXiv: 2008.00423.

    Article  ADS  Google Scholar 

  11. M. Ezawa, Phys. Rev. B 100, 081401 (2019), arXiv: 1904.03823.

    Article  ADS  Google Scholar 

  12. K. Luo, R. Yu, and H. Weng, Research 2018(18), 1 (2018).

    Google Scholar 

  13. X. X. Zhang, and M. Franz, Phys. Rev. Lett. 124, 046401 (2020), arXiv: 1909.09129.

    Article  ADS  Google Scholar 

  14. W. Zhang, D. Zou, J. Bao, W. He, Q. Pei, H. Sun, and X. Zhang, Phys. Rev. B 102, 100102 (2020), arXiv: 2001.07931.

    Article  ADS  Google Scholar 

  15. R. R. Parker, Proc. IEEE 57, 39 (1969).

    Article  MathSciNet  Google Scholar 

  16. E. F. Kuester, Theory of Waveguides and Transmission Lines (CRC Press, Colorado, 2020).

    Book  Google Scholar 

  17. E. J. Bergholtz, J. C. Budich, and F. K. Kunst, arXiv: 1912.10048.

  18. K. Kawabata, K. Shiozaki, M. Ueda, and M. Sato, Phys. Rev. X 9, 041015 (2019), arXiv: 1812.09133.

    Google Scholar 

  19. S. Q. Shen, Topological Insulators, Springer Series in Solid-State Sciences, Vol. 174 (Springer, Berlin, Heidelberg, 2012).

    Google Scholar 

  20. S. Ryu, A. P. Schnyder, A. Furusaki, and A. W. W. Ludwig, New J. Phys. 12, 065010 (2010), arXiv: 0912.2157.

    Article  ADS  Google Scholar 

  21. R. M. Kaufmann, D. Li, and B. Wehefritz-Kaufmann, Rev. Math. Phys. 28, 1630003 (2016), arXiv: 1501.02874.

    Article  MathSciNet  Google Scholar 

  22. E. Prodan, and H. Schulz-Baldes, J. Funct. Anal. 271, 1150 (2016).

    Article  MathSciNet  Google Scholar 

  23. M. Ezawa, Phys. Rev. B 99, 201411 (2019), arXiv: 1810.04527.

    Article  ADS  Google Scholar 

  24. J. K. Asbóth, L. Oroszlány, and A. Pályi, A Short Course on Topological Insulators, Lecture Notes in Physics, Vol. 919 (Springer International Publishing, Cham, 2016).

    Book  MATH  Google Scholar 

  25. S. R. Pocock, P. A. Huidobro, and V. Giannini, Nanophotonics 8, 1337 (2019), arXiv: 1902.00467.

    Article  Google Scholar 

  26. S. de Léséleuc, V. Lienhard, P. Scholl, D. Barredo, S. Weber, N. Lang, H. P. Büchler, T. Lahaye, and A. Browaeys, Science 365, 775 (2019), arXiv: 1810.13286.

    Article  ADS  MathSciNet  Google Scholar 

  27. L. Pickup, H. Sigurdsson, J. Ruostekoski, and P. G. Lagoudakis, Nat. Commun. 11, 4431 (2020), arXiv: 2001.07616.

    Article  ADS  Google Scholar 

  28. C. H. Lee, S. Imhof, C. Berger, F. Bayer, J. Brehm, L. W. Molenkamp, T. Kiessling, and R. Thomale, Commun. Phys. 1, 39 (2018), arXiv: 1705.01077.

    Article  Google Scholar 

  29. E. Zhao, Ann. Phys. 399, 289 (2018), arXiv: 1810.10318.

    Article  ADS  Google Scholar 

  30. C. Yin, H. Jiang, L. Li, R. Lu, and S. Chen, Phys. Rev. A 97, 052115 (2018), arXiv: 1802.04169.

    Article  ADS  Google Scholar 

  31. A. Ghatak, and T. Das, J. Phys.-Condens. Matter 31, 263001 (2019), arXiv: 1902.07972.

    Article  ADS  Google Scholar 

  32. Z. Gong, Y. Ashida, K. Kawabata, K. Takasan, S. Higashikawa, and M. Ueda, Phys. Rev. X 8, 031079 (2018), arXiv: 1802.07964.

    Google Scholar 

  33. K. Xu, X. Zhang, K. Luo, R. Yu, D. Li, and H. Zhang, Phys. Rev. B 103, 125411 (2021).

    Article  ADS  Google Scholar 

  34. D. Tong, The Quantum Hall Effect, Technical Report (Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, Cambridge, 2016).

    Google Scholar 

  35. L. Li, Z. Xu, and S. Chen, Phys. Rev. B 89, 1 (2014).

    Google Scholar 

  36. T. Helbig, T. Hofmann, C. H. Lee, R. Thomale, S. Imhof, L. W. Molenkamp, and T. Kiessling, Phys. Rev. B 99, 161114 (2019), arXiv: 1807.09555.

    Article  ADS  Google Scholar 

  37. K. Kumar, Electric Circuits and Networks, 1st ed. (Pearson Education Inc., London, 2009).

    Google Scholar 

  38. F. Song, S. Yao, and Z. Wang, Phys. Rev. Lett. 123, 170401 (2019).

    Article  ADS  MathSciNet  Google Scholar 

  39. Z. Fu, N. Fu, H. Zhang, Z. Wang, D. Zhao, and S. Ke, Appl. Sci. 10, 3425 (2020).

    Article  Google Scholar 

  40. S. Lieu, Phys. Rev. B 97, 1 (2018).

    Article  Google Scholar 

  41. I. Mondragon-Shem, T. L. Hughes, J. Song, and E. Prodan, Phys. Rev. Lett. 113, 046802 (2014), arXiv: 1311.5233.

    Article  ADS  Google Scholar 

  42. B. Perez-Gonzalez, M. Bello, A. Gomez-Leon, and G. Platero, Phys. Rev. B 99, 035146 (2019).

    Article  ADS  Google Scholar 

  43. K. I. Imura, and Y. Takane, Phys. Rev. B 100, 165430 (2019), arXiv: 1908.09438.

    Article  ADS  Google Scholar 

  44. B. Perez-Gonzalez, M. Bello, A. Gomez-Leon, and G. Platero, arXiv: 1802.03973.

  45. M. Maffei, A. Dauphin, F. Cardano, M. Lewenstein, and P. Massignan, New J. Phys. 20, 013023 (2018), arXiv: 1708.02778.

    Article  ADS  MathSciNet  Google Scholar 

  46. V. M. Martinez Alvarez, J. E. Barrios Vargas, M. Berdakin, and L. E. F. Foa Torres, Eur. Phys. J. Spec. Top. 227, 1295 (2018), arXiv: 1805.08200.

    Article  Google Scholar 

  47. N. Okuma, K. Kawabata, K. Shiozaki, and M. Sato, Phys. Rev. Lett. 124, 086801 (2020), arXiv: 1910.02878.

    Article  ADS  MathSciNet  Google Scholar 

  48. K. Zhang, Z. Yang, and C. Fang, Phys. Rev. Lett. 125, 126402 (2020), arXiv: 1910.01131.

    Article  ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Instituto de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia, Medellín, 050010, Colombia

    David-Andres Galeano & Jorge Mahecha

  2. Unidad Transacciones T & D Energía, Gerencia Comercial T & D Energía, V. P. T & D Energía, EPM, Medellín, 050015, Colombia

    David-Andres Galeano

  3. Department of Physics and Astronomy & Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, V6T 1Z4, Canada

    Xiao-Xiao Zhang

  4. RIKEN Center for Emergent Matter Science (CEMS), Saitama, 351-0198, Japan

    Xiao-Xiao Zhang

  5. Department of Chemistry, University of British Columbia, Vancouver, V6T 1Z4, Canada

    Jorge Mahecha

Authors
  1. David-Andres Galeano
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiao-Xiao Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jorge Mahecha
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to David-Andres Galeano or Xiao-Xiao Zhang.

Additional information

D.-A. Galeano and J. Mahecha acknowledge partial support from the Universidad de Antioquia, Colombia under Initiative (Grant No. CODI ES84180154), Estrategia de sostenibilidad del Grupo de Física Atómica y Molecular, and Projects (Grant Nos. CODI 251594, and 2019-24770). X.-X. Zhang thanks the support from the Riken Special Postdoctoral Researcher Program and the Max Planck-UBC-UTokyo Center for Quantum Materials.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Galeano, DA., Zhang, XX. & Mahecha, J. Topological circuit of a versatile non-Hermitian quantum system. Sci. China Phys. Mech. Astron. 65, 217211 (2022). https://doi.org/10.1007/s11433-021-1783-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11433-021-1783-3

Search

Navigation