Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Topological edge states in the Su-Schrieffer-Heeger model subject to balanced particle gain and loss

Abstract

We investigate the Su-Schrieffer-Heeger model in presence of an injection and removal of particles, introduced via a master equation in Lindblad form. It is shown that the dynamics of the density matrix follows the predictions of calculations in which the gain and loss are modeled by complex PT-symmetric potentials. In particular it is found that there is a clear distinction in the dynamics between the topologically different cases known from the stationary eigenstates.

Graphical abstract

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

References

  1. 1.

    M.Z. Hasan, C.L. Kane, Rev. Mod. Phys. 82, 3045 (2010)

  2. 2.

    J. Alicea, Rep. Prog. Phys. 75, 076501 (2012)

  3. 3.

    A. Altland, M.R. Zirnbauer, Phys. Rev. B 55, 1142 (1997)

  4. 4.

    A.P. Schnyder, S. Ryu, A. Furusaki, A.W.W. Ludwig, Phys. Rev. B 78, 195125 (2008)

  5. 5.

    M. Leijnse, K, Flensberg, Semicond. Sci. Technol. 27, 124003 (2012)

  6. 6.

    K.v. Klitzing, G. Dorda, M. Pepper, Phys. Rev. Lett. 45, 494 (1980)

  7. 7.

    K.v. Klitzing, Rev. Mod. Phys. 58, 519 (1986)

  8. 8.

    D.J. Thouless, M. Kohmoto, M.P. Nightingale, M.d. Nijs, Phys. Rev. Lett. 49, 405 (1982)

  9. 9.

    V. Mourik, K. Zuo, S.M. Frolov, S.R. Plissard, E.P.A.M. Bakkers, L.P. Kouwenhoven. Science 336, 1003 (2012)

  10. 10.

    T.D. Stanescu, S. Tewari, J. Phys.: Condens. Matter 25, 233201 (2013)

  11. 11.

    S.R. Elliott, M. Franz, Rev. Mod. Phys. 87, 137 (2015)

  12. 12.

    A. Carmele, M. Heyl, C. Kraus, M. Dalmonte, Phys. Rev. B 92, 195107 (2015)

  13. 13.

    Y.C. Hu, T.L. Hughes, Phys. Rev. B 84, 153101 (2011)

  14. 14.

    K. Esaki, M. Sato, K. Hasebe, M. Kohmoto, Phys. Rev. B 84, 205128 (2011)

  15. 15.

    P.K. Ghosh, J. Phys.: Condens. Matter 24, 145302 (2012)

  16. 16.

    O. Viyuela, A. Rivas, M.A. Martin-Delgado, Phys. Rev. B 86, 155140 (2012)

  17. 17.

    H. Schomerus, Opt. Lett. 38, 1912 2013

  18. 18.

    A. Rivas, O. Viyuela, M.A. Martin-Delgado, Phys. Rev. B 88, 155141 (2013)

  19. 19.

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

  20. 20.

    C. Yuce, Phys. Lett. A 379, 1213 (2015)

  21. 21.

    B. Zhu, R. Lü, S. Chen, Phys. Rev. A 89, 062102 (2014)

  22. 22.

    C. Yuce, Eur. Phys. J. D 69, 184 (2015)

  23. 23.

    X. Wang, T. Liu, Y. Xiong, P. Tong, Phys. Rev. A 92, 012116 (2015)

  24. 24.

    C. Yuce, Phys. Rev. A 93, 062130 (2016)

  25. 25.

    M. Benito, M. Niklas, G. Platero, S. Kohler, Phys. Rev. B 93, 115432 (2016)

  26. 26.

    M. Niklas, M. Benito, S. Kohler, G. Platero, Nanotechnology 27, 454002 (2016)

  27. 27.

    N. Sedlmayr, M. Fleischhauer, J. Sirker, Phys. Rev. B 97, 045147 (2018)

  28. 28.

    N. Sedlmayr, P. Jaeger, M. Maiti, J. Sirker, Phys. Rev. B 97, 064304 (2018)

  29. 29.

    C.-E. Bardyn, M.A. Baranov, C.V. Kraus, E. Rico, A. Imamoglu, P. Zoller, S. Diehl, New J. Phys. 15, 085001 (2013)

  30. 30.

    P. San-Jose, J. Cayao, E. Prada, R. Aguado, Sci. Rep. 6, 21427 (2016)

  31. 31.

    N. Moiseyev, Non-Hermitian Quantum Mechanics (Cambridge University Press, Cambridge, 2011)

  32. 32.

    S. Klaiman, U. Günther, N. Moiseyev, Phys. Rev. Lett. 101, 080402 (2008)

  33. 33.

    J. Wiersig, Phys. Rev. Lett. 112, 203901 (2014)

  34. 34.

    S. Bittner, B. Dietz, H. L. Harney, M. Miski-Oglu, A. Richter, F. Schäfer, Phys. Rev. E 89, 032909 (2014)

  35. 35.

    J. Doppler, A.A. Mailybaev, J. Böhm, U. Kuhl, A. Girschik, F. Libisch, T.J. Milburn, P. Rabl, N. Moiseyev, S. Rotter, Nature 537, 76 (2016)

  36. 36.

    T. Stehmann, W.D. Heiss, F.G. Scholtz, J. Phys. A 37, 7813 (2004)

  37. 37.

    H. Xu, D. Mason, L. Jiang, J.G.E. Harris, Nature 537, 80 (2016)

  38. 38.

    W.D. Heiss, Eur. Phys. J. D 7, 1 (1999)

  39. 39.

    A.I. Magunov, I. Rotter, S.I. Strakhova, J. Phys. B 34, 29 (2001)

  40. 40.

    O. Latinne, N.J. Kylstra, M. Dörr, J. Purvis, M. Terao-Dunseath, C.J. Joachain, P.G. Burke, C.J. Noble. Phys. Rev. Lett. 74, 46 (1995)

  41. 41.

    E Hernández, A Jáuregui, and A Mondragán, J. Phys. A 39, 10087 (2006)

  42. 42.

    E.-M. Graefe, H. Korsch, A. E. Niederle. Phys. Rev. A 82, 013629 (2010)

  43. 43.

    R. Lefebvre, O. Atabek, M. Šindelka, N. Moiseyev, Phys. Rev. Lett. 103, 123003 (2009)

  44. 44.

    H. Cartarius, N. Moiseyev, Phys. Rev. A 84, 013419 (2011)

  45. 45.

    W.D. Heiss, H. Cartarius, G. Wunner, J. Main, J. Phys. A 46, 275307 (2013)

  46. 46.

    T. Gao, E. Estrecho, K.Y. Bliokh, T.C.H. Liew, M.D. Fraser, S. Brodbeck, M. Kamp, C. Schneider, S. Hofling, Y. Yamamoto, F. Nori, Y.S. Kivshar, A.G. Truscott, R.G. Dall, E.A. Ostrovskaya, Nature 526, 554 (2015)

  47. 47.

    H. Menke, M. Klett, H. Cartarius, J. Main, G. Wunner, Phys. Rev. A 93, 013401 (2016)

  48. 48.

    L. Schwarz, H. Cartarius, G. Wunner, W.D. Heiss, J. Main, Eur. Phys. J. D 69, 196 (2015)

  49. 49.

    N. Abt, H. Cartarius, G. Wunner, Int. J. Theor. Phys. 54, 4054 (2015)

  50. 50.

    C.M. Bender, Rep. Progr. Phys. 70, 947 (2007)

  51. 51.

    C.E. Rüter, K.G. Makris, R. El-Ganainy, D.N. Christodoulides, M. Segev, D. Kip, Nat. Phys. 6, 192 (2010)

  52. 52.

    B. Peng, S.K. Ozdemir, F. Lei, F. Monifi, M. Gianfreda, G.L. Long, S. Fan, F. Nori, C.M. Bender, L. Yang, Nat. Phys. 10, 394 (2014)

  53. 53.

    A. Guo, G.J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G.A. Siviloglou, D.N. Christodoulides, Phys. Rev. Lett. 103, 093902 (2009)

  54. 54.

    E.-M. Graefe, J. Phys. A 45, 444015 (2012)

  55. 55.

    F. Single, H. Cartarius, G. Wunner, J. Main, Phys. Rev. A 90, 042123 (2014)

  56. 56.

    M. Kreibich, J. Main, H. Cartarius, G. Wunner, Phys. Rev. A 90, 033630 (2014)

  57. 57.

    R. Gutöhrlein, J. Schnabel, I. Iskandarov, H. Cartarius, J. Main, G. Wunner, J. Phys. A 48, 335302 (2015)

  58. 58.

    A. Yu. Kitaev, Sov. Phys.-Usp. 44, 131 (2001)

  59. 59.

    W.P. Su, J.R. Schrieffer, A.J. Heeger, Phys. Rev. Lett. 42, 1698 (1979)

  60. 60.

    M. Klett, H. Cartarius, D. Dast, J. Main, G. Wunner, Phys. Rev. A 95, 053626 (2017)

  61. 61.

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

  62. 62.

    H.-P. Breuer, F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2002)

  63. 63.

    D. Dast, D. Haag, H. Cartarius, G. Wunner, Phys. Rev. A 90, 052120 (2014)

  64. 64.

    O. Viyuela, A. Rivas, M.A. Martin-Delgado, Phys. Rev. Lett. 112, 130401 (2014)

  65. 65.

    D. Linzner, L. Wawer, F. Grusdt, M. Fleischhauer, Phys. Rev. B 94, 201105 (2016)

  66. 66.

    H. Schomerus, Phys. Rev. Lett. 104, 233601 (2010)

  67. 67.

    K. Mølmer, Y. Castin, J. Dalibard, J. Opt. Soc. Am. B 10, 524 (1993)

  68. 68.

    J. Zak, Phys. Rev. Lett. 62, 2747 (1989)

  69. 69.

    D. Dast, D. Haag, H. Cartarius, J. Main, G. Wunner, Phys. Rev. A 96, 023625 (2017)

  70. 70.

    S. Lieu, Phys. Rev. B 97, 045106 (2018)

  71. 71.

    M. Wagner, F. Dangel, H. Cartarius, G. Wunner, J. Main, Acta Polytech. 57, 470 (2017)

Download references

Author information

Correspondence to Günter Wunner.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Klett, M., Cartarius, H., Dast, D. et al. Topological edge states in the Su-Schrieffer-Heeger model subject to balanced particle gain and loss. Eur. Phys. J. D 72, 214 (2018). https://doi.org/10.1140/epjd/e2018-90502-3

Download citation

Keywords

  • Atomic Physics