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Photoexcitation in two-dimensional topological insulators

Generating and controlling electron wavepackets in Quantum Spin Hall systems
  • Fabrizio Dolcini
  • Fausto Rossi
Regular Article
  • 16 Downloads
Part of the following topical collections:
  1. Topological States of Matter: Theory and Applications

Abstract

One of the most fascinating challenges in Physics is the realization of an electron-based counterpart of quantum optics, which requires the capability to generate and control single electron wave packets. The edge states of quantum spin Hall (QSH) systems, i.e., two-dimensional (2D) topological insulators realized in HgTe/CdTe and InAs/GaSb quantum wells, may turn the tide in the field, as they do not require the magnetic field that limits the implementations based on quantum Hall effect. However, the band structure of these topological states, described by a massless Dirac fermion Hamiltonian, prevents electron photoexcitation via the customary vertical electric dipole transitions of conventional optoelectronics. So far, proposals to overcome this problem are based on magnetic dipole transitions induced via Zeeman coupling by circularly polarised radiation, and are limited by the g-factor. Alternatively, optical transitions can be induced from the edge states to the bulk states, which are not topologically protected though.

Here we show that an electric pulse, localized in space and/or time and applied at a QSH edge, can photoexcite electron wavepackets by intra-branch electrical transitions, without invoking the bulk states or the Zeeman coupling. Such wavepackets are spin-polarised and propagate in opposite directions, with a density profile that is independent of the initial equilibrium temperature and that does not exhibit dispersion, as a result of the linearity of the spectrum and of the chiral anomaly characterising massless Dirac electrons. We also investigate the photoexcited energy distribution and show how, under appropriate circumstances, minimal excitations (Levitons) are generated. Furthermore, we show that the presence of a Rashba spin–orbit coupling can be exploited to tailor the shape of photoexcited wavepackets. Possible experimental realizations are also discussed.

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References

  1. 1.
    A. Bertoni, P. Bordone, R. Brunetti, C. Jacoboni, S. Reggiani, Phys. Rev. Lett. 84, 5912 (2000) ADSCrossRefGoogle Scholar
  2. 2.
    M.D. Blumenthal, B. Kaestner, L. Li, S. Giblin, T.J. B.M. Janssen, M. Pepper, D. Anderson, G. Jones, D.A. Ritchie, Nat. Phys. 3, 343 (2007) CrossRefGoogle Scholar
  3. 3.
    E. Bocquillon, F.D. Parmentier, C. Grenier, J.-M. Berroir, P. Degiovanni, B. Plaçais, A. Cavanna, Y. Jin, G.Fève, Phys. Rev. Lett. 108, 196803 (2012) ADSCrossRefGoogle Scholar
  4. 4.
    G. Fève, A. Mahé, J.-M. Berroir, T. Kontos, B. Plaçais, D.C. Glattli, A. Cavanna, B. Etienne, Y. Jin, Science 316, 1169 (2007) ADSCrossRefGoogle Scholar
  5. 5.
    P. Roulleau, F. Portier, P. Roche, A. Cavanna, G. Faini, U. Gennser, D. Mailly, Phys. Rev. Lett. 100, 126802 (2008) ADSCrossRefGoogle Scholar
  6. 6.
    A. Mahé, F.D. Parmentier, E. Bocquillon, J.-M. Berroir, D.C. Glattli, T. Kontos, B. Plaçais, G. Fève, A. Cavanna, Y. Jin, Phys. Rev. B 82, 201309(R) (2010) ADSCrossRefGoogle Scholar
  7. 7.
    Ch. Grenier, R. Hervé, E. Bocquillon, F.D. Parmentier, B. Plaçais, J.M. Berroir, G. Fève, P. Degiovanni, New J. Phys. 13, 093007 (2011) ADSCrossRefGoogle Scholar
  8. 8.
    E. Bocquillon, V. Freulon, J.-M. Berroir, P. Degiovanni, B. Plaçais, A. Cavanna, Y. Jin, G. Fève, Nat. Commun. 4, 1839 (2013) CrossRefGoogle Scholar
  9. 9.
    E. Bocquillon, V. Freulon, J.-M Berroir, P. Degiovanni, B. Plaçais, A. Cavanna, Y. Jin, G. Fève, Science 339, 1054 (2013) ADSCrossRefGoogle Scholar
  10. 10.
    J.D. Fletcher, P. See, H. Howe, M. Pepper, S.P. Giblin, J.P. Griffiths, G.A.C. Jones, I.Farrer, D.A. Ritchie, T.J.B. M. Janssen, M. Kataoka, Phys. Rev. Lett. 111, 216807 (2013) ADSCrossRefGoogle Scholar
  11. 11.
    E. Bocquillon, V. Freulon, F.D. Parmentier, J.-M Berroir, B. Plaçais, C. Wahl, J. Rech, T.Jonckheere, T. Martin, C. Grenier, D. Ferraro, P. Degiovanni, G. Fève, Ann. Phys. (Berlin) 526, 1 (2014) ADSCrossRefGoogle Scholar
  12. 12.
    C. Wahl, J. Rech, T. Jonckheere, T. Martin, Phys. Rev. Lett. 112, 046802 (2014) ADSCrossRefGoogle Scholar
  13. 13.
    V. Freulon, A. Marguerite, J.-M. Berroir, B. Plaçais, A. Cavanna, Y. Jin, and G. Fève, Nature Commun. 6, 6854 (2015) ADSCrossRefGoogle Scholar
  14. 14.
    J. Waldie, P. See, V. Kashcheyevs, J.P. Griffiths, I. Farrer, G.A.C. Jones, D.A. Ritchie, T.J.B.M. Janssen, M. Kataoka, Phys. Rev. B 92, 125305 (2015) ADSCrossRefGoogle Scholar
  15. 15.
    M. Kataoka, N. Johnson, C. Emary, P. See, J.P. Griffiths, G.A.C. Jones, I. Farrer, D.A. Ritchie, M. Pepper, T.J.B.M. Janssen, Phys. Rev. Lett. 116, 126803 (2016) ADSCrossRefGoogle Scholar
  16. 16.
    C. L. Kane, E. J. Mele, Phys. Rev. Lett. 95, 146802 (2005) ADSCrossRefGoogle Scholar
  17. 17.
    C. L. Kane, E. J. Mele, Phys. Rev. Lett. 95, 226801 (2005) ADSCrossRefGoogle Scholar
  18. 18.
    B.A. Bernevig, T.L. Hughes, S.-C. Zhang, Science 314, 1757 (2006) ADSCrossRefGoogle Scholar
  19. 19.
    M.König, S. Wiedmann, C. Brüne, A. Roth, H. Buhmann, L.W. Molenkamp, X.-L. Qi, S.-C. Zhang, Science 318, 766 (2006) CrossRefGoogle Scholar
  20. 20.
    M.König, H. Buhmann, L W. Molenkamp, T.L. Hughes, C.-X. Liu, X.-L. Qi, S.-C. Zhang, J. Phys. Soc. Jpn. 77, 031007 (2008) CrossRefGoogle Scholar
  21. 21.
    A. Roth, C. Brüne, H. Buhmann, L.W. Molenkamp, J. Maciejko, X.-L. Qi, S.-C. Zhang, Science 325, 294 (2009) ADSCrossRefGoogle Scholar
  22. 22.
    C. Brüne, A. Roth, H. Buhmann, E.M. Hankiewicz, L. W. Molenkamp, J. Maciejko, X.-L. Qi, S.-C. Zhang, Nat. Phys. 8, 485 (2012) CrossRefGoogle Scholar
  23. 23.
    C. Liu, T.L. Hughes, X.-L. Qi, K. Wang, S.-C. Zhang, Phys. Rev. Lett. 100, 236601 (2008) ADSCrossRefGoogle Scholar
  24. 24.
    I. Knez, R.-R. Du, G. Sullivan, Phys. Rev. Lett. 107, 136603 (2011) ADSCrossRefGoogle Scholar
  25. 25.
    I. Knez, C.T. Rettner, S.-H. Yang, S.S.P. Parkin, L. Du, R.-R. Du, G. Sullivan, Phys. Rev. Lett. 112, 026602 (2014) ADSCrossRefGoogle Scholar
  26. 26.
    E.M. Spanton, K.C. Nowack, L. Du, G. Sullivan, R.-R. Du, K.A. Moler, Phys. Rev. Lett. 113, 026804 (2014) ADSCrossRefGoogle Scholar
  27. 27.
    A. Inhofer, D. Bercioux, Phys. Rev. B 88, 235412 (2013) ADSCrossRefGoogle Scholar
  28. 28.
    P.P. Hofer, M.Büttiker, Phys. Rev. B 88, 241308 (2013) ADSCrossRefGoogle Scholar
  29. 29.
    D. Ferraro, C. Wahl, J. Rech, T. Jonckheere, T. Martin, Phys. Rev. B 89, 075407 (2014) ADSCrossRefGoogle Scholar
  30. 30.
    A. Ström, H. Johannesson, P. Recher, Phys. Rev. B 91, 245406 (2015) ADSCrossRefGoogle Scholar
  31. 31.
    A. Calzona, M. Acciai, M. Carrega, F. Cavaliere, M. Sassetti, Phys. Rev. B 94, 035404 (2016) ADSCrossRefGoogle Scholar
  32. 32.
    F. Dolcini, R.C. Iotti, A. Montorsi, F. Rossi, Phys. Rev. B 94, 165412 (2016) ADSCrossRefGoogle Scholar
  33. 33.
    F. Dolcini, Phys. Rev. B 95, 085434 (2017) ADSCrossRefGoogle Scholar
  34. 34.
    B. Dóra, J. Cayssol, F. Simon, R. Moessner, Phys. Rev. Lett. 108, 056602 (2012) ADSCrossRefGoogle Scholar
  35. 35.
    S.N. Artemenko, V.O. Kaladzhyan, JETP Lett. 97, 82 (2013) ADSCrossRefGoogle Scholar
  36. 36.
    G. Dolcetto, F. Cavaliere, M. Sassetti, Phys. Rev. B 89, 125419 (2014) ADSCrossRefGoogle Scholar
  37. 37.
    V. Kaladzhyan, P.P. Aseev, S.N. Artemenko, Phys. Rev. B 92, 155424 (2015) ADSCrossRefGoogle Scholar
  38. 38.
    L.S. Levitov, H. Lee, G.B. Lesovik, J. Math. Phys. 37, 4845 (1996) Google Scholar
  39. 39.
    D.A. Ivanov, H.W. Lee, L.S. Levitov, Phys. Rev. B 56, 6839 (1997) ADSCrossRefGoogle Scholar
  40. 40.
    J. Keeling, I. Klich, L.S. Levitov, Phys. Rev. Lett. 97, 116403 (2006) ADSCrossRefGoogle Scholar
  41. 41.
    M. Moskalets, Phys. Rev. B 89, 045402 (2014) ADSCrossRefGoogle Scholar
  42. 42.
    D. Dasenbrook, C. Flindt, Phys. Rev. B 92, 161412 (2015) ADSCrossRefGoogle Scholar
  43. 43.
    M. Moskalets, Phys. Rev. Lett. 117, 046801 (2016) ADSCrossRefGoogle Scholar
  44. 44.
    M. Moskalets, Low Temp. Phys. 43, 865 (2017) Google Scholar
  45. 45.
    J. Rech, D. Ferraro, T. Jonckheere, L. Vannucci, M. Sassetti, T. Martin, Phys. Rev. Lett. 118, 076801 (2017) ADSCrossRefGoogle Scholar
  46. 46.
    L. Vannucci, F. Ronetti, J. Rech, D. Ferraro, T. Jonckheere, T. Martin, M. Sassetti, Phys. Rev. B 95, 245415 (2017) ADSCrossRefGoogle Scholar
  47. 47.
    J. Dubois, T. Jullien, F. Portier, P. Roche, A. Cavanna, Y. Jin, W. Wegscheider, P. Roulleau, D.C. Glattli, Nature 502, 659 (2013) ADSCrossRefGoogle Scholar
  48. 48.
    J. Dubois, T. Jullien, C. Grenier, P. Degiovanni, P. Roulleau, D.C. Glattli, Phys. Rev. B 88, 085301 (2013) ADSCrossRefGoogle Scholar
  49. 49.
    T. Jullien, P. Roulleau, B. Roche, A. Cavanna, Y. Jin, D.C. Glattli, Nature 514, 603 (2014) ADSCrossRefGoogle Scholar
  50. 50.
    D.C. Glattli, P.S. Roulleau, Phys. Status Sol. 254, 1600650 (2017) ADSCrossRefGoogle Scholar
  51. 51.
    S.L. Adler, Phys. Rev. 177, 2426 (1969) ADSCrossRefGoogle Scholar
  52. 52.
    J.S. Bell, R. Jackiw, Nuovo Cim. A 60, 47 (1969) Google Scholar
  53. 53.
    H.B. Nielsen, N. Ninomiya, Phys. Lett. B130, 389 (1983) ADSCrossRefGoogle Scholar
  54. 54.
    R.A. Bertlmann, Anomalies in quantum field theory (Clarendon Press, Oxford, 1996) Google Scholar
  55. 55.
    A.A. Zyuzin, A.A. Burkov, Phys. Rev. B 86, 115133 (2012) ADSCrossRefGoogle Scholar
  56. 56.
    H.-J. Kim, K.-S. Kim, J.-F. Wang, M. Sasaki, N. Satoh, A. Ohnishi, M. Kitaura, M. Yang, L. Li, Phys. Rev. Lett 111, 246603 (2013) ADSCrossRefGoogle Scholar
  57. 57.
    S.A. Parameswaran, T. Grover, D.A. Abanin, D.A. Pesin, A. Vishwanath, Phys. Rev. X 4, 031035 (2014) Google Scholar
  58. 58.
    Y. Takane, J. Phys. Soc. Jpn 85, 013706 (2016) CrossRefGoogle Scholar
  59. 59.
    Z.K. Liu, B. Zhou, Y. Zhang, Z.J. Wang, H.M. Weng, D. Prabhakaran, S.-K. Mo, Z.X. Shen, Z. Fang, X. Dai, Z. Hussain, Y.L. Chen, Science 343, 864 (2014) ADSCrossRefGoogle Scholar
  60. 60.
    S.-Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z. Yuan, C.-C. Lee, S.-M. Huang, H. Zheng, J. Ma, D.S. Sanchez, B.Wang,A. Bansil, F. Chou, P.P. Shibayev, H. Lin, S. Jia, M.Z. Hasan, Science 349, 613 (2015) ADSCrossRefGoogle Scholar
  61. 61.
    S.-Y. Xu, I. Belopolski, D.S. Sanchez, C. Zhang, G. Chang, C. Guo, G. Bian, Z. Yuan, H. Lu, T.-R. Chang, P.P. Shibayev, M.L. Prokopovych, N. Alidoust, H. Zheng, C.-C. Lee, S.-M. Huang, R. Sankar, F. Chou, C.-H. Hsu, H.-T. Jeng, A. Bansil, T. Neupert, V.N. Strocov, H. Lin, S. Jia, M.Z. Hasan, Science 349, 622 (2015) ADSMathSciNetCrossRefGoogle Scholar
  62. 62.
    J. Xiong, S.K. Kushwaha, T. Liang, J.W. Krizan, M. Hirschberger, W. Wang, R.J. Cava, N.P. Ong, Science 350, 413 (2015) ADSMathSciNetCrossRefGoogle Scholar
  63. 63.
    C. Fleckenstein, N. Traverso Ziani, B. Trauzettel, Phys. Rev. B 94, 241406(R) (2016) ADSCrossRefGoogle Scholar
  64. 64.
    R. Rosati, F. Dolcini, F. Rossi, Appl. Phys. Lett. 106, 243101 (2015) ADSCrossRefGoogle Scholar
  65. 65.
    Ch. Grenier, J. Dubois, T. Jullien, P. Roulleau, D.C. Glattli, P. Degiovanni, Phys. Rev. B 88, 085302 (2013) ADSCrossRefGoogle Scholar
  66. 66.
    E.Ya. Sherman, Phys. Rev. B 67, 161303 (2003) ADSCrossRefGoogle Scholar
  67. 67.
    E.Ya. Sherman, Appl. Phys. Lett. 82, 209 (2003) ADSCrossRefGoogle Scholar
  68. 68.
    M.V. Entin, L.I. Magarill, Phys. Rev. B 64, 085330 (2001) ADSCrossRefGoogle Scholar
  69. 69.
    J.I.Väyrynen, T. Ojanen, Phys. Rev. Lett. 106, 076803 (2011) ADSCrossRefGoogle Scholar
  70. 70.
    C. Ortix, Phys. Rev. B 91, 245412 (2015) ADSCrossRefGoogle Scholar
  71. 71.
    P. Gentile, M. Cuoco, C. Ortix, Phys. Rev. Lett. 115, 256801 (2015) ADSCrossRefGoogle Scholar
  72. 72.
    Z.-J. Ying, P. Gentile, C. Ortix, M. Cuoco, Phys. Rev. B 94, 081406(R) (2016) ADSCrossRefGoogle Scholar
  73. 73.
    J. Hinz, H. Buhmann, M. Schäfer, V. Hock, C.R. Becker, L.W. Molenkamp, Semi. Sci. Tech. 21, 501 (2006) ADSCrossRefGoogle Scholar
  74. 74.
    Z. Qiao, X. Li, W.K. Tse, H. Jiang, Y. Yao, Q. Niu, Phys. Rev. B 87, 125405 (2013) ADSCrossRefGoogle Scholar
  75. 75.
    Y.H. Park, S.-H. Shin, J.D. Song, J. Chang, S.H. Han, H.-J. Choi, H.C. Koo, Solid-State Electron. 82, 23 (2013) CrossRefGoogle Scholar
  76. 76.
    P. Wójcik, J. Adamowski, B.J. Spisak, M. Wołoszyn, J. Appl. Phys. 115, 104310 (2014) Google Scholar
  77. 77.
    L. Novotny, S.J. Stranick, Ann. Rev. Phys. Chem. 57, 303 (2006) ADSCrossRefGoogle Scholar
  78. 78.
    B. Hanewinkel, A. Knorr, P. Thomas, S.W. Koch, Phys. Rev. B 55, 13715 (1997) ADSCrossRefGoogle Scholar
  79. 79.
    A. Hartschuh, E.J. Sánchez, X.S. Xie, L. Novotny, Phys. Rev. Lett. 90, 095503 (2003) ADSCrossRefGoogle Scholar
  80. 80.
    H. Ito, K. Furuya, Y. Shibata, S. Kashiwaya, M. Yamaguchi, T. Akazaki, H. Tamura, Y. Ootuka, S. Nomura, Phys. Rev. Lett. 107, 256803 (2011) ADSCrossRefGoogle Scholar
  81. 81.
    S. Mamyouda, H. Ito, Y. Shibata, S. Kashiwaya, M. Yamaguchi, T. Akazaki, H. Tamura, Y. Ootuka, S. Nomura, Nanolett. 15, 4127 (2015) CrossRefGoogle Scholar
  82. 82.
    F. Dolcini, Phys. Rev. B 85, 033306 (2012) ADSCrossRefGoogle Scholar
  83. 83.
    M. Acciai, A. Calzona, G. Dolcetto, T.L. Schmidt, M. Sassetti, Phys. Rev. B 96, 075144 (2017) ADSCrossRefGoogle Scholar
  84. 84.
    C. Altimiras, H. le Sueur, U. Gennser, A. Cavanna, D. Mailly, F. Pierre, Nat. Phys. 6, 34 (2009) CrossRefGoogle Scholar
  85. 85.
    A. Brenneis, L. Gaudreau, M. Seifert, H. Karl, M.S. Brandt, H. Huebl, J.A. Garrido, F.H.L. Koppens, A.W. Holleitner, Nat. Nanotech. 10, 135 (2014) ADSCrossRefGoogle Scholar
  86. 86.
    H. Kamata, N. Kumada, M. Hashisaka, K. Muraki, T. Fujisawa, Nat. Nanotech. 9, 177 (2014) ADSCrossRefGoogle Scholar
  87. 87.
    C. Kastl, C. Karnetzky, H. Karl, A.W. Holleitner, Nature Commun. 6, 6617 (2015) ADSCrossRefGoogle Scholar
  88. 88.
    A. Woessner, P. Alonso-González, M.B. Lundeberg, Y. Gao, J.E. Barrios-Vargas, G. Navickaite, Q. Ma, D. Janner, K. Watanabe, A.W. Cummings, T. Taniguchi, V. Pruneri, S. Roche, P. Jarillo-Herrero, J. Hone, R. Hillenbrand, F.H.L. Koppens, Nat. Commun. 7, 10783 (2016) ADSCrossRefGoogle Scholar
  89. 89.
    M. Hashisaka, N. Hiyama, T. Akiho, K. Muraki, T. Fujisawa, Nat. Phys. 13, 559 (2017) CrossRefGoogle Scholar

Copyright information

© EDP Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Dipartimento di Scienza Applicata e Tecnologia, Politecnico di Torino corso DucaTorinoItaly

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