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
  • Letter
  • Open Access

Propagation, dissipation, and breakdown in quantum anomalous Hall edge states probed by microwave edge plasmons

Torsten Röper1, Hugo Thomas1, Daniel Rosenbach1, Anjana Uday1, Gertjan Lippertz1, Anne Denis2, Pascal Morfin2, Alexey A. Taskin1, Yoichi Ando1 et al.

Erwann Bocquillon1,*

  • *Contact author: bocquillon@ph2.uni-koeln.de

Phys. Rev. B 110, L161403 – Published 7 October, 2024

DOI: https://doi.org/10.1103/PhysRevB.110.L161403

Abstract

The quantum anomalous Hall (QAH) effect, with its single chiral, topologically protected edge state, offers a platform for flying Majorana states as well as nonreciprocal microwave devices. While recent research showed the nonreciprocity of edge plasmons in Cr-doped (BixSb1−x)2Te3, the understanding of their dissipation remains incomplete. Our study explores edge plasmon dissipation in V-doped (BixSb1−x)2Te3 films, analyzing microwave transmission across various conditions. We identify interactions with charge puddles as a primary source, providing insights critical for developing improved QAH-based technologies.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (39)

  1. C.-Z. Chang et al., Experimental observation of the quantum anomalous Hall effect in a magnetic topological insulator, Science 340, 167 (2013).
  2. C.-Z. Chang, W. Zhao, D. Y. Kim, H. Zhang, B. A. Assaf, D. Heiman, S.-C. Zhang, C. Liu, M. H. W. Chan, and J. S. Moodera, High-precision realization of robust quantum anomalous Hall state in a hard ferromagnetic topological insulator, Nat. Mater. 14, 473 (2015).
  3. R. Yu, W. Zhang, H.-J. Zhang, S.-C. Zhang, X. Dai, and Z. Fang, Quantized anomalous Hall effect in magnetic topological insulators, Science 329, 61 (2010).
  4. A. J. Bestwick, E. J. Fox, X. Kou, L. Pan, K. L. Wang, and D. Goldhaber-Gordon, Precise quantization of the anomalous Hall effect near zero magnetic field, Phys. Rev. Lett. 114, 187201 (2015).
  5. M. Götz, K. M. Fijalkowski, E. Pesel, M. Hartl, S. Schreyeck, M. Winnerlein, S. Grauer, H. Scherer, K. Brunner, C. Gould, F. J. Ahlers, and L. W. Molenkamp, Precision measurement of the quantized anomalous Hall resistance at zero magnetic field, Appl. Phys. Lett. 112, 072102 (2018).
  6. E. J. Fox, I. T. Rosen, Y. Yang, G. R. Jones, R. E. Elmquist, X. Kou, L. Pan, K. L. Wang, and D. Goldhaber-Gordon, Part-per-million quantization and current-induced breakdown of the quantum anomalous Hall effect, Phys. Rev. B 98, 075145 (2018).
  7. K. M. Fijalkowski, N. Liu, M. Klement, S. Schreyeck, K. Brunner, C. Gould, and L. W. Molenkamp, A balanced quantum Hall resistor, Nat. Electron. 7, 438 (2024).
  8. G. Viola and D. P. DiVincenzo, Hall effect gyrators and circulators, Phys. Rev. X 4, 021019 (2014).
  9. A. C. Mahoney, J. I. Colless, L. Peeters, S. J. Pauka, E. J. Fox, X. Kou, L. Pan, K. L. Wang, D. Goldhaber-Gordon, and D. J. Reilly, Zero-field edge plasmons in a magnetic topological insulator, Nat. Commun. 8, 1836 (2017).
  10. A. Uday, G. Lippertz, K. Moors, H. Legg, A. Bliesener, L. Pereira, A. Taskin, and Y. Ando, Induced superconducting correlations in a quantum anomalous Hall insulator, Nat. Phys. 8, 1836 (2024).
  11. C. W. J. Beenakker, P. Baireuther, Y. Herasymenko, I. Adagideli, L. Wang, and A. R. Akhmerov, Deterministic creation and braiding of chiral edge vortices, Phys. Rev. Lett. 122, 146803 (2019).
  12. C. Beenakker, A. Grabsch, and Y. Herasymenko, Electrical detection of the Majorana fusion rule for chiral edge vortices in a topological superconductor, SciPost Phys. 6, 022 (2019).
  13. G. M. Ferguson, R. Xiao, A. R. Richardella, D. Low, N. Samarth, and K. C. Nowack, Direct visualization of electronic transport in a quantum anomalous Hall insulator, Nat. Mater. 22, 1100 (2023).
  14. S. Komiyama and Y. Kawaguchi, Heat instability of quantum Hall conductors, Phys. Rev. B 61, 2014 (2000).
  15. G. Lippertz, A. Bliesener, A. Uday, L. M. C. Pereira, A. A. Taskin, and Y. Ando, Current-induced breakdown of the quantum anomalous Hall effect, Phys. Rev. B 106, 045419 (2022).
  16. L. A. Martinez, G. Qiu, P. Deng, P. Zhang, K. G. Ray, L. Tai, M.-T. Wei, H. He, K. L. Wang, J. L. DuBois, and D.-X. Qu, Edge magnetoplasmon dispersion and time-resolved plasmon transport in a quantum anomalous Hall insulator, Phys. Rev. Res. 6, 013081 (2024).
  17. N. Kumada, N.-H. Tu, K.-I. Sasaki, T. Ota, M. Hashisaka, S. Sasaki, K. Onomitsu, and K. Muraki, Suppression of gate screening on edge magnetoplasmons by highly resistive ZnO gate, Phys. Rev. B 101, 205205 (2020).
  18. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevB.110.L161403 for information about the sample preparation, the rf setup and its calibration, the circuit model, the fitting of the data, and the results of other samples, which includes Refs.  [9, 16, 20].
  19. K. M. Fijalkowski, N. Liu, P. Mandal, S. Schreyeck, K. Brunner, C. Gould, and L. W. Molenkamp, Quantum anomalous Hall edge channels survive up to the Curie temperature, Nat. Commun. 12, 5599 (2021).
  20. A. Gourmelon, E. Frigerio, H. Kamata, L. Lunczer, A. Denis, P. Morfin, M. Rosticher, J.-M. Berroir, G. Fève, B. Plaçais, H. Buhmann, L. W. Molenkamp, and E. Bocquillon, Velocity and confinement of edge plasmons in HgTe-based two-dimensional topological insulators, Phys. Rev. B 108, 035405 (2023).
  21. C. Jozwiak, J. A. Sobota, K. Gotlieb, A. F. Kemper, C. R. Rotundu, R. J. Birgeneau, Z. Hussain, D.-H. Lee, Z.-X. Shen, and A. Lanzara, Spin-polarized surface resonances accompanying topological surface state formation, Nat. Commun. 7, 13143 (2016).
  22. Y. L. Chen, J.-H. Chu, J. G. Analytis, Z. K. Liu, K. Igarashi, H.-H. Kuo, X. L. Qi, S. K. Mo, R. G. Moore, D. H. Lu, M. Hashimoto, T. Sasagawa, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z. X. Shen, Massive Dirac fermion on the surface of a magnetically doped topological insulator, Science 329, 659 (2010).
  23. N. Kumada, H. Kamata, and T. Fujisawa, Edge magnetoplasmon transport in gated and ungated quantum Hall systems, Phys. Rev. B 84, 045314 (2011).
  24. C. de C. Chamon and X. G. Wen, Sharp and smooth boundaries of quantum Hall liquids, Phys. Rev. B 49, 8227 (1994).
  25. D. B. Chklovskii, B. I. Shklovskii, and L. I. Glazman, Electrostatics of edge channels, Phys. Rev. B 46, 4026 (1992).
  26. H. Kamata, H. Irie, N. Kumada, and K. Muraki, Time-resolved measurement of ambipolar edge magnetoplasmon transport in InAs/InGaSb composite quantum wells, Phys. Rev. Res. 4, 033214 (2022).
  27. N. Kumada, P. Roulleau, B. Roche, M. Hashisaka, H. Hibino, I. Petkovic, and D. C. Glattli, Resonant edge magnetoplasmons and their decay in graphene, Phys. Rev. Lett. 113, 266601 (2014).
  28. A. Gourmelon, H. Kamata, J.-M. Berroir, G. Fève, B. Plaçais, and E. Bocquillon, Characterization of helical Luttinger liquids in microwave stepped-impedance edge resonators, Phys. Rev. Res. 2, 043383 (2020).
  29. M. C. Dartiailh, S. Hartinger, A. Gourmelon, K. Bendias, H. Bartolomei, H. Kamata, J.-M. Berroir, G. Fève, B. Plaçais, L. Lunczer, R. Schlereth, H. Buhmann, L. W. Molenkamp, and E. Bocquillon, Dynamical separation of bulk and edge transport in HgTe-based 2D topological insulators, Phys. Rev. Lett. 124, 076802 (2020).
  30. A. Inhofer, J. Duffy, M. Boukhicha, E. Bocquillon, J. Palomo, K. Watanabe, T. Taniguchi, I. Estève, J. M. Berroir, G. Fève, B. Plaçais, and B. A. Assaf, rf quantum capacitance of the topological insulator Bi2Se3 in the bulk depleted regime for field-effect transistors, Phys. Rev. Appl. 9, 024022 (2018).
  31. C. Lin, M. Hashisaka, T. Akiho, K. Muraki, and T. Fujisawa, Time-resolved investigation of plasmon mode along interface channels in integer and fractional quantum Hall regimes, Phys. Rev. B 104, 125304 (2021).
  32. M. Bagchi, L. Pitz-Paal, C. P. Grams, O. Breunig, N. Borgwardt, Z. Wang, Y. Ando, M. Grüninger, and J. Hemberger, Large positive magnetoconductivity at microwave frequencies in the compensated topological insulator BiSbTeSe2, Phys. Rev. B 99, 161121(R) (2019).
  33. F. Zhang, C. Ding, J. Zhou, and Y. Yao, Chiral edge plasmons in quantum anomalous Hall insulators, arXiv:2404.13930.
  34. C.-Z. Chang, W. Zhao, D. Y. Kim, P. Wei, J. K. Jain, C. Liu, M. H. W. Chan, and J. S. Moodera, Zero-field dissipationless chiral edge transport and the nature of dissipation in the quantum anomalous Hall state, Phys. Rev. Lett. 115, 057206 (2015).
  35. M. Kawamura, R. Yoshimi, A. Tsukazaki, K. S. Takahashi, M. Kawasaki, and Y. Tokura, Current-driven instability of the quantum anomalous Hall effect in ferromagnetic topological insulators, Phys. Rev. Lett. 119, 016803 (2017).
  36. D. Yoshioka, The Quantum Hall Effect (Springer Verlag, Berlin, 2002).
  37. M. Allen, Y. T. Cui, E. Y. Ma, M. Mogi, M. Kawamura, I. C. Fulga, D. Goldhaber-Gordon, Y. Tokura, and Z. X. Shen, Visualization of an axion insulating state at the transition between 2 chiral quantum anomalous Hall states, Proc. Natl. Acad. Sci. USA 116, 14511 (2019).
  38. E. Frigerio, G. Rebora, M. Ruelle, H. Souquet-Basiège, Y. Jin, U. Gennser, A. Cavanna, B. Plaçais, E. Baudin, J. M. Berroir, I. Safi, P. Degiovanni, G. Fève, and G. Ménard, Gate tunable edge magnetoplasmon resonators, Commun. Phys. 7, 314 (2024).
  39. T. Röper and E. Bocquillon, Propagation, dissipation and breakdown in quantum anomalous Hall edge states probed by microwave edge plasmons, Zenodo (2024), doi: 10.5281/zenodo.11344274.

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation