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Terahertz cyclotron emission from two-dimensional Dirac fermions


Since the emergence of graphene, we have seen several proposals for the realization of Landau lasers tunable over the terahertz frequency range. The hope was that the non-equidistance of the Landau levels from Dirac fermions would suppress the harmful non-radiative Auger recombination. Unfortunately, even with this non-equidistance, an unfavourable non-radiative process persists in Landau-quantized graphene, and so far no cyclotron emission from Dirac fermions has been reported. One way to eliminate this last non-radiative process is to sufficiently modify the dispersion of the Landau levels by opening a small gap in the linear band structure. HgTe quantum wells close to the topological phase transition are a proven example of such gapped graphene-like materials. In this work we experimentally demonstrate Landau emission from Dirac fermions in such HgTe quantum wells, where the emission is tunable by both the magnetic field and the carrier concentration. Consequently, these results represent an advance in the realization of terahertz Landau lasers tunable by a magnetic field and gate voltage.

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Fig. 1: Landau levels of Dirac fermions in graphene and HgTe QWs.
Fig. 2: Cyclotron emission observed on 8 nm HgTe QWs, measured on two different samples at T = 4 K.
Fig. 3: Analysis of the cyclotron emission energies.

Data availability

Data are available from the corresponding author on reasonable request. The dataset will also be uploaded on the Recherche Data Gouv repository ( once the manuscript is accepted and published.


  1. Twiss, R. Q. Radiation transfer and the possibility of negative absorption in radio astronomy. Aust. J. Phys. 11, 564 (1958).

    Article  ADS  Google Scholar 

  2. Hirshfield, J. L. & Wachtel, J. M. Electron cyclotron maser. Phys. Rev. Lett. 12, 533 (1964).

    Article  ADS  Google Scholar 

  3. Chu, K. R. The electron cyclotron maser. Rev. Mod. Phys. 76, 489 (2004).

    Article  ADS  Google Scholar 

  4. O’Shea, P. G. & Freund, H. P. Free-electron lasers: status and applications. Science 292, 1853–1858 (2001).

    Google Scholar 

  5. Dornhaus, H., Muller, K.-H., Nimtz, G. & Schifferdecker, M. Magnetic quantum oscillations in the Auger transition rate. Phys. Rev. Lett. 37, 710 (1976).

    Article  ADS  Google Scholar 

  6. Morimoto, T., Hatsugai, Y. & Aoki, H. Cyclotron radiation and emission in graphene—a possibility of Landau level laser. J. Phys. Conf. Ser. 150, 022059 (2009).

    Article  Google Scholar 

  7. Wendler, F. & Malic, E. Towards a tunable graphene based Landau level laser in the terahertz regime. Sci. Rep. 5, 12646 (2015).

  8. Wang, Y., Tokman, M. & Belyanin, A. Continuous-wave lasing between Landau levels in graphene. Phys. Rev. A 91, 033821 (2015).

    Article  ADS  Google Scholar 

  9. Brem, S., Wendler, F. & Malic, E. Microscopic modeling of tunable graphene-based terahertz Landau-level lasers. Phys. Rev. B 96, 045427 (2017).

    Article  ADS  Google Scholar 

  10. Brem, S., Wendler, F., Winnerl, S. & Malic, E. Electrically pumped graphene-based Landau-level laser. Phys. Rev. Materials 2, 034002 (2018).

    Article  Google Scholar 

  11. Wang, Y., Tokman, M. & Belyanin, A. Continuous wave lasing between Landau levels in graphene. Phys. Rev. A 91, 033821 (2015).

    Article  ADS  Google Scholar 

  12. But, D. B. et al. Suppressed Auger scattering and tunable light emission of Landau-quantized massless Kane electrons. Nat. Photon. 13, 783–787 (2019).

    Article  ADS  Google Scholar 

  13. Mittendorff, M. et al. Carrier dynamics in Landau-quantized graphene featuring strong Auger scattering. Nat. Phys. 11, 75–81 (2015).

    Article  Google Scholar 

  14. Wendler, F., Knorr, A. & Malic, E. Ultrafast carrier dynamics in Landau-quantized graphene. Nanophotonics 4, 224–249 (2015).

    Article  Google Scholar 

  15. König-Otto, J. C. et al. Four-wave mixing in Landau-quantized graphene. Nano Lett. 17, 2184–2188 (2017).

    Article  ADS  Google Scholar 

  16. Büttner, B. et al. Single valley Dirac fermions in zero-gap HgTe quantum wells. Nat. Phys. 7, 418 (2011).

    Article  Google Scholar 

  17. Marcinkiewicz, M. et al. Temperature-driven single-valley Dirac fermions in HgTe quantum wells. Phys. Rev. B 96, 035405 (2017).

    Article  ADS  Google Scholar 

  18. Krishtopenko, S. S. & Teppe, F. Quantum spin Hall insulator with a large bandgap, Dirac fermions, and bilayer graphene analog. Sci. Adv. 4, eaap7529 (2018).

    Article  ADS  Google Scholar 

  19. Krishtopenko, S. S. et al. Massless Dirac fermions in III–V semiconductor quantum wells. Phys. Rev. B 99, 121405(R) (2019).

    Article  ADS  Google Scholar 

  20. Bernevig, B. A., Hughes, T. L. & Zhang, S.-C. Quantum spin Hall effect and topological phase transition in HgTe quantum wells. Science 314, 1757–1761 (2006).

    Article  Google Scholar 

  21. Sirtori, Carlo Bridge for the terahertz gap. Nature 417, 132–133 (2002).

    Article  ADS  Google Scholar 

  22. Dmowski, L. H., Cheremisin, M., Skierbiszewski, C. & Knap, W. Far-infrared narrow-band photodetector based on magnetically tunable cyclotron resonance-assisted transitions in pure n-type InSb. Acta Phys. Pol. A 92, 733–736 (1997).

    Article  ADS  Google Scholar 

  23. Witowski, A. M. et al. Quasiclassical cyclotron resonance of Dirac fermions in highly doped graphene. Phys. Rev. B 82, 165305 (2010).

    Article  ADS  Google Scholar 

  24. Hilton, D. J., Arikawa, T. & Kono, J. in Characterization of Materials (ed. Kaufmann, E. N.) Vol. 2 (2012).

  25. Gornik, E. in (ed. Zawadzki, W.) Narrow Gap Semiconductors Physics and Applications 133 (Springer, 1980).

  26. Chaubet, C., Raymond, A. & Dur, D. Heating of two-dimensional electrons by a high electric field in a quantizing magnetic field: consequences in Landau emission and in the quantum Hall effect. Phys. Rev. B 52, 11178 (1995).

    Article  ADS  Google Scholar 

  27. Hensel, J. C. & Peter, Martin Stark effect for cyclotron resonance in degenerate bands. Phys. Rev. 114, 411 (1959).

    Article  ADS  MATH  Google Scholar 

  28. Gornik, E., Schawarz, R., Lindeman, G. & Tsui, D. C. Emission spectroscopy on two-dimensional systems. Surf. Sci. 98, 493 (1980).

    Article  ADS  Google Scholar 

  29. Komiyama, S. Streaming motion and population inversion of hot carriers in crossed electric and magnetic fields. Adv. Phys. 31, 255–297 (1982).

    Article  ADS  Google Scholar 

  30. Ushakov, D. et al. HgCdTe-based quantum cascade lasers operating in the GaAs phonon Reststrahlen band predicted by the balance equation method. Opt. Express 28, 25371–25382 (2020).

    Article  ADS  Google Scholar 

  31. Komiyama, S., Masumi, T. & Kajita, K. Definite evidence for population inversion of hot electrons in silver halides. Solid State Commun. 31, 447–452 (1979).

    Article  Google Scholar 

  32. Tkachov, G. et al. Backscattering of Dirac fermions in HgTe quantum wells with a finite gap. Phys. Rev. Lett. 106, 076802 (2011).

    Article  ADS  Google Scholar 

  33. Saleh, B. E. A. & Teich, M. C. Fundamentals of Photonics 3rd edn (Wiley, 2019).

  34. Unterrainer, K. et al. Tunable cyclotron-resonance laser in germanium. Phys. Rev. Lett. 64, 2277 (1990).

    Article  ADS  Google Scholar 

  35. Hubers, H.-W., Pavlov, S. G. & Shastin, V. N. Terahertz lasers based on germanium and silicon. Semicond. Sci. Technol. 20, S211–S221 (2005).

    Article  Google Scholar 

  36. Morimoto, T., Hatsugai, Y. & Aoki, H. Cyclotron radiation and emission in graphene. Phys. Rev. B 78, 073406 (2008).

    Article  ADS  Google Scholar 

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This work was supported by the Terahertz Occitanie Platform (F.T., J.T.); by the CNRS through IRP ‘TeraMIR’ (F.T., M.O., V.I.G.); by the French Agence Nationale pour la Recherche for Colector (ANR-19-CE30-0032; F.T., M.O., V.I.G.), Stem2D (ANR-19-CE24-0015; J.T.) and Equipex+ Hybat (ANR-21 -ESRE-0026; F.T.) projects; by the European Union through the Flag-Era JTC 2019—DeMeGras project (ANR-19-GRF1-0006; F.T.) and the Marie-Curie grant agreement no. 765426 (S.G.), from the Horizon 2020 research and innovation program; and by the Center of Excellence (Center of Photonics), funded by The Ministry of Science and Higher Education of the Russian Federation (contract no. 075-15-2022-316; S.V.M., V.I.G.). We would like to acknowledge C. Lhenoret for technical support, L. Varani for financial support and W. Knap for fruitful discussions and valuable support. F.T. and C.C. would also like to thank S. Bonifacie for all of the passionate discussions, and for his friendship and his timeless presence.

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Authors and Affiliations



The experiment was proposed by F.T. The samples were fabricated by N.N.M., S.A.D., X.B. and P.B. Terahertz cyclotron emission experiments were performed by S.G. and C.C. Characterization measurements were conducted and analysed by S.R., M.S., C.B. and B.J. S.G., C.C. and M.S. handled the data and prepared the figures. F.T. and S.S.K. wrote the manuscript and S.G., M.O., S.V.M. and V.I.G. corrected it. All co-authors discussed the experimental data and the interpretation of the results.

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Correspondence to F. Teppe.

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Nature Photonics thanks Erich Gornik and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Figs. 1–8, Discussion, and Tables 1 and 2.

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Gebert, S., Consejo, C., Krishtopenko, S.S. et al. Terahertz cyclotron emission from two-dimensional Dirac fermions. Nat. Photon. 17, 244–249 (2023).

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