Observation of Dirac plasmons in a topological insulator

Journal name:
Nature Nanotechnology
Year published:
Published online


Plasmons are quantized collective oscillations of electrons and have been observed in metals and doped semiconductors. The plasmons of ordinary, massive electrons have been the basic ingredients of research in plasmonics and in optical metamaterials for a long time1. However, plasmons of massless Dirac electrons have only recently been observed in graphene, a purely two-dimensional electron system2. Their properties are promising for novel tunable plasmonic metamaterials in the terahertz and mid-infrared frequency range3. Dirac fermions also occur in the two-dimensional electron gas that forms at the surface of topological insulators as a result of the strong spin–orbit interaction existing in the insulating bulk phase4. One may therefore look for their collective excitations using infrared spectroscopy. Here we report the first experimental evidence of plasmonic excitations in a topological insulator (Bi2Se3). The material was prepared in thin micro-ribbon arrays of different widths W and periods 2W to select suitable values of the plasmon wavevector k. The linewidth of the plasmon was found to remain nearly constant at temperatures between 6 K and 300 K, as expected when exciting topological carriers. Moreover, by changing W and measuring the plasmon frequency in the terahertz range versus k we show, without using any fitting parameter, that the dispersion curve agrees quantitatively with that predicted for Dirac plasmons.

At a glance


  1. Extinction coefficients of the microribbon arrays of Bi2Se3 topological insulators in the terahertz range.
    Figure 1: Extinction coefficients of the microribbon arrays of Bi2Se3 topological insulators in the terahertz range.

    a, Scanning electron microscope (SEM) image of the W = 2.5 µm patterned film. b, Extinction coefficient of the as-grown, unpatterned film at 6 K (blue lines) and 300 K (red lines). c, Optical microscope images of the five patterned films with different widths W and periods 2W. Red arrows indicate the direction of the radiation electric field E, either perpendicular or parallel to the ribbons. Film thickness is indicated under the images, where 1 QL ~ 1 nm (QL, quintuple layers). d, Extinction coefficient at 6 K and 300 K for the five patterned films, with the radiation electric field parallel to the ribbons. e, Extinction coefficient of the five patterned films, with the radiation electric field applied perpendicularly to the ribbons, at 6 K and 300 K. All data are normalized by their respective peak values.

  2. Extraction of the bare plasmon and phonon contributions from the extinction data through a Fano fit.
    Figure 2: Extraction of the bare plasmon and phonon contributions from the extinction data through a Fano fit.

    Normalized extinction coefficient E(ν) versus frequency ν for the five patterned films, for the radiation electric field E perpendicular to the ribbons, at 6 K (circles), as well as fits to equation (1) (black lines). Bare plasmon and α(β) phonon contributions, extracted through the fits, are shown by the red and green (magenta) lines, respectively. In the top and bottom panels, the bump at 2.6 THz is due to insufficient compensation of the Mylar beamsplitter absorption. Inset (bottom panel): plasmon linewidth Γp versus ribbon width W at 6 K. The dotted line is the Drude contribution to Γp as extracted from data with polarization parallel to the ribbons. The dashed line is a guide to the eye.

  3. Experimental and theoretical dispersion of plasmons in Bi2Se3.
    Figure 3: Experimental and theoretical dispersion of plasmons in Bi2Se3.

    Main panel: experimental values of νp versus k at 6 K (blue circles) compared with the plasmon dispersion for Dirac (dashed black line) and massive (dotted blue line) electrons calculated with no fitting parameters using equations (2) and (3), respectively. The additional point (green diamond) refers to a seventh sample with W = 1.8 µm and period L = 4 µm (L = 2.2W), for which the raw data are reported in Supplementary Fig. S1. Inset: linear dependence of νp on W−1/2, where W = π/k is the ribbon width.


  1. Maier, S. A. Plasmonics: Fundamentals and Applications (Springer, 2007).
  2. Ju, L. et al. Graphene plasmonics for tunable terahertz metamaterials. Nature Nanotech. 6, 630634 (2011).
  3. Grigorenko, A. N., Polini, M. & Novoselov, K. S. Graphene plasmonics. Nature Photon. 6, 749758 (2012).
  4. Hasan, M. Z. & Kane, C. L. Colloquium: topological insulators. Rev. Mod. Phys. 82, 30453067 (2010).
  5. Kane, C. L. & Mele, E. J. Quantum spin Hall effect in graphene. Phys. Rev. Lett. 95, 226801 (2005).
  6. Moore, J. E. The birth of topological insulators. Nature 464, 194198 (2010).
  7. Collins, G. P. Computing with quantum knots. Sci. Am. 294, 5763 (2006).
  8. Kitaev, A. & Preskill, J. Topological entanglement entropy. Phys. Rev. Lett. 96, 110404 (2006).
  9. Zhang, X., Wang, J. & Zhang, S.-C. Topological insulators for high-performance terahertz to infrared applications. Phys. Rev. B 82, 245107 (2010).
  10. Chen, Y. et al. Experimental realization of a three-dimensional topological insulator, Bi2Te3. Science 325, 178181 (2009).
  11. Allen, S. J., Tsui, D. C. & Logan R. A. Observation of the two-dimensional plasmon in silicon inversion layers. Phys. Rev. Lett. 38, 980983 (1977).
  12. Koppens, F. H. L., Chang, D. E. & de Abajo, J. C. Graphene plasmonics: a platform for strong light–matter interactions. Nano Lett. 11, 33703377 (2011).
  13. Nikitin, A. Yu., Guinea, F., Garcia Vidal, F. J. & Martin Moreno, L. Edge and waveguide terahertz surface plasmon modes in graphene microribbons. Phys. Rev. B 84, 161407 (2011).
  14. Nikitin, A. Yu., Garcia Vidal, F. J. & Martin Moreno, L. Surface plasmon enhanced absorption and suppressed transmission in periodic arrays of graphene ribbons. Phys. Rev. B 85, 081405(R) (2012).
  15. Bansal, N., Kim, Y. S., Brahlek, M., Edrey, E. & Oh, S. Thickness-independent transport channels in topological insulator Bi2Se3 thin films. Phys. Rev. Lett. 109, 116804 (2012).
  16. Bansal, N., et al. Epitaxial growth of topological insulator Bi2Se3 thin film on Si(111) with atomically sharp interface. Thin Solid Film 520, 224229 (2011).
  17. Di Pietro, P. et al. Optical conductivity of bismuth-based topological insulators. Phys. Rev. B 86, 4701 (2012).
  18. Valdes Aguilar, R. et al. THz response and colossal Kerr rotation from the surface states of the topological insulator Bi2Se3. Phys. Rev. Lett. 86, 045439 (2012).
  19. Fei, Z. et al. Infrared nanoscopy of Dirac plasmons at the graphene–SiO2 interface. Nano Lett. 11, 47014705 (2011).
  20. Giannini, V., Francescato, Y., Amrania, H., Phillips, C. C. & Maier, S. A. Fano resonances in nanoscale plasmonic systems: a parameter-free modeling approach. Nano Lett. 11, 28352840 (2011).
  21. Landau, L. On the vibration of the electronic plasma. J. Phys. USSR 10, 25 (1946).
  22. Yan, H. et al. Damping pathways of mid-infrared plasmons in graphene nanostructures. Nature Photon. 7, 394399 (2013).
  23. Baumberg, J. J. & Williams, D. A. Coherent phonon–plasmon modes in GaAs:Alx Ga1–xAs heterostructures. Phys. Rev. B 53, R16140R16143 (1996).
  24. Cho, G. C., Dekorsy, T., Bakker, H. J., Hovel, R. & Kurz, H. Generation and relaxation of coherent majority plasmons. Phys. Rev. Lett. 77, 40624065 (1996).
  25. Pan, Z.-H et al., Measurement of an exceptionally weak electron–phonon coupling on the surface of the topological insulator Bi2Se3 using angle-resolved photoemission spectroscopy. Phys. Rev. Lett. 108, 187001 (2012).
  26. Zhu, X. et al. Electron–phonon coupling on the surface of the topological insulator Bi2Se3 determined from surface-phonon dispersion measurements. Phys. Rev. Lett. 108, 185501 (2012).
  27. Profumo, R. E. V. et al. Double-layer graphene and topological insulator thin-film plasmons. Phys. Rev. B 85, 085443 (2012).
  28. Das Sarma, S. & Hwang, E. H. Collective modes of the massless Dirac plasma. Phys. Rev. Lett. 102, 206412 (2009).
  29. Cao, Y., et al. In-plane helical orbital texture switch near the Dirac point in the topological insulator Bi2Se3. Preprint at http://lanl.arxiv.org/abs/1209.1016 (2012).

Download references

Author information


  1. CNR–SPIN, Corso F. Perrone, 16152 Genoa, Italy

    • P. Di Pietro &
    • P. Calvani
  2. Dipartimento di Fisica, Università di Roma ‘La Sapienza’, Piazzale A. Moro 2, I-00185 Rome, Italy,

    • P. Di Pietro,
    • M. Ortolani,
    • O. Limaj,
    • V. Giliberti,
    • F. Giorgianni,
    • P. Calvani &
    • S. Lupi
  3. CNR–IFN, Via Cineto Romano, 42 00156 Rome, Italy

    • M. Ortolani,
    • A. Di Gaspare &
    • V. Giliberti
  4. INFN, Piazza dei Caprettari 70, 00186 Rome, Italy

    • O. Limaj,
    • F. Giorgianni &
    • S. Lupi
  5. Department of Physics and Astronomy Rutgers, The State University of New Jersey, 136 Frelinghuysen Road, Piscataway, New Jersey 08854-8019, USA

    • M. Brahlek,
    • N. Bansal,
    • N. Koirala &
    • S. Oh
  6. CNR–IOM, Area Science Park, Basovizza, Ed. MM, Strada Statale 14 Km 163,5, I-34149 Trieste, Italy

    • S. Lupi


M.B., N.B., N.K. and S.O. fabricated and characterized the Bi2Se3 films. M.O., A.D.G. and V.G. performed electron-beam lithography and etching. P.D.P., F.G., O.L. and M.O. carried out the terahertz experiments and data analysis. P.C., M.O. and S.L. planned and managed the project, with inputs from all authors. All authors discussed the results. P.C., M.O. and S.L. wrote the manuscript.

Competing financial interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to:

Author details

Supplementary information

PDF files

  1. Supplementary information (624 KB)

    Supplementary information

Additional data