Graphene plasmonics for tunable terahertz metamaterials

Journal name:
Nature Nanotechnology
Volume:
6,
Pages:
630–634
Year published:
DOI:
doi:10.1038/nnano.2011.146
Received
Accepted
Published online

Abstract

Plasmons describe collective oscillations of electrons. They have a fundamental role in the dynamic responses of electron systems and form the basis of research into optical metamaterials1, 2, 3. Plasmons of two-dimensional massless electrons, as present in graphene, show unusual behaviour4, 5, 6, 7 that enables new tunable plasmonic metamaterials8, 9, 10 and, potentially, optoelectronic applications in the terahertz frequency range8, 9, 11, 12. Here we explore plasmon excitations in engineered graphene micro-ribbon arrays. We demonstrate that graphene plasmon resonances can be tuned over a broad terahertz frequency range by changing micro-ribbon width and in situ electrostatic doping. The ribbon width and carrier doping dependences of graphene plasmon frequency demonstrate power-law behaviour characteristic of two-dimensional massless Dirac electrons4, 5, 6. The plasmon resonances have remarkably large oscillator strengths, resulting in prominent room-temperature optical absorption peaks. In comparison, plasmon absorption in a conventional two-dimensional electron gas was observed only at 4.2 K (refs 13, 14). The results represent a first look at light–plasmon coupling in graphene and point to potential graphene-based terahertz metamaterials.

At a glance

Figures

  1. Plasmon resonance in gated graphene micro-ribbon arrays.
    Figure 1: Plasmon resonance in gated graphene micro-ribbon arrays.

    a, Top-view illustration of a typical graphene micro-ribbon array. The array was fabricated on transferred large-area CVD graphene using optical lithography and plasma etching. b, Side view of a typical device incorporating the graphene micro-ribbon array on a Si/SiO2 substrate. The carrier concentration in graphene is controlled using the ion-gel top gate. c, AFM image of a graphene micro-ribbon array sample with a ribbon width of 4 µm and a ribbon and gap width ratio of 1:1. d, Gate-dependent electrical resistance of this graphene micro-ribbon array. The resistance has a maximum at charge neutral point VCNP = 0.2 V. e,f, Gate-induced change of transmission spectra, −(T − TCNP)/TCNP (red solid line), with incident light polarized parallel (e) and perpendicular (f) to the ribbon length, respectively. The gate voltage was set at Vg = −2 V. For parallel polarization in e, the response originates from free carrier oscillation and can be well reproduced by a Drude fit (black dashed line). For perpendicular polarization in f, the spectrum shows a prominent absorption peak at 3 THz (1 THz = 33.3 cm−1) because of plasmon excitation. Plasmon resonance is characterized by a Lorentzian lineshape (blue dashed line). A small free carrier contribution described by Drude absorption (magenta dashed line) is also present as a result of graphene absorption outside the fabricated micro-ribbon array area. The plasmon absorption of over 13% is remarkably strong, and its integrated oscillator strength is more than an order of magnitude larger than that achieved in 2DEGs in conventional semiconductors.

  2. Control of plasmon resonance through electrical gating and micro-ribbon width.
    Figure 2: Control of plasmon resonance through electrical gating and micro-ribbon width.

    a, Mid-infrared transmission spectra, T/TCNP, of the graphene ribbon array in Fig. 1 as gate voltage Vg − VCNP varies from −0.3 to −2.2 V. The voltages corresponding to the unlabelled lines, starting with the red line and alternating downwards, are: −2.0 V, −1.6 V, −1.2 V, −0.7 V and −0.3 V. On electrical gating, optical transmission is increased up to a threshold energy of 2|EF| as a result of blocked interband optical transitions. This threshold energy provides direct determination of Fermi energy EF and carrier concentration n = (|EF|/planckvF)2/π in gated graphene. b, Control of terahertz resonance of plasmon excitations through electrical gating. Terahertz radiation was polarized perpendicular to the graphene ribbons. The plasmon resonance shifts to higher energy and gains oscillator strength with increased carrier concentration. For comparison, the inset shows corresponding spectra due to free carrier absorption for terahertz radiation polarized parallel to the ribbons. For this polarization, absorption strength increases with carrier concentration, but spectral shape remains the same. c, AFM images of samples with micro-ribbon widths (w) of 1, 2 and 4 µm. d, Change of transmission spectra with different graphene micro-ribbon widths for the same doping concentration of 1.5 × 1013 cm−2. The Drude background contributed by unpatterned graphene around the arrays (as in Fig. 1f) was subtracted, and all spectra were normalized by their respective peak values for convenience of comparison. Plasmon resonance frequency ωp shifts from 3 to 6 THz when micro-ribbon width decreases from 4 to 1 µm.

  3. Scaling laws of graphene plasmon resonance frequency.
    Figure 3: Scaling laws of graphene plasmon resonance frequency.

    a, Plasmon resonance frequency ωp as a function of |EF| (or equivalently |n|1/2 in the top label) for micro-ribbon arrays of different widths. b, Plasmon excitation ωp was normalized by 1/w for micro-ribbon arrays of different widths, which fits all data points (symbols) into a universal curve (solid line). This w−1/2 scaling of ωp is characteristic of 2D electron systems. The universal doping dependence of plasmon resonances is described by a scaling law of ωp  |EF|1/2  n1/4. This n1/4 scaling law is a signature of massless Dirac fermions. In comparison, ωp scales as n1/2 (dashed line) in conventional semiconductors.

  4. Simulation of plasmon excitations.
    Figure 4: Simulation of plasmon excitations.

    a, Transmission change spectrum −ΔT/TCNP simulated by finite element analysis (dashed line) for the sample in Fig. 1 at carrier concentration of 1.5 × 1013 cm−2. It reproduces well the experimentally observed spectrum (solid line) when the effective environment dielectric constant κ was set as 5, and corresponds to an electron–electron interaction strength of e2/κplanckvF  0.4. bd, Simulation results for current density amplitude (upper panel) and phase (lower panel) of the device at frequencies below resonance (1 THz, b), at resonance (3 THz, c) and above resonance (5 THz, d). The charge carriers oscillate perpendicular to the graphene ribbons on terahertz irradiation. The oscillating current is highest at the plasmon resonance frequency. The relative phase of the oscillating current with reference to the incident electrical field also varies quickly and changes sign at the resonance frequency. Both are characteristics of a resonant excitation.

References

  1. Yen, T. J. et al. Terahertz magnetic response from artificial materials. Science 303, 14941496 (2004).
  2. Pendry, J. B., Holden, A. J., Stewart, W. J. & Youngs, I. Extremely low frequency plasmons in metallic mesostructures. Phys. Rev. Lett. 76, 47734776 (1996).
  3. Chen, H. T. et al. Active terahertz metamaterial devices. Nature 444, 597600 (2006).
  4. Wunsch, B., Stauber, T., Sols, F. & Guinea, F. Dynamical polarization of graphene at finite doping. New J. Phys. 8, 318 (2006).
  5. Polini, M., MacDonald, A. H. & Vignale, G. Drude weight, plasmon dispersion, and pseudospin response in doped graphene sheets. Preprint at http://arXiv.org/abs/0901.4528 (2009).
  6. Hwang, E. H. & Das Sarma, S. Dielectric function, screening, and plasmons in two-dimensional graphene. Phys. Rev. B 75, 205418 (2007).
  7. Brey, L. & Fertig, H. A. Elementary electronic excitations in graphene nanoribbons. Phys. Rev. B 75, 125434 (2007).
  8. Vakil Ashkan & Engheta, N. One-atom-thick IR metamaterials and transformation optics using graphene. Preprint at http://arXiv.org/abs/1101.3585 (2011).
  9. Jablan, M., Buljan, H. & Soljacic, M. Plasmonics in graphene at infrared frequencies. Phys. Rev. B 80, 245435 (2009).
  10. Koppens, F. H. L., Chang, D. E. & Abajo, F. J. G. d. Graphene plasmonics: a platform for strong light-matter interaction. Preprint at http://arXiv.org/abs/1104.2068v1 (2011).
  11. Rana, F. Graphene terahertz plasmon oscillators. IEEE Trans Nanotechnol. 7, 9199 (2008).
  12. Ryzhii, M. & Ryzhii, V. Injection and population inversion in electrically induced p-n junction in graphene with split gates. Jpn. J. Appl. Phys. 2 46, L151L153 (2007).
  13. Allen, S. J., Tsui, D. C. & Logan, R. A. Observation of 2-dimensional plasmon in silicon inversion layers. Phys. Rev. Lett. 38, 980983 (1977).
  14. Batke, E., Heitmann, D. & Tu, C. W. Plasmon and magnetoplasmon excitation in two-dimensional electron space-charge layers on gaas. Phys. Rev. B 34, 69516960 (1986).
  15. Novoselov, K. S. et al. Two-dimensional gas of massless Dirac fermions in graphene. Nature 438, 197200 (2005).
  16. Zhang, Y. B., Tan, Y. W., Stormer, H. L. & Kim, P. Experimental observation of the quantum Hall effect and Berry's phase in graphene. Nature 438, 201204 (2005).
  17. Katsnelson, M. I., Novoselov, K. S. & Geim, A. K. Chiral tunnelling and the Klein paradox in graphene. Nature Phys. 2, 620625 (2006).
  18. Young, A. F. & Kim, P. Quantum interference and Klein tunnelling in graphene heterojunctions. Nature Phys. 5, 222226 (2009).
  19. Mak, K. F. et al. Measurement of the optical conductivity of graphene. Phys. Rev. Lett. 101, 246803 (2008).
  20. Nair, R. R. et al. Fine structure constant defines visual transparency of graphene. Science 320, 13081308 (2008).
  21. Li, Z. Q. et al. Dirac charge dynamics in graphene by infrared spectroscopy. Nature Phys. 4, 532535 (2008).
  22. Wang, F. et al. Gate-variable optical transitions in graphene. Science 320, 206209 (2008).
  23. Bostwick, A., Ohta, T., Seyller, T., Horn, K. & Rotenberg, E. Quasiparticle dynamics in graphene. Nature Phys. 3, 3640 (2007).
  24. Bostwick, A. et al. Observation of plasmarons in quasi-freestanding doped graphene. Science 328, 9991002 (2010).
  25. Liu, Y., Willis, R. F., Emtsev, K. V. & Seyller, T. Plasmon dispersion and damping in electrically isolated two-dimensional charge sheets. Phys. Rev. B 78, 201403 (2008).
  26. Tegenkamp, C., Pfnur, H., Langer, T., Baringhaus, J. & WSchumacher, H. Plasmon electron-hole resonance in epitaxial graphene. J. Phys. Condens. Matter 23, 012001 (2011).
  27. Brar, V. W. et al. Observation of carrier-density-dependent many-body effects in graphene via tunneling spectroscopy. Phys. Rev. Lett. 104, 036805 (2010).
  28. Cho, J. H. et al. Printable ion-gel gate dielectrics for low-voltage polymer thin-film transistors on plastic. Nature Mater. 7, 900906 (2008).
  29. Yamamoto, K., Tani, M. & Hangyo, M. Terahertz time-domain spectroscopy of imidazolium ionic liquids. J. Phys. Chem. B 111, 48544859 (2007).
  30. Palik, E. D. Handbook of Optical Constants of Solids (Elsevier, 1998).
  31. Li, X. S. et al. Large-area synthesis of high-quality and uniform graphene films on copper foils. Science 324, 13121314 (2009).

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Author information

Affiliations

  1. Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA

    • Long Ju,
    • Baisong Geng,
    • Jason Horng,
    • Caglar Girit,
    • Alex Zettl,
    • Y. Ron Shen &
    • Feng Wang
  2. Advanced Light Source Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

    • Michael Martin,
    • Zhao Hao &
    • Hans A. Bechtel
  3. Earth Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

    • Zhao Hao
  4. Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

    • Xiaogan Liang
  5. Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

    • Alex Zettl,
    • Y. Ron Shen &
    • Feng Wang
  6. School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China

    • Baisong Geng

Contributions

F.W. and L.J. conceived the experiment. L.J. carried out optical measurements, B.G., J.H., X.L. and C.G. contributed to sample growth and fabrication, and L.J. and F.W. performed theoretical analysis. All authors discussed the results and wrote the paper.

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The authors declare no competing financial interests.

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