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Tuning quantum nonlocal effects in graphene plasmonics

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Science  14 Jul 2017:
Vol. 357, Issue 6347, pp. 187-191
DOI: 10.1126/science.aan2735
  • Fig. 1 Concept for enhancing nonlocal effects by slowing down the graphene plasmon velocity.

    (A) Effect on graphene plasmon velocity from changing separation d in the graphene-metal system. Insets show plasmon electric field distribution (red and blue colors) for large or small separation d. The separation d is controlled by the thickness of the dielectric h-BN. (B) Frequency–wave number dispersion of plasmon at various d; the solid lines are all computed with equal carrier density ns = 1012 cm–2, whereas the dashed line shows the smallest-d case with a factor-10-lower carrier density ns = 1011 cm–2. The horizontal dashed gray line indicates the frequency for which the experiment has been performed. (C) Plasmon velocity dependence on d and carrier density ns. Contours indicate discrepancy between local and nonlocal plasmon models.

  • Fig. 2 Experimental setup and near-field imaging data.

    (A) A metallized tip (inverted pyramid) scans over a graphene sheet that has been encapsulated in h-BN and placed on a split metallic film. Terahertz laser light illuminates the entire device, launching plasmons (orange arrows) at the tip and split. Gate voltages VL and VR control the electron density and the junction photocurrent sensitivity. (B) Photocurrent traces in three different devices, each at ns = 1.0 × 1012 cm–2, showing interference fringes used to extract the plasmon wavelength λ [and hence velocity vp = λ(ω/2π)] via the indicated fits.

  • Fig. 3 Tunable nonlocal effects.

    Extracted plasmon wavelength dependence on carrier density ns, for three devices of differing separation d, show parameter-free agreement with the full theory (color map) and considerable deviation from a local-response theory (dashed line). The red color map indicates the inverse of the left side of Eq. 1, so that plasmons appear as a red peak, the width being associated with propagation distance. The hatched region below the solid line indicates phase velocities below vF. The upper and lower rows show the same data, plotted differently.

  • Fig. 4 Nonlocal conductivity of graphene.

    (A) Schematic representations of the three main mechanisms governing graphene response beyond the local approximation. (B) Experimentally extracted σ(ω,q) at ns = 1.0 × 1012 cm–2, compared with theoretical approximations for the interacting electron system in graphene: RPA, with added velocity renormalization (RPA+VR), and then with compressibility correction (RPA+VR+CC); local RPA appears as a horizontal line.

Supplementary Materials

  • Tuning quantum nonlocal effects in graphene plasmonics

    Mark B. Lundeberg, Yuanda Gao, Reza Asgari, Cheng Tan, Ben Van Duppen, Marta Autore, Pablo Alonso-González, Achim Woessner, Kenji Watanabe, Takashi Taniguchi, Rainer Hillenbrand, James Hone, Marco Polini, Frank H. L. Koppens

    Materials/Methods, Supplementary Text, Tables, Figures, and/or References

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    • Materials and Methods
    • Figs. S1 and S2
    • References

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