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Stacking symmetry governed second harmonic generation in graphene trilayers

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Science Advances  15 Jun 2018:
Vol. 4, no. 6, eaat0074
DOI: 10.1126/sciadv.aat0074
  • Fig. 1 Stacking orders in few-layer graphene.

    (A) Graphene monolayer. (B) AB-stacked graphene bilayer. (C and D) Two most common polymorphs of a graphene trilayer, ABA (Bernal) and ABC (rhombohedral), respectively. The top, middle, and bottom layers are labeled yellow, purple, and green, respectively. In ABA stacking, the top layer lies exactly on top of the bottom layer; in ABC stacking, one sublattice of the upper layer lies above the center of the hexagons in the lower layer.

  • Fig. 2 Optical microscopy and spectroscopy of few-layer graphene.

    (A) Bright-field optical microscopy of mechanically exfoliated few-layer graphene on silicon wafer with 300-nm-thick SiO2. The crystalline orientation was overlaid on the image, as determined from the azimuthal polarization patterns in Fig. 3. (B) Up-converted NPL microscopy of the same area as (A). The sample was excited by femtosecond pulses at a wavelength of 1300 nm and an average power of 0.5 mW without any damages. The collected signal had a spectral range from 425 to 675 nm. (C) Corresponding up-converted optical spectra from monolayer (1L), bilayer (2L), trilayer (3L), and bare substrate, respectively. Besides the broad spectra from NPL, THG at 433 nm and SHG at 650 nm were also observed. The inset of (C) plotted the power dependence of SHG, after subtracting the NPL background, on graphene trilayer in a log-log scale. The dotted data were fitted linearly with a slope of 2.02 ± 0.18. a.u., arbitrary units.

  • Fig. 3 Azimuthal polarization patterns of SHG and up-converted NPL on the ABA trilayer.

    (A and B) The polarizations of the excitation and signal beams are set in parallel (XX) and perpendicular (XY), respectively. The NPL and SHG signals were shown in black and blue symbols, respectively. The intensity of NPL was integrated from 640 to 660 nm and reduced by 10 times for clarity. While the NPL was fitted with a constant azimuthally, the SHG signals were fitted to functions of Acos2(3θ) and Embedded Image for (A) and (B), respectively.

  • Fig. 4 Imaging the stacking order of ABA and ABC trilayers.

    (A) Bright-field optical microscopy image of few-layer graphene with trilayer on the left and bilayer on the right. The crystalline orientation was also overlaid on the image. (B) Corresponding nonlinear microscopy of the same area as (A) with an excitation wavelength of 1266 nm. The spectral band-pass range for the nonlinear signal was centered at 633 nm and narrowed to 6 nm, so that SHG could be more pronounced over NPL. The dwell time at each pixel was 25 ms. The dimmer region from graphene trilayer in (B) is enclosed by dotted lines and attributed to ABC stacking. (C and D) Nonlinear optical spectra from ABA and ABC trilayer regions, marked in (B), when both the excitation and signal beams were linearly polarized along the armchair or zigzag directions, respectively. (E and F) Corresponding G and 2D Raman peaks from ABA (red) and ABC (black) trilayers, respectively. The spectra were excited at a wavelength of 532 nm and a power of 1 mW.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/6/eaat0074/DC1

    fig. S1. Raman spectra of the sample from a monolayer (1L), a bilayer (2L), and a trilayer (3L), along with the background from the bare substrate.

    fig. S2. Comparison of nonlinear microscopy at different excitation wavelengths.

    fig. S3. Schematic showing the resonant transitions in the SHG process.

    fig. S4. Stacking-dependent properties in ABA and ABC trilayers.

  • Supplementary Materials

    This PDF file includes:

    • fig. S1. Raman spectra of the sample from a monolayer (1L), a bilayer (2L), and a trilayer (3L), along with the background from the bare substrate.
    • fig. S2. Comparison of nonlinear microscopy at different excitation wavelengths.
    • fig. S3. Schematic showing the resonant transitions in the SHG process.
    • fig. S4. Stacking-dependent properties in ABA and ABC trilayers.

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