Extremely flat band in bilayer graphene

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Science Advances  09 Nov 2018:
Vol. 4, no. 11, eaau0059
DOI: 10.1126/sciadv.aau0059
  • Fig. 1 Angle-resolved photoemission spectroscopy.

    (A) Data for the sample with 1.2 monolayer graphene (MLG) coverage around the Embedded Image point of the graphene Brillouin zone. The MLG Dirac cone dispersion, the faint BLG dispersion, and an intense nondispersing flattened band at 255-meV binding energy, marked by a white arrow, can be seen. Measurements were done at hν = 62 eV and T = 60 K. (B) First derivative with respect to energy from the same data as in (A) where dispersions of all bands are much more visible. A blue arrow shows the possible presence of one more flat band. (C) Measurements in the Embedded Image direction showing a destructive interference effect for the monolayer and bilayer bands and its absence for the flat band. (D) Constant energy cuts taken at 235- and 255-meV binding energies. (E) Same data as in (A) presented as a stack of spectra (only every 10th spectrum is shown). (F) Spectra at the Embedded Image point showing the flattened band intensity and its narrow width. (G) Dispersion of the maxima extracted from the spectra.

  • Fig. 2 DFT calculations.

    (A) Calculated band structures of MLG (blue) and BLG (red) on SiC around the Embedded Image point with k perpendicular to the Embedded Image direction. Width of lines corresponds to the contribution of pz orbitals to the top graphene layer. (B) DOS calculated from the data in (A), taking into account the wave function contribution to both layers of BLG and assuming rotational symmetry of the calculated bands around the Embedded Image point. (C) Magnified view of the calculated flat band dispersion around the Embedded Image point. (D) Slab structure of BLG on 6H-SiC(0001) used in DFT calculations. Between the BLG and the SiC substrate, there is a graphene buffer (zero) layer. The back side of the slab is H passivated. The inset shows the model of the BLG/6H-SiC unit cell used in the calculations (only BLG is shown), with definition of sublattices A, B, and C used in the present work. (E) Effect of BLG interaction with the ZLG/SiC system (ZLG/SiC). Yellow-colored isosurfaces show gain of charge, and light blue–colored isosurfaces show loss of charge, indicating charge transfer from the ZLG/SiC system to the BLG (mainly bottom layer) and emergence of a strong sublattice asymmetry. Letters A, B, and C in the top-left part of the figure indicate A, B, and C sublattices, correspondingly. (F) Same as (E) with tilted view for better clarity.

  • Fig. 3 Interlayer/sublattice asymmetry.

    Demonstration of the possibility of transforming the flat band electronic structure into a band with either positive or negative effective mass by changing (A) the interlayer asymmetry and (B) the sublattice asymmetry of the bottom layer. The calculation is based on the Hamiltonian H2.

Supplementary Materials

  • Supplementary Materials

    This PDF file includes:

    • Fig. S1. BLG ARPES.
    • Fig. S2. MLG, BLG, and TLG/SiC.
    • Fig. S3. BLG sublattice contributions.
    • Fig. S4. TLG/SiC.
    • Fig. S5. Graphene/Ir thickness dependence.
    • Fig. S6. Unsupported BLG.

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