Atomic arrangements of quasicrystal bilayer graphene: Interlayer distance expansion

Bilayer graphene exhibits outstanding characteristics that can be modified by adjusting the twist angle between two layers. An exact ${30}^{\circ }$-twisted bilayer graphene forms a material comprising two-dimensional quasicrystals accompanied by a relativistic Dirac fermion. In this study, the atomic arrangements of quasicrystal bilayer graphene on a SiC(0001) substrate are identified using positron diffraction. The interlayer distance in quasicrystal bilayer graphene is determined to be 3.46 Å, revealing an expansion of 0.17 Å as compared with that of Bernal-stacked bilayer graphene. This result provides important insights for elucidating the origin of the magnitude of coupling between graphene layers.

Figure 1

Structure models of (a) QC-BLG and (b) B-BLG on SiC(0001) substrate. Small gray and large magenta circles denote C and Si atoms, respectively. Only bilayer graphene is depicted in top view.

Figure 2

RHEED patterns obtained from QC-BLG ((a) $\left[1\overline{1}00\right]$ and (b) $\left[11\overline{2}0\right]$) and from B-BLG ((c) $\left[1\overline{1}00\right]$ and (d) $\left[11\overline{2}0\right]$) on SiC(0001) substrate. Energy and glancing angle of electron beam were 15 keV and $\sim 4^{\circ }$, respectively. In the patterns, “Gr” indicates graphene.

Figure 3

TRHEPD rocking curves of 00 spot for QC-BLG (red, top) and B-BLG (blue, bottom) on SiC(0001) substrate under one-beam condition. Open circles indicate experimental data. Solid lines denote curves calculated using best-fit parameters. Dotted lines provide visual guide.

Figure 4

TRHEPD rocking curves from QC-BLG ((a) $\left[1\overline{1}00\right]$ and (b) $\left[11\overline{2}0\right]$) and from B-BLG ((c) $\left[1\overline{1}00\right]$ and (d) $\left[11\overline{2}0\right]$) on SiC(0001) substrate. Open circles and solid lines indicate experimental and calculated values, respectively. Thick (red) and thin (gray) lines represent results calculated assuming AB and AA stacking at interface between bottom layer of bilayer graphene and buffer layer of SiC(0001) substrate, respectively.