Scanning tunneling microscopy study of the quasicrystalline 30° twisted bilayer graphene

Twisted bilayer graphene with a twist angle of exactly 30° (30°-TBG) is a unique two-dimensional (2D) van der Waals (vdW) system because of its quasicrystalline nature. Here we report, for the first time, scanning tunneling microscopy (STM) measurements of the quasicrystalline 30°-TBG that was obtained in a controllable way by using transfer-assisted fabrication of a pair of graphene sheets. The quasicrystalline order of the 30°-TBG, showing a 12-fold rotational symmetry, was directly visualized in atomic-resolved STM images. In the presence of high magnetic fields, we observed Landau quantization of massless Dirac fermions, demonstrating that the studied 30°-TBG is a relativistic Dirac fermion quasicrystal. Because of a finite interlayer coupling between the adjacent two layers of the 30°-TBG, a suppression of density-of-state (DOS) at the crossing point between the original and mirrored Dirac cones was observed. Moreover, our measurements also observe strong intervalley scattering in the defect-free quasicrystal, indicating that the electronic properties of the 30°-TBG should be quite different from that of its component: the graphene monolayer.