CWY), hand@kias.re.kr (YWS) † These authors contributed equally to this work.2 ABSTRACT Quantum states of quasiparticles in solids are dictated by symmetry. Thus, a discovery of unconventional symmetry can provide a new opportunity to reach a novel quantum state. Recently, Dirac and Weyl electrons have been observed in crystals with discrete translational symmetry. Here we experimentally demonstrate Dirac electrons in a two-dimensional quasicrystal without translational symmetry. A dodecagonal quasicrystal was realized by epitaxial growth of twisted bilayer graphene rotated exactly 30°.The graphene quasicrystal was grown up to a millimeter scale on SiC(0001) surface while maintaining the single rotation angle over an entire sample and was successfully isolated from a substrate, demonstrating its structural and chemical stability under ambient conditions. Multiple Dirac cone replicated with the 12-fold rotational symmetry were observed in angle resolved photoemission spectra, showing its unique electronic structures with anomalous strong interlayer coupling with quasi-periodicity.Our study provides a new way to explore physical properties of relativistic fermions with controllable quasicrystalline orders.
ONE SENTENCE SUMMARY:A Dirac fermion quasicrystal with 12-fold rotational symmetry and without any translational symmetry can be realized from twisted bilayer graphene rotated exactly 30°. Microscopy, Graphene. by ×10 9 . (B-D) Umklapp scattering paths from the Dirac point of the upper layer with the shortest three wave vectors |q| involved in the Umklapp process (see text). Each panel shows the scattering involving different G. (E) A schematic drawing of the locations of Dirac cones in calculations, where the Dirac cones were ranked by the length of |q| and the size of circle is proportional to the intensity calculated theoretically (see Figs. S8 and S9 in SI also). (F) A schematic drawing of the locations of Dirac cones in ARPES measurements, where the Dirac cones were also ranked by the length of |q| and the intensity and size of circle is proportional to the intensity measured experimentally. (G) The theoretical calculations of the contribution to the ARPES intensity from the single (multiple) scattering plotted as a function of |q|. Red (grey) circles in (G) show the contribution from the single (multiple) scattering (see SI and Fig. S8 also). (H) The experimental intensities of Dirac cones plotted as a function of |q|. 19 FIGURE 4. ARPES spectra and Fermi velocities of graphene quasicrystal. (A) Constant energy maps of ARPES spectra of graphene quasicrystal with different binding energies. (B) Energy-momentum dispersions of Dirac cones at the K points of the upper and lower layer graphene. (C) The fitted lines of energy-momentum dispersions of Dirac cones used to extract Fermi velocities (see Fig. S4F in SI also for detailed comparison between the experimental dispersions and the fitted lines), where the Fermi velocities of the A, B, C and D Dirac cones (see Fig. 3(A) for the notations of the Dirac cones) a...
