  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 degree. 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.
