Quantum states of quasiparticles in solids are dictated by symmetry. We have experimentally demonstrated quantum states of Dirac electrons in a two-dimensional quasicrystal without translational symmetry. A dodecagonal quasicrystalline order was realized by epitaxial growth of twisted bilayer graphene rotated exactly 30°. We grew the graphene quasicrystal up to a millimeter scale on a silicon carbide surface while maintaining the single rotation angle over an entire sample and successfully isolated the quasicrystal from a substrate, demonstrating its structural and chemical stability under ambient conditions. Multiple Dirac cones replicated with the 12-fold rotational symmetry were observed in angle-resolved photoemission spectra, which revealed anomalous strong interlayer coupling with quasi-periodicity. Our study provides a way to explore physical properties of relativistic fermions with controllable quasicrystalline orders.
Bibliographical noteFunding Information:
We thank S.-H. Kang, H. J. Choi, E.-G. Moon, L. A. Wray, A. Kent, M. Yang, and K. Ihm for fruitful discussions. This work was supported by the National Research Foundation (NRF) of Korea (NRF-2015R1A2A2A01004853 and NRF-2017M2A2A6A01019384). M.K. was supported by JSPS KAKENHI grants JP25107005 and JP15K21722. Y.-W.S was supported by the NRF of Korea (grant 2017R1A5A1014862, SRC program vdWMRC center). P.M. was supported by the NYU Shanghai (start-up funds), the NYU-ECNU Institute of Physics, the NYU Global Seed Grant for Collaborative Research program, and the NSF of China (grant 11550110177, Research Fund for International Young Scientists program). P.K. was supported by the Global Research Laboratory program (2015K1A1A2033332) through the NRF of Korea. C.-W.Y. was supported by the National Research Council of Science and Technology (NST) (CRC-15-06-KIGAM) and the NRF of Korea (NRF-2011-0030058 and NRF-2015R1D1A1A01059653).
2017 © The Authors.
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