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.

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The convenient synthesis of one-dimensional nanostructures of chalcogenide compounds with a visible band-gap is an essential research topic in developing next-generation photoelectronic devices. In particular, the design of a theoretically predictable synthesis process provides great flexibility and has a considerable ripple effect in nanotechnology. In this study, a novel rational growth approach is designed using the spinodal decomposition phenomenon for the synthesis of the Sb2Se3 nanowires, which is based on the thermodynamic phase diagram. Using a stacked elemental layer (Sb/Sb-Se/Se) and heat treatment at 623 K for 30 min under an N2 atmosphere, the vertically inclined one-dimensional nanostructures are experimentally demonstrated. An additional annealing process at 523 K in a vacuum effectively removed excess Se elements due to their high vapor pressure, resulting in highly dense single crystal Sb2Se3 nanowire arrays. Adaption of our synthesis approach enables significantly improved photocurrent generation in the vertically stacked structure (glass/ITO/Sb2Se3 nanowires/ITO/PEN) from 6.4 (dark) to under 690 μA (at 3 V under AM 1.5G). In addition, a photoelectrochemical test demonstrated their p-type conductivity and robust photocorrosion performance in 0.5 M H2SO4.