The uniform growth of single-crystal graphene over wafer-scale areas remains a challenge in the commercial-level manufacturability of various electronic, photonic, mechanical, and other devices based on graphene. Here, we describe wafer-scale growth of wrinkle-free single-crystal monolayer graphene on silicon wafer using a hydrogen-terminated germanium buffer layer. The anisotropic twofold symmetry of the germanium (110) surface allowed unidirectional alignment of multiple seeds, which were merged to uniform single-crystal graphene with predefined orientation. Furthermore, the weak interaction between graphene and underlying hydrogen-terminated germanium surface enabled the facile etch-free dry transfer of graphene and the recycling of the germanium substrate for continual graphene growth.

The ground state property of a Au-induced atomic wire array on a stepped Si(553) surface with interesting 1D metallic bands was investigated. Electron diffraction and scanning tunneling microscopy reveal an intriguing coexistence of triple- and double-period lattice distortions at low temperature. Angle-resolved photoemission observes both the nearly 1/3- and 1/2-filled bands to gradually open energy gaps upon cooling. We explain these unusual findings as due to the occurrence of Peierls distortions of triple and double periods on the two different atomic-scale chain elements, respectively, within a single unit wire. The two Peierls distortions are suggested to have different transition temperatures and little lateral correlation between each other.

One-dimensional atomic chains on Au/Si(557) feature two proximal 1D bands near the Fermi level, which were controversially attributed as a spinon-holon pair of a Luttinger liquid. Angle-resolved photoemission shows that only one band is metallic with the neighboring one gapped at room temperature. Furthermore, even the metallic branch is found to undergo a metal-insulator transition upon cooling, which follows a mean-field-type behavior. Scanning tunneling microscopy observes two apparently unequivocal chains on the surface, one of which exhibits periodicity doubling accompanying the metal-insulator transition. The surface 1D structure is thus concluded to be insulating at low temperature with a Peierls-type instability.

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.