Moiré Superlattices And Graphene Quasicrystal

When repetitive structures are overlaid against each other, a new superimposed moire pattern emerges and is observed in various macroscopic phenomena. Likewise, in case the lattice periods do not coincide between atomically thin layers, the moire interference between the lattices makes a new class of superlattices where the influence of the exceptionally long-period interlayer interaction is crucial to determine its electronic structures.In this talk, I will first discuss the impact of two-dimensional moire superlattice formation for graphene systems and for hybrid layered-structures, and show that their electronic and optical properties are significantly altered if compared with those of the pristine graphene. I will also show that the moire superlattice affords a unique opportunity to study the fundamental problems, such as Hofstadter’s butterfly and incommensurate double-walled nanotubes. Then, I will introduce a graphene quasicrystal. As θ increases to 30°in twisted bilayer graphene, the moiré period competes with the atomic length scale and quasicrystalline nature emerges. I will introduce a momentum-space tight-binding model which can reveal the electronic structures of general incommensurately stacked atomic layers, and reveal the electronic structures of graphene quasicrystal by fully respecting both the dodecagonal rotational symmetry and the massless Dirac nature. The resulting quasi-band structure is composed of the nearly flat bands with spiky peaks in the density of states, where the wave functions exhibit characteristic patterns which fit to the fractal inflations of the quasicrystal tiling. I also demonstrate that the 12-fold resonant states appear as spatially-localized states in a finite-size geometry, which is another hallmark of quasicrystal. While conventional quasicrystals can be viewed as “intrinsic quasicrystals”,where all atomic sites are intrinsically arranged in quasiperiodic order, the quasicrystals emerging from the van der Waal stacking of atomic layers can be viewed as “extrinsic quasicrystals” of which quasiperiodic nature arises from the interaction between periodic layers. I will show that the flat band area as well as the quasicrystalline nature can be widely tunable by external pressure or interlayer potential asymmetry. The theoretical method based on the k-space tight-binding approach developed in this study is applicable to any kind of extrinsic quasicrystals as well as heterostructures of two-dimensional materials having different lattice symmetries (e.g., the combination of rectangle and hexagon).