Mikito Koshino

Here, the authors show how magnetic fields expose the hidden quasiband structure of 30\ifmmode^\circ\else\textdegree\fi{} twisted bilayer graphene, a quasicrystal with 12-fold rotational symmetry but no translational symmetry. Their Landau-level theory reveals quantized orbits of quasiband pockets, unusual spectral patterns, and magneto-optical selection rules enforced by quasicrystalline symmetry, providing a route to quantum magneto-optics in broader quasiperiodic van der Waals materials.

Moiré flat bands in rhombohedral multilayer graphene provide a platform for exploring interaction-driven topological phases, where a single isolated band often forms a Chern band. However, non-Abelian degenerate Chern bands with internal symmetries such as SU(N) have so far been realized only in highly engineered systems. Here, we show that a doubly degenerate non-Abelian Chern band with Chern number |C|=1 emerges spontaneously at filling ν=2 in rhombohedral three-, four-, and five-layer graphene, regardless of the presence of a hexagonal boron nitride substrate. Using self-consistent Hartree-Fock calculations, we map out phase diagrams as functions of displacement field and electronic periodicity and analytically demonstrate that the Fock term drives spontaneous symmetry breaking and generates non-Abelian Berry curvature. We further show that this non-Abelian topology is characterized by SU(2) gauge flux threading the noncontractible cycles of the Brillouin zone, leading to a global non-Abelian holonomy. Our findings unveil a new class of interaction-driven non-Abelian topological phases, distinct from quantum anomalous Hall and fractional Chern phases.

One-dimensional (1D) moiré superlattices provide a new route to engineering reduced-dimensional electronic states in van der Waals materials, yet their electronic structure and microscopic origin remain largely unexplored. Here, we investigate the structural relaxation and electronic properties of a 1D moiré superlattice formed in twisted bilayer 1T$'$-WTe$_2$ using density functional theory calculations, complemented by high-angle annular dark-field scanning transmission electron microscopy. We show that lattice relaxation strongly reconstructs the moiré stripes, leading to stacking-dependent stripe widths that are in excellent agreement with experimental observations. The relaxed structure hosts quasi-one-dimensional electronic bands near the Fermi level, characterized by strong dispersion along the stripe direction and nearly flat dispersion in the perpendicular direction. By comparing the full bilayer with isolated relaxed layers, we establish that these 1D electronic states are governed predominantly by an intralayer moiré potential induced by in-plane lattice relaxation, rather than by interlayer hybridization. We extract this position-dependent moiré potential directly from DFT calculations and construct an effective tight-binding model that reproduces both the band dispersion and the real-space localization of the electronic wave functions. Our results identify lattice relaxation as the key mechanism underlying 1D electronic states in 1D moiré superlattices. %and establish twisted bilayer WTe$_2$ as a promising platform for exploring emergent one-dimensional moiré physics. The framework developed here provides a unified theoretical basis for realizing and exploring one-dimensional moiré physics in a broad class of anisotropic two-dimensional materials.