Takuto Kawakami

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.