Moiré Structures Beyond Small Twist Angles

Twisted moiré bilayers at small twist angles have defined the paradigm for flat bands and correlated topological phases. In this talk, I shift the focus to the less-charted territory of moiré structures formed at large twist angles where commensurability occurs only accidentally at discreate angles. Using twisted WSe₂ as a model system, at 30°, we realize a dodecagonal moiré quasicrystal that lacks translational symmetry. Valley-resolved scanning tunneling spectroscopy visualizes dense quasi-minigaps arising from strong interlayer Umklapp scattering. Moving to the twist angles near but deviate from large commensurate angles (e.g. 21.8˚ and 27.8˚), instead of forming incommensurate moiré structure, the lattice reconstructs into a periodic super-moiré comprising three inequivalent commensurate rotational faults. The resulting zone-folding produces a cascade of minibands, including narrow bands near the valence-band maximum. Together, these results extend moiré physics well beyond the small-angle paradigm and open routes to engineered correlated and topological phases without relying on magic-angle conditions.