Speaker
Description
Moiré engineering has moved from a few canonical systems to a rapidly expanding materials space, but this expansion raises a basic question: given a parent monolayer, what low-energy quantum model will its moiré bands realize? We address this question by developing a valley–orbital–symmetry framework and applying it to more than 600 fully relaxed, commensurate twisted bilayers spanning four 2D lattice classes. By combining first-principles electronic structure, band unfolding, orbital analysis, and elementary band-representation analysis, we go beyond identifying narrow bands and determine the effective degrees of freedom and symmetry content of the low-energy manifolds. We find a broad hierarchy of emergent moiré models, including single- and multi-orbital triangular, honeycomb, square, checkerboard, and kagome-like Hubbard systems. We further identify symmetry-driven topological and nonsymmorphic semimetallic bands, quasi-one-dimensional flat bands associated with boundary valleys, and coupled multi-valley manifolds originating from generic-momentum band edges. These results reveal that the momentum-space location and orbital character of the parent band edge, together with moiré symmetry, provide a systematic route from microscopic materials to emergent Hamiltonians.