Quantum Geometry of Moiré Flat Bands Beyond the Valley Paradigm
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Abstract: Moiré superlattices provide platforms for strongly correlated and topological phenomena governed by quantum geometry. The prevailing ``valley paradigm''---which relies on well-defined valley structures at high-symmetry Brillouin zone points---successfully describes systems like twisted bilayer graphene and transition metal dichalcogenides, but fails for materials lacking valley degrees of freedom. Here, we establish a general framework for engineering flat-band quantum geometry in twisted bipartite heterobilayers through sublattice-selective interlayer tunneling. Using twisted graphene-on-dice heterobilayers as a prototype, we demonstrate that preserving bipartiteness while hybridizing layers produces isolated, zero-energy flat bands with twist-angle-tunable multiplicity and Chern-insulator-scale Berry curvature. Crucially, these bands exhibit finite quantum metric arising from controlled interlayer hybridization rather than valley physics. Our results provide a systematic route to quantum geometry engineering in moiré systems beyond existing paradigms, with realizations in oxide heterostructures, molecular lattices, and synthetic quantum matter.