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【摘要】

Beyond twisted bilayer graphene, Moiré flat bands can emerge in various engineered platforms. We propose a novel method for realizing flat band physics in monolayer graphene by using a modulation potential from substrates as a prototypical example. The periodic substrate potential manifests intervalley coupling that mimics Dirac cone coupling in twisted bilayer graphene. By adjusting the lattice constant of the periodic substrate, we can control this coupling, leading to the emergence of Moiré flat bands at certain "magic" lattice constants. Back to twisted bilayer systems, we present a systematic classification of topological nodes in base layers, focusing on their specific locations within the Brillouin zone. This enables us to identify the conditions under which flat bands are locked at zero energy, thereby elucidating the foundational physics behind band flatness and opening up new avenues for studying complex and enriched correlation physics.