Direct observation of moiré flat-band breakdown at the edge of magic-angle twisted bilayer graphene

Abstract: Low-energy moir\'e flat bands in magic-angle twisted bilayer graphene (tBG) have demonstrated incredible potentials to exhibit rich exotic quantum phenomena. Theoretically, the moir\'e flat bands of tBG are based on the extended structures, i.e., the moir\'e patterns with periodic boundary conditions. However, a fundamental question of whether the flat bands can exist in the graphene moir\'e patterns with a reduced structure symmetry, such as sample edges, remains unanswered. Here, via scanning tunneling microscopy and spectroscopy, we study the local electronic properties of a magic-angle tBG near the sample terminated edge and report a direct observation of breakdown of the moir\'e flat bands. We show that the moir\'e electronic structures, including the low-energy flat bands, can sufficiently exist in a complete moir\'e spot, i.e., a moir\'e supercell, right at the edge even the translational symmetry of the moir\'e patterns is broken in one direction. However, the flat-band characteristic is obviously absent in the incomplete moir\'e spots that are partly terminated by the edge. Our results indicate that a whole moir\'e spot is sufficient and indispensable for the generation of the effective moir\'e flat bands in tBG.