This research demonstrates that higher-order topological insulator (HOTI) phases in twisted bilayer graphene (TBG), characterized by localized corner states, appear as replicas of the original HOTIs, reflecting the self-similarity of the Hofstadter spectrum. The study establishes the existence of exact flux translational symmetry in TBG at all commensurate angles. Replica HOTIs, similar to original HOTIs, exhibit localized corner states and edge-localized real-space topological markers, stemming from the different interaction scales (intralayer and interlayer couplings) in TBG. This work highlights symmetry-protected topology in quantum fractals.

Sun-Woo Kim, Sunam Jeon, Moon Jip Park, Youngkuk Kim