Multilayer moir\'e materials can exhibit topological electronic features yet are inherently quasiperiodic -- leading to wave function interference whose Anderson-localizing tendency can be mitigated by topology. We consider a quasiperiodic variant of the chiral Bistritzer-MacDonald model for twisted bilayer graphene with two incommensurate moir\'e potentials that serves as a toy model for twisted trilayer. We observe "filaments" linking magic angles with enhanced density of states and fractal wave functions that evade localization; states away from the filaments mimic fractal surface states of dirty topological superconductors. We demonstrate that topological quasiperiodicity can broadly enhance superconductivity without magic-angle fine-tuning.
Categories: cond-mat.mes-hall cond-mat.dis-nn cond-mat.supr-con