Critical filaments and superconductivity in quasiperiodic twisted bilayer graphene

Xinghai Zhang; Justin H. Wilson; Matthew S. Foster

doi:10.1103/PhysRevB.111.024207

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Critical filaments and superconductivity in quasiperiodic twisted bilayer graphene

Xinghai Zhang, Justin H. Wilson, Matthew S. Foster

DOI 10.1103/PhysRevB.111.024207 · Physical Review B

T1

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Abstract

Multilayer moiré 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 moiré 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.