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arXiv · 2406.06676

Critical Filaments and Superconductivity in Quasiperiodic Twisted Bilayer Graphene

Xinghai Zhang·Justin H. Wilson·Matthew S. Foster
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Abstract

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.

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Xinghai Zhang, Justin H. Wilson, Matthew S. Foster. 2024-06-10. Critical Filaments and Superconductivity in Quasiperiodic Twisted Bilayer Graphene. https://doi.org/10.1103/physrevb.111.024207

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