Critical Filaments and Superconductivity in Quasiperiodic Twisted Bilayer Graphene

TL;DR

This paper explores how topological quasiperiodicity in twisted bilayer graphene can create filamentary states that enhance superconductivity, potentially broadening the conditions for superconductivity beyond magic angles.

Contribution

It introduces a quasiperiodic model for twisted bilayer graphene showing filamentary states linked to enhanced density of states and demonstrates broad superconductivity enhancement without fine-tuning.

Findings

Filaments link magic angles with high density of states.

Fractal wave functions evade localization.

Superconductivity is broadly enhanced by quasiperiodicity.

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.