Incommensurate Twisted Bilayer Graphene: emerging quasi-periodicity and stability
Ian Jauslin, Vieri Mastropietro
2025
Abstract
We consider a lattice model of Twisted Bilayer Graphene (TBG). The presence of incommensurate angles produces an emerging quasi-periodicity manifesting itself in large momenta Umklapp interactions that almost connect the Dirac points. We rigorously establish the stability of the semimetallic phase via a Renormalization Group analysis combined with number theoretical properties of irrationals, similar to the ones used in Kolmogorov-Arnold-Moser (KAM) theory for the stability of invariant tori. The interlayer hopping is weak and short ranged and the angles are chosen in a large measure set. The result provides a justification, in the above regime, to the effective continuum description of TBG in which large momenta interlayer interactions are neglected.
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Talks
This work has been presented at the following conferences:
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[BenMem25]: A Renormalization Group based framework to study twisted bilayer graphene
A Tribute to Giosi Benfatto, University of Roma Tre, Italy, Sep 18 2025
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