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.
Download
PDF:
LaTeX source:
- tarball: 25jm-0.0.tar.gz
- git repository: 25jm-git (the git repository contains detailed information about the changes in the paper as well as the source code for all previous versions).
Other releases
- arXiv preprint: arXiv:2510.12918.
Talks
This work has been presented at the following conferences:
-
[Pr25]: A framework to study twisted bilayer graphene in a tight binding model
Princeton University, New Jersey, USA, Oct 21 2025
pdf -
[BenMem25]: A Renormalization Group based framework to study twisted bilayer graphene
A Tribute to Giosi Benfatto, University of Roma Tre, Italy, Sep 18 2025
pdf