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Fine structure of flat bands in a chiral model of magic angles

Mathematical Physics 2023-06-02 v2 Materials Science Strongly Correlated Electrons math.MP Spectral Theory Quantum Physics

Abstract

We analyze symmetries of Bloch eigenfunctions at magic angles for the Tarnopolsky--Kruchkov--Vishwanath chiral model of the twisted bilayer graphene (TBG) following the framework introduced by Becker--Embree--Wittsten--Zworski. We show that vanishing of the first Bloch eigenvalue away from the Dirac points implies its vanishing at all momenta, that is the existence of a flat band. We also show how the multiplicity of the flat band is related to the nodal set of the Bloch eigenfunctions. We conclude with two numerical observations about the structure of flat bands.

Keywords

Cite

@article{arxiv.2208.01628,
  title  = {Fine structure of flat bands in a chiral model of magic angles},
  author = {Simon Becker and Tristan Humbert and Maciej Zworski},
  journal= {arXiv preprint arXiv:2208.01628},
  year   = {2023}
}