Work

Fine Structure of Flat Bands in a Chiral Model of Magic Angles

Year: 2024

Type: article

Abstract: We analyse 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.

Source: Annales Henri Poincaré

DOI: 10.1007/s00023-024-01478-3

Authors: Simon Becker, Tristan Humbert, Maciej Zworski

Institutions: ETH Zurich, Institute for Mathematical Research, University of California, Berkeley

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funders: National Science Foundation, Simons Foundation, Directorate for Mathematical and Physical Sciences