An abstract formulation of the flat band condition

2023/07/10 by Jeffrey Galkowski, Galkowski, Jeffrey, Maciej Zworski +1 · 1 citation
Engineering · Materials Science · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Graphene research and applications #Mathematical Physics (math-ph) #Molecular Junctions and Nanostructures #Quantum and electron transport phenomena #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.2307.04896

openalex publication_date 2023/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Motivated by the study of flat bands in models of twisted bilayer graphene (TBG), we give abstract conditions which guarantee the existence of a discrete set of parameters for which periodic Hamiltonians exhibit flat bands. As an application, we show that a scalar operator derived from the chiral model of TBG has flat bands for a discrete set of parameters.

Cited by

• Flat bands, Dirac cones, and higher-order band crossings in twisted multilayer graphene

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