Symmetries as the Guiding Principle for Flattening Bands of Dirac Fermions

Abstract

Since the discovery of magic-angle twisted bilayer graphene, flat bands in Dirac materials have become a prominent platform for realizing strong correlation effects in electronic systems. Here we show that the symmetry group protecting the Dirac cone in such materials determines whether a Dirac band may be flattened by the tuning of a small number of parameters. We devise a criterion that, given a symmetry group, allows for the calculation of the number of parameters required to make the Dirac velocity vanish. This criterion is employed to study band flattening in twisted bilayer graphene and in surface states of 3D topological insulators. Following this discussion, we identify the symmetries under which the vanishing of the Dirac velocity implies the emergence of perfectly flat bands. Our analysis allows us to construct additional model Hamiltonians that display perfectly flat bands at certain points in the space of parameters: the first is a toy model of two coupled 3D topological insulator surfaces, and the second is a quasicrystalline generalization of the chiral model of twisted bilayer graphene.6 MoreReceived 11 June 2022Revised 6 March 2023Accepted 27 March 2023DOI:https://doi.org/10.1103/PhysRevX.13.021012Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasElectronic structurePhysical SystemsStrongly correlated systemsTopological insulatorsTopological materialsTwisted bilayer grapheneCondensed Matter, Materials & Applied Physics