Flat bands, quantum Hall effect and superconductivity in twisted bilayer graphene at magic angles (10 pages)

• L.A. Navarro-Labastida ^[1] ; G.G. Naumis ^[1]
  1. [1] Universidad Nacional Autónoma de México

     Universidad Nacional Autónoma de México

     México

     
• Localización: Revista Mexicana de Física, ISSN-e 0035-001X, Vol. 69, Nº. 4, 2023
• Idioma: inglés
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• Resumen

  • Flat band electronic modes are responsible for superconductivity in twisted bilayer graphene rotated at magic angles. From there other magic angles can be found for any multilayered twisted graphene systems. Eventually this lead to the discovery of the highest ever known electron-electron correlated material. Moreover, the quantum phase diagram of twisted bilayer graphene is akin to those observed among high-T_(c) superconductors and thus there is a huge research effort to understand twisted bilayer graphene in the hope of clarifying the physics behind such strong correlations. A particularity of the twisted bilayer graphene is the coexistence of superconductivity and the fractional Quantum Hall effect, yet this relationship is not understood. In this work, a simple 2 × 2 matrix model for twisted bilayer graphene is obtained by taking the square of the original 4 × 4 chiral twisted bilayer graphene hamiltonian. Such squared Hamiltonian contains the magic angles and due to the intrinsic chiral symmetry in twisted bilayer graphene, a lowest energy level related to the quantum Hall effect. The non-Abelian properties of this squared Hamiltonian play a central role in the electronic localization to produce the flat bands and here it is proved that the squared Hamiltonian of the chiral TBG model is equivalent to a single electron Hamiltonian inside of a non-Abelian pseudo-magnetic field produced by electrons in other layers. Therefore, the basic and fundamental elements in the physics of magic angles are determined. In particular, an study is made on these fundamental energy contributions at theΓ-point due to its relation to the recurrence of magic angles and its relationship with the Quantum Hall effect.