Twisted bilayer graphene: A new perspective of the Bistritzer-MacDonald model and th rise of itinerancy

The Bistritzer-MacDonald (BM) model predicted the existence of the narrow bands in the twisted bilayer graphene (TBG), and nowadays is a starting point for most theoretical works. In this talk, this model with Coulomb interactions will be reviewed from a rather different perspective. We treat this model as an effective field theory defined at atomic energy scale and find that the theory flows toward a fixed point in which the bands are exactly flat [1]. Additionally, our theory explains the consistency of the magic angle between the theoretical value and the experimentally discovered one. With the Hamiltonian obtained, we further derived the exact excitation spectrum in the strong coupling limit at the even integer fillings [1]. Combined with the variational method, we studied the Landau fan, the electron mass measured by quantum oscillations, and the recently discovered cascade transitions near the integer fillings [2]. Our results not only qualitatively agree with the measurements, but also reveal the emergence of the Fermi liquid at the fractional fillings.1. Oskar Vafek and Jian Kang, Phys. Rev. Lett, 122, 257602 (2020).2. Jian Kang, B. Andrei Bernevig, and Oskar Vafek, arXiv:2104.01145.