Hidden wave function of twisted bilayer graphene: The flat band as a Landau level
Fedor K. Popov, Alexey Milekhin
Abstract
We study zero-energy states of the chirally symmetric continuum model (CS-CM) of twisted bilayer graphene. The zero-energy state obeys the Dirac equation on a torus in the external non-Abelian magnetic field. These zero-energy states could form a flat band---a band where the energy is constant across the Brillouin zone. We prove that the existence of the flat band implies that the wave function of any state from the flat band has a zero and vice versa. We found a hidden flat band of unphysical states in the CS-CM that has a pole instead of a zero. Our main result is that in the basis of the flat band and hidden wave functions the flat band could be interpreted as a Landau level in the external magnetic field. From that interpretation we show the existence of extra flat bands in the magnetic field.