Hidden Wave Function of Twisted Bilayer Graphene: Flat Band as a Landau Level

Abstract

We study the chirally symmetric continuum model (CS-CM) of the twisted bilayer graphene. The equation on a flat band could be interpreted as a Dirac equation on a torus in the external non-abelian magnetic field. We prove that the existence of the flat band implies that the wave-function has a zero and vice verse. We found a hidden solution in the CS-CM model 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 Landau level in the external magnetic field. From that interpretation we show the existence of extra flat bands in the magnetic field.