Magic-angle twisted bilayer graphene under orthogonal and in-plane magnetic fields

We investigate the effect of a magnetic field on the band structure of bilayer graphene with a magic twist angle of 1.08 ∘ . The coupling of a tight-binding model and the Peierls phase allows the calculation of the energy bands of periodic two-dimensional systems. For an orthogonal magnetic field, the Landau levels are dispersive, particularly for magnetic lengths comparable to or larger than the twisted bilayer cell size. A high in-plane magnetic field modifies the low-energy bands and gap, which we demonstrate to be a direct consequence of the minimal coupling.