Electronic band structure of magnetic bilayer graphene superlattices

Electronic band structure of the bilayer graphene superlattices with δ-function magnetic barriers and zero average magnetic flux is studied within the four-band continuum model, using the transfer matrix method. The periodic magnetic potential effects on the zero-energy touching point between the lowest conduction and the highest valence minibands of pristine bilayer graphene are exactly analyzed. Magnetic potential is shown also to generate the finite-energy touching points between higher minibands at the edges of Brillouin zone. The positions of these points and the related dispersions are determined in the case of symmetric potentials.