  Starting from the effective Hamiltonian arising from the tight binding model,
we study the behaviour of low-lying excitations for bilayer graphene placed in
periodic external magnetic fields by using irreducible second order
supersymmetry transformations. The coupled system of equations describing these
excitations is reduced to a pair of periodic Schr\"odinger Hamiltonians
intertwined by a second order differential operator. The direct implementation
of more general second-order supersymmetry transformations allows to create
nonsingular Schr\"odinger potentials with periodicity defects and bound states
embedded in the forbidden bands, which turn out to be associated to
quasiperiodic magnetic superlattices. Applications in quantum metamaterials
stem from the ability to engineer and control such bound states which could
lead to a fast development of the subject in the near future.
