  We formulate a low energy effective Hamiltonian to study superlattices in
bilayer graphene (BLG) using a minimal model which supports quadratic band
touching points. We show that a one dimensional (1D) periodic modulation of the
chemical potential or the electric field perpendicular to the layers leads to
the generation of zero energy anisotropic massless Dirac fermions and finite
energy Dirac points with tunable velocities. The electric field superlattice
maps onto a coupled chain model comprised of 'topological' edge modes. 2D
superlattice modulations are shown to lead to gaps on the mini-Brillouin zone
boundary but do not, for certain symmetries, gap out the quadratic band
touching point. Such potential variations, induced by impurities and rippling
in biased BLG, could lead to subgap modes which are argued to be relevant to
understanding transport measurements.
