  We investigate the magnetic minibands of a heterostructure consisting of
bilayer graphene (BLG) and hexagonal boron nitride (hBN) by numerically
diagonalizing a two-band Hamiltonian that describes electrons in BLG in the
presence of a moire potential. Due to inversion-symmetry breaking
characteristic for the moire potential, the valley symmetry of the spectrum is
broken, but despite this, the zero-energy Landau level in BLG survives, albeit
with reduced degeneracy. In addition, we derive effective models for the
low-energy features in the magnetic minibands and demonstrate the appearance of
secondary Dirac points in the valence band, which we confirm by numerical
simulations. Then, we analyze how single-particle gaps in the fractal energy
spectrum produce a sequence of incompressible states observable under a
variation of carrier density and magnetic field.
