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We investigate the magnetic minibands of a heterostructure consisting ofbilayer graphene (BLG) and hexagonal boron nitride (hBN) by numericallydiagonalizing a two-band Hamiltonian that describes electrons in BLG in thepresence of a moire potential. Due to inversion-symmetry breakingcharacteristic for the moire potential, the valley symmetry of the spectrum isbroken, but despite this, the zero-energy Landau level in BLG survives, albeitwith reduced degeneracy. In addition, we derive effective models for thelow-energy features in the magnetic minibands and demonstrate the appearance ofsecondary Dirac points in the valence band, which we confirm by numericalsimulations. Then, we analyze how single-particle gaps in the fractal energyspectrum produce a sequence of incompressible states observable under avariation of carrier density and magnetic field.

Zero-energy modes and valley asymmetry in the Hofstadter spectrum of bilayer graphene van der Waals heterostructures with hBN