Chen, Xi and Wallbank, John and Mucha-Kruczynski, Marcin and McCann, Edward and Falko, Vladimir (2016) Zero-energy modes and valley asymmetry in the Hofstadter spectrum of bilayer graphene van der Waals heterostructures with hBN. Physical review B, 94 (4). ISSN 1098-0121
Hofstadter_spectrum_of_BLG_author_accepted.pdf - Accepted Version
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Abstract
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 moiré potential. Due to inversion-symmetry breaking characteristic for the moiré 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.