We investigate the electronic properties of bilayer Bernal graphene subject to the influence of a spatially modulated magnetic field by using the Peierls tight-binding method. The energy dispersion has many oscillatory parabolic subbands, which are left-right asymmetric and exhibit composite degeneracy. The density of states displays many asymmetric square-root divergent peaks originating from the oscillatory parabolic subbands. These electronic properties are strongly dependent on the strength and period of the field. The evolution of the density of states peak with the field strength and period is explored. The principal peaks first show linear, then square-root dependence on the field strength. These predictions can be validated by measuring the spectra of STS or performing magneto transmission experiments.
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