Effect of a nonuniform magnetic field on the Landau states in a biased AA-stacked graphene bilayer

We study the Landau states in the biased AA-stacked graphene bilayer under an exponentially decaying magnetic field along one spatial dimension. The results show that the energy eigenvalues of the system are strongly dependent on the inhomogeneity of the magnetic field and the bias voltage between the graphene layers, and in particular the reordering and mixing of finite Landau states could occur. Moreover, we also demonstrate that the current carrying states induced by the decaying magnetic field propagate vertically to the magnetic-field gradient within the graphene sample and can be further modulated by the bias voltage between the layers.