Double Barriers and Magnetic Field in Bilayer Graphene

We study the transmission probability in an AB-stacked bilayer graphene of Dirac fermions scattered by a double-barrier structure in the presence of a magnetic field. We take into account the full four bands structure of the energy spectrum and use the suitable boundary conditions to determine the transmission probability. Our numerical results show that for energies higher than the interlayer coupling, four ways for transmission are possible while for energies less than the height of the barrier, Dirac fermions exhibit transmission resonances and only one transmission channel is available. We show that, for AB-stacked bilayer graphene, there is no Klein tunneling at normal incidence. We find that the transmission displays sharp peaks inside the transmission gap around the Dirac point within the barrier regions while they are absent around the Dirac point in the well region. The effect of the magnetic field, interlayer electrostatic potential, and various barrier geometry parameters on the transmission probabilities is also discussed.