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Electrostatic and Magnetic Fields in Bilayer Graphene

We compute the transmission probability through rectangular potential barriers and p-n junctions in the presence of a magnetic and electric fields in bilayer graphene taking into account contributions from the full four bands of the energy spectrum. For energy $E$ higher than the interlayer coupling $γ_1$ ($E > γ_1$) two propagation modes are available for transport giving rise to four possible ways for transmission and reflection coefficients. However, when the energy is less than the height of the barrier the Dirac fermions exhibit transmission resonances and only one mode of propagation is available for transport. We study the effect of the interlayer electrostatic potential denoted by $δ$ and variations of different barrier geometry parameters on the transmission probability.