Transport Properties in Gapped Bilayer Graphene

We investigate transport properties through a rectangular potential barrier in AB-stacked bilayer graphene (AB-BLG) gapped by dielectric layers. Using the Dirac-like Hamiltonian with a transfer matrix approach we obtain transmission and reflection probabilities as well as the associated conductance. For two-band model and at normal incidence, we find extra resonances appearing in transmission compared to biased AB-BLG, which are Fabry-P\'erot resonance type. Now by taking into account the inter-layer bias, we show that both of transmission and anti-Klein tunneling are diminished. Regarding four band model, we find that the gap suppresses transmission in an energy range by showing some behaviors look like "Mexican hats". We examine the total conductance and show that it is affected by the gap compared to AA-stacked bilayer graphene. In addition, we find that the suppression in conductance is more important than that for biased AB-BLG.