Magnetic field effect on tunneling through triple barrier in AB bilayer graphene

We investigate electron tunneling in AB bilayer graphene through a triple electrostatic barrier of heights $U_i (i=2,3,4)$ subjected to a perpendicular magnetic field. By way of the transfer matrix method and using the continuity conditions at the different interfaces, the transmission probability is determined. Additional resonances appear for two-band tunneling at normal incidence, and their number is proportional to the value of $U_4$ in the case of $U_2<U_4$. However, when $U_2>U_4$, anti-Klein tunneling increases with $U_2$. The transmission probability exhibits an interesting oscillatory behavior when $U_3>U_2=U_4$ and $U_3 <U_2=U_4$. For fixed energy $E=0.39\gamma_1$, increasing barrier widths increases the number of oscillations and decreases Klein tunneling. The interlayer bias creates a gap for $U_2<U_3<U_4$ and $U_3>U_2=U_4$. In the four-band tunneling case, the transmission decreases in $T^+_+$, $T^-_+$ and $T^-_-$ channels in comparison with the single barrier case. It does, however, increase for $T^+_-$ when compared to the single barrier case. Transmission is suppressed in the gap region when an interlayer bias is introduced. This is reflected in the total conductance $G_{\text{tot}}$ in the region of zero conductance. Our results are relevant for electron confinement in AB bilayer graphene and for the development of graphene-based transistors.