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

Abstract

We investigate electron tunneling in AB bilayer graphene through a triple electrostatic barrier of heights Ui(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 U4 in in the case of U2<U4. However, when U2>U4, anti-Klein tunneling increases with U2. The transmission probability exhibits an interesting oscillatory behavior when U3>U2=U4 and U3<U2=U4. For fixed energy E=0.39γ1, increasing barrier widths increases the number of oscillations and decreases Klein tunneling. The interlayer bias creates a gap for U2<U3<U4 and U3>U2=U4. 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 Gtot 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.