Effect of a perpendicular magnetic field on bilayer graphene under dual gating

By studying the impact of a perpendicular magnetic field $B$ on AB-bilayer graphene (AB-BLG) under dual gating, we yield several key findings for the ballistic transport of gate $U_{\infty }$. Firstly, we discover that the presence of $B$ leads to a decrease in transmission. At a high value of $B$, we notice the occurrence of anti-Klein tunneling over a significant area. Secondly, in contrast to the results reported in the literature, where high peaks were found with an increasing in-plane pseudomagnetic field applied to AB-BLG, we find a decrease in conductivity as $B$ increases. However, it is worth noting that in both cases, the number of oscillations decreases compared to the result in the study where no magnetic field was present $(B=0)$. Thirdly, at the neutrality point, we demonstrate that the conductivity decreases and eventually reaches zero for a high value of $B$, which contrasts with the result that the conductivity remains unchanged regardless of the value taken by the in-plane field. Finally, we consider the diffusive transport with gate $U_{\infty }=0.2{\gamma }_1$ and observe two scenarios. The amplitude of conductivity oscillations increases with $B$ for energy $E$ less than $U_{\infty }$ but decreases in the opposite case $E>U_{\infty }$.