Effect of parallel magnetic field on Klein tunneling in $pn$ and $pnp$ graphene trilayer junctions

Abstract

The effect of a parallel magnetic field $B$ and a potential substrate on the transmission, conductivity, and Fano factor of a biased ABC-stacked $pn$ and $pnp$ trilayer graphene junction (ABC-TLG) is investigated theoretically at low energy. We discovered that, in the presence of a high magnetic field $B=1400$T, the ABC-TLG can exhibit new Klein tunneling at two new incidence $k_y$ values, in addition to the usual value of $k_y=0$ and whatever the energy value is. Indeed, the transmission of ABC-TLG via $ pn $ and $ pnp $ junctions is transformed into a three-separate transmission of single-like graphene (SLG), with Klein tunneling appearing at $k_y=0$ and $k_y=\pm\kappa$ ($\kappa$ is highly dependent on $B$). Furthermore, the conductivity $\sigma$ and Fano factor $F$ behave similarly to SLG, with ABC-TLG having the lowest $\sigma=3g_0/\pi$ and highest $F=1/3$ at $B=1400$T and $\sigma_{\text{TLG}}=3\sigma_{\text{SLG}}$.