Tunneling in ABC trilayer graphene superlattice

We study the transport properties of Dirac fermions in ABC trilayer graphene (ABC-TLG) superlattices. More specifically, we analyze the impact of varying the physical parameters -- the number of cells, barrier/well width, and barrier heights -- on electron tunneling in the ABC-TLG. In the initial stage, we solved the eigenvalue equation to determine the energy spectrum solutions for the ABC-TLG superlattices. Subsequently, we applied boundary conditions to the eigenspinors and employed the transfer matrix method to calculate transmission probabilities and conductance. For the two-band model, we identified the presence of Klein tunneling, with a notable decrease as the number of cells increased. The introduction of interlayer bias opened a gap as the number of cells increased, accompanied by an asymmetry in scattered transmission. Increasing the barrier/well width and the number of cells resulted in an amplified number of gaps and oscillations in both two-band and six-band cases. We observed a corresponding decrease in conductance as the number of cells increased, coinciding with the occurrence of a gap region. Our study demonstrates that manipulating parameters such as the number of cells, the width of the barrier/well, and the barrier heights provides a means of controlling electron tunneling and the occurrence of gaps in ABC-TLG. Specifically, the interplay between interlayer bias and the number of cells is identified as a crucial factor influencing gap formation and transmission asymmetry.