Tunneling in rippled graphene superlattice with spin dependence and a mass term

The insertion of the band gap $\Delta$ in the rippled graphene superlattice leads to new outcomes, as demonstrated. The essential thing is the appearance of opposite-spin transmissions, which increase with $\Delta$ and vanish without it. Furthermore, compared to the $\Delta=0$ scenario, the duration of the suppression of the transmission with the same spin is longer, with many peaks. The maximum value of transmissions with the same spin declines and remains around unity. Furthermore, for particular energy values, a shift in the behavior of the transmission channels is found. As a result, we demonstrate that with $\Delta$, transmission filtering becomes crucial. Finally, as a result of the band gap, distinct variations in total conductance are discovered.