Tunneling in a Rippled Graphene Superlattice with Spin Dependence and a Mass Term

The insertion of the band gap Delta in a rippled graphene superlattice leads to new outcomes, as demonstrated. The essential thing is the appearance of opposite-spin transmissions, which increases with Delta and vanishes without it. Furthermore, compared to the Delta=0$\Delta =0$ 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, it is demonstrated that with Delta, transmission filtering becomes crucial. Finally, as a result of the band gap, distinct variations in total conductance are discovered.