Spin-dependent transmission in curved graphene superlattice

We investigate spin-dependent transmission in a curved graphene superlattice of $N$ cells where each one is made up of four regions. The first is concave, and the third is convex, two arcs of circles separated by a distance $d$ from flat graphene sheets. The tunneling analysis allows us to determine all transmission and reflection channels associated with our system. As a result, we show that the number of cells acts by decreasing the transmissions with the same spin. We predict a solid spin-filtering effect when $d$ and $N$ are sufficiently large. Finally, it is determined that the degree and duration of suppression of the transmissions with the same spin over a range of energy are controllable using $d$.