Spin transport in a rippled graphene periodic chain

We discuss the solution of the scattering problem of ballistic electrons on the finite periodic chain. Each element of this chain is composed of a combination of a planar and rippled graphene elements. The analysis is carried out in the effective mass approximation when only the interaction between nearest neighbour atoms is taken into account. We find that, with the increase of number of elements, the chain becomes more transparent for electrons with spin up travelling in one direction and for electrons with spin down travelling in the opposite direction.