We analyze spin scattering in ballistic transport of electrons through a ripple at a normal incidence of an electron flow. The model of a ripple consists of a curved graphene surface in the form of an arc of a circle connected from the left-hand and right-hand sides to two flat graphene sheets. At certain conditions the curvature-induced spin-orbit coupling creates a transparent window for incoming electrons with one spin polarization simultaneously with a backscattering of those with opposite polarization. This window is equally likely transparent for electrons with spin up and spin down that move in opposite directions. The spin-filtering effect that is small in one ripple becomes prominent with the increase of $N$ consequently connected ripples that create a graphene sheet of the sinusoidal type. We present the analytical expressions for spin-up and spin-down transmission probabilities as a function of $N$ connected ripples.

• Received 17 June 2015
• Revised 28 September 2015

DOI:https://doi.org/10.1103/PhysRevB.92.205432