Tuning gap in corrugated graphene with spin dependence

We study transmission in a system consisting of a curved graphene surface as an arc (ripple) of circle connected to two flat graphene sheets on the left and right sides. We introduce a mass term in the curved part and study the effect of a generated band gap in spectrum on transport properties for spin-up/-down. The tunneling analysis allows us to find all transmission and reflections channels in terms of the band gap. This later acts by decreasing the transmissions with spin-up/-down but increasing those with spin opposite, which exhibit different behaviors. We find resonances appearing in reflection with the same spin, thus backscattering with a spin-up/-down is not null in ripple. Some spatial shifts for the total conduction are observed in our model and the magnitudes of these shifts can be efficiently controlled by adjusting the band gap. This high order tunability of the tunneling effect can be used to design highly accurate devices based on graphene.