Title: Tuning Gap in Corrugated Graphene with Spin Dependence

Abstract: 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 modeled by the band gap. This later acts by decreasing the transmissions with spin-up/-down but increasing with spin opposite, which exhibit some behaviors look like bell-shaped curve. We find resonances appearing in reflection with the same spin, thus backscattering with a spin-up/-down is not null in ripple. We observe huge spatial shifts for the total conduction 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 devises based on graphene.