Low-energy quantum scattering induced by graphene ripples

We report a quantum study of the carrier scattering induced by graphene ripples. Crucial differences between the scattering induced by the ripple and ordinary scattering were found. In contrast to the latter, in which the Born approximation is valid for high-energy process, the former is valid for the low-energy process with a quite broad energy range. Furthermore, in polar symmetry ripples, the scattering amplitude exhibits a pseudo-spin structure, an additional factor $\cos \theta \mathrm{/}2$, which leads to an absence of backward scattering. We also elucidate that the scattering cross sections are proportional to the energy cubed of the incident carrier.