Low-energy quantum scattering induced by graphene ripples

• We explore the quantum study on the scattering process induced by graphene ripple.
• The Hamiltonian for general ripple is constructed.
• The Born approximation in ripple-inducing scattering shows an opposite validity compared to ordinary scattering.
• The factor cosθ/2 leads to an absence of backward scattering for polar symmetry ripple.
• The scattering cross sections depend on the cubed amount of incident carrier energy.

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⁡θ/2cos⁡θ/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.