Intervalley scattering of graphene massless Dirac fermions at 3-periodic grain boundaries

We study how low-energy charge carriers scatter off periodic and linear graphene grain boundaries oriented along the zigzag direction with a periodicity three times greater than that of pristine graphene. These defects map the two Dirac points into the same position, and thus allow for intervalley scattering to occur. Starting from graphene's first-neighbor tight-binding model we show how can we compute the boundary condition seen by graphene's massless Dirac fermions at such grain boundaries. We illustrate this procedure for the 3-periodic pentagon-only grain boundary, and then work out the low-energy electronic scattering off this linear defect. We also compute the effective generalized potential seen by the Dirac fermions at the grain boundary region.