Coulomb scattering of Weyl fermions through a potential barrier

We investigate the effects of the Coulomb interaction on the two-dimensional relativistic quantum-mechanical scattering of two Weyl fermions, injected on the opposite sides of a potential barrier. We consider the Coulomb interaction in the standard two-body problem and evaluate the corresponding scattering amplitude. We apply our formalism to describe the scattering of Weyl fermions in two-dimensional materials exhibiting Dirac cones, such as graphene and the surface of 3d topological insulators. We obtain a complex shape for the scattering amplitude due to the angle-dependent Klein tunneling through a potential barrier. We show that the Coulomb interaction leads to shifts and broadenings of the transmission peaks. .