Long-range scattering theory for discrete Schrödinger operators on graphene

We consider a long-range scattering theory for discrete Schrödinger operators on the hexagonal lattice, which describe tight-binding Hamiltonians on the graphene sheet. We construct Isozaki-Kitada modifiers for a pair of the difference Laplacian on the hexagonal lattice and perturbed operators with long-range potentials. We prove that these modified wave operators exist and that they are complete.