Assessing the role of interatomic position matrix elements in tight-binding calculations of optical properties

We study the role of hopping matrix elements of the position operator (r) over cap in tight-binding calculations of linear and nonlinear optical properties of solids. Our analysis relies on a Wannier-interpolation scheme based on ab initio calculations, which automatically includes matrix elements of (r) over cap between different Wannier orbitals. A common approximation, both in empirical tight-binding and in Wannier-interpolation calculations, is to discard those matrix elements, in which case the optical response only depends on the on-site energies, Hamiltonian hoppings, and orbital centers. We find that interatomic (r) over cap -hopping terms make a sizeable contribution to the shift photocurrent in monolayer BC2N, a covalent acentric crystal. If a minimal basis of p(z) orbitals on the carbon atoms is used to model the band-edge response, even the dielectric function becomes strongly dependent on those terms.