| Sumario: | We study the role of hopping matrix elements of the position operator ^r 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 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-hopping terms make a sizeable contribution to the shift photocurrent in monolayer BC2N, a covalent acentric crystal. If a minimal basis of pz orbitals on the carbon atoms is used to model the band-edge response, even the dielectric function becomes strongly dependent on those terms.
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