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

Abstract

We study the role of hopping matrix elements of the position operator $\hat{\mathbf{r}}$ in tight-binding calculations of linear and nonlinear optical properties of solids. Our analysis relies on a Wannier-interpolation scheme based on \textit{ab initio} calculations, which automatically includes matrix elements of $\hat{\mathbf{r}}$ 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 $\hat{\mathbf{r}}$-hopping terms make a sizeable contribution to the shift photocurrent in monolayer BC${}_2$N, 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.

19 pages, 9 figures

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