Abstract
We study the role of hopping matrix elements of the position operator \hat{r}r̂ in tight-binding calculations of linear and nonlinear optical properties of solids. Our analysis relies on a Wannier-interpolation scheme based on calculations, which automatically includes matrix elements of \hat{r}r̂ 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{r}r̂-hopping terms make a sizeable contribution to the shift photocurrent in monolayer BC_22N, a covalent acentric crystal. If a minimal basis of p_zpz orbitals on the carbon atoms is used to model the band-edge response, even the dielectric function becomes strongly dependent on those terms.
Highlights
After the ab initio total-energy calculation, we construct in a post-processing step a set of welllocalized Wannier functions (WFs)
The largest corrections to the σy y x matrix element again come from 2nd nearest neighbors (NNs) rhoppings, as expected from Figs. 5(b,c)
Consistent with the preceeding analysis, those corrections are fairly minor for εx x, but they are significant for σy x x in the band-edge region, where rhoppings up to 2nd NN have a sizeable impact on the computed spectrum
Summary
Empirical tight-binding (TB) is the method of choice for obtaining a simple and intuitive description of the electronic structure of solids [1]. Where τm is the center of the mth Wannier orbital in the home cell This minimal spatial embedding of a TB model already allows to incorporate electromagnetic fields in a gaugeinvariant manner [2]. After performing an ab initio calculation of the electronic structure, we construct, in a postprocessing step, well-localized WFs spanning the relevant bands We take those WFs and use them as an orthogonal TB basis to evaluate the band structure and the optical matrix elements. The optical responses analyzed in this work are the dielectric function and the shift photoconductivity The latter is a quadratic response associated with a shift in the center of mass of an electron as it is optically excited from a valence band to a conduction band in a piezoelectric crystal [12–14], and is known to be quite sensitive to the spatial embedding of the TB model [15, 16].
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