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

TL;DR

This paper investigates how interatomic position matrix elements influence the calculation of optical properties in solids using tight-binding methods, revealing their significant impact on shift photocurrent and dielectric response.

Contribution

It demonstrates that including interatomic position matrix elements in tight-binding calculations significantly affects optical property predictions, especially in covalent acentric crystals.

Findings

Interatomic position matrix elements significantly affect shift photocurrent in BC₂N.

Dielectric function calculations are strongly dependent on these matrix elements with minimal basis.

Neglecting these elements can lead to inaccurate optical property predictions.

Abstract

We study the role of hopping matrix elements of the position operator $\mathbf{\hat{r}}$ 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 $\mathbf{\hat{r}}$ 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 $\mathbf{\hat{r}}$-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.