SciPost Physics

SciPost Phys. 12, 070 (2022) · published 22 February 2022

• doi: 10.21468/SciPostPhys.12.2.070
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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 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.

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