Assessing the role of interatomic position matrix elements in tight-binding calculations of optical properties
Julen Ibañez-Azpiroz, Fernando de Juan, Ivo Souza
Abstract
We study the role of hopping matrix elements of the position operator \hat{r} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mover> <mml:mi>r</mml:mi> <mml:mo accent="true">̂</mml:mo> </mml:mover> </mml:math> 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} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mover> <mml:mi>r</mml:mi> <mml:mo accent="true">̂</mml:mo> </mml:mover> </mml:math> 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} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mover> <mml:mi>r</mml:mi> <mml:mo accent="true">̂</mml:mo> </mml:mover> </mml:math> -hopping terms make a sizeable contribution to the shift photocurrent in monolayer BC _2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi/> <mml:mn>2</mml:mn> </mml:msub> </mml:math> N, a covalent acentric crystal. If a minimal basis of p_z <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>p</mml:mi> <mml:mi>z</mml:mi> </mml:msub> </mml:math> orbitals on the carbon atoms is used to model the band-edge response, even the dielectric function becomes strongly dependent on those terms.