SciPost Physics

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

Julen Ibañez-Azpiroz, Fernando de Juan, Ivo Souza

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

• doi: 10.21468/SciPostPhys.12.2.070
• pdf
• BiBTeX
• RIS
• Submissions/Reports
• 

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.

• Esteve-Paredes et al., A comprehensive study of the velocity, momentum and position matrix elements for Bloch states: Application to a local orbital basis
  SciPost Phys. Core 6, 002 (2023) [Crossref]
• Murakami et al., Doping and gap size dependence of high-harmonic generation in graphene: Importance of consistent formulation of light-matter coupling
  Phys. Rev. B 106, 035204 (2022) [Crossref]
• Wu et al., Multiscale numerical tool for studying nonlinear dynamics in solids induced by strong laser pulses
  Phys. Rev. E 105, 055306 (2022) [Crossref]
• Garcia-Goiricelaya et al., Including many-body effects into the Wannier-interpolated quadratic photoresponse tensor
  Phys. Rev. B 107, 205101 (2023) [Crossref]
• Gu et al., Full-Brillouin-zone calculation of high-order harmonic generation from solid-state media
  Phys. Rev. A 106, 063516 (2022) [Crossref]