Perturbative second-order optical susceptibility of bulk materials: a symmetry-enforced return to non-orthogonal localized basis sets

TL;DR

This paper introduces a new method for calculating the second-order optical susceptibility of bulk materials using localized pseudoatomic orbitals within perturbation theory, emphasizing symmetry and two-center integrals.

Contribution

It presents a novel approach relying on numerical pseudoatomic orbitals and symmetry-enforced two-center integrals for calculating second-order optical susceptibilities.

Findings

Successfully tested on cubic silicon carbide and gallium arsenide.

Demonstrates compatibility with symmetry considerations in localized basis sets.

Provides an alternative to plane-wave and Wannier-based methods.

Abstract

The second-order optical susceptibility of semiconductors $\chi_{ijk}^{(2)}(-2\omega;\omega,\omega)$ finds application in metrology, spectroscopy, telecommunications, material characterization, and quantum information. Pioneering calculations of $\chi_{ijk}^{(2)}(-2\omega;\omega,\omega)$ utilized non-orthogonal Gaussian orbitals centered at atoms. That formulation transitioned into plane-wave-based algorithms as time went by. As of late, nevertheless, multiple tools for calculating optical susceptibilities have recast the problem using Wannier ({\em i.e.}, {\em localized}) orbitals, making a comeback onto frameworks based on localized basis sets. Here, we present an approach for calculating $\chi_{ijk}^{(2)}(-2\omega;\omega,\omega)$ reliant on numerical pseudoatomic orbitals (PAOs) within perturbation theory in the velocity gauge. Its salient feature is a calculation of `Slater-Koster-like' two-center integrals of the momentum operator in between PAOs identified by symmetry. The approach was successfully tested on paradigmatic cubic silicon carbide (3C-SiC) and gallium arsenide, for which linear responses are contributed as well.