Second Harmonic Generation Susceptibilities from Symmetry Adapted Wannier Functions

Elucidating the orbital level origin of second harmonic generation (SHG) in materials and identifying the local contributions is a long-standing challenge. We report a first principles approach for the SHG where the contributions from individual orbitals or atoms can be evaluated via symmetry adapted Wannier functions without semiempirical parameters. We apply this method to the common SHG materials ${\mathrm{KBe}}_{2}{\mathrm{BO}}_{3}{\mathrm{F}}_{2}$, ${\mathrm{KCaCO}}_{3}\mathrm{F}$, and $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{BaB}}_{2}{\mathrm{O}}_{4}$, and show that the orbitals on noncentrosymmetric sublattices are responsible for SHG effect and the energies of these orbitals control the magnitude.