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We fully implement the Aversa and Sipe sum-over-states formulism and make afull ab initio band structure analysis of interband and intraband contributionsfor the third-order nonlinear optical susceptibilities of bulk silicon. Theband structure and momentum matrix elements were calculated by using the highlyaccurate all-electron full potential linearized augmented plane wave methodwithin the local density approximation. The convergence tests including thescissor correction with different k-points meshes and empty states wereperformed. Both real and imaginary parts of susceptibility were directlycalculated and checked by the Kramers-Kronig relation. The converged resultsare compared with other theoretical and experimental ones and in agreement withthe recent ab initio real-time-based calculation. The nonlinear opticalcoefficient comes from three parts: the pure interband contribution (Pinter),the modulation of interband terms by intraband terms (Pmod), and the intrabandcontribution (Jintra). For each part, the origin of enhanced peaks is exploredby tracing the sum-over-states process. The interband contribution is found tobe dramatically modulated by the intraband contribution.

computational condensed matter

Full ab initio band structure analysis of interband and intraband  contributions for third harmonic generation coefficient of bulk silicon:  implementation and application of the sum-over-states