Efficient ab initio method for the calculation of frequency-dependent second-order optical response in semiconductors

Sergey N. Rashkeev, Walter R.L. Lambrecht, Benjamin Segall

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247 Citations (Scopus)


The development of a method for calculating the frequency-dependent second harmonic generation coefficient of insulators and semiconductors based on the self-consistent linearized muffin-tin orbitals band structure method is reported. The calculations are at the independent particle level and are based on the formulation introduced by Aversa and Sipe [Phys. Rev. B 52, 14 636 (1995)]. The terms are rearranged in such a way as to exhibit explicitly all required symmetries including the Kleinman symmetry in the static limit. Computational details and convergence tests are presented. The calculated frequency-dependent (Formula presented) for the zinc-blende materials GaAs, GaP and wurtzite GaN and AlN are found to be in excellent agreement with that obtained by other first-principles calculations when corrections to the local density approximation are implemented in the same manner, namely, using the “scissors” approach. Similar agreement is found for the static values of (Formula presented) for zinc-blende GaN, AlN, BN, and SiC. The strict validity of the usual “scissors” operator implementation is, however, questioned. We show that better agreement with experiment is obtained when the corrections to the low-lying conduction bands are applied at the level of the Hamiltonian, which guarantees that eigenvectors are consistent with the eigenvalues. Results are presented for the frequency-dependent (Formula presented) for (Formula presented). The approach is found to be very efficient and flexible, which indicates that it will be useful for a wide variety of material systems including those with many atoms in the unit cell.

Original languageEnglish
Pages (from-to)3905-3919
Number of pages15
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number7
Publication statusPublished - 1 Jan 1998


ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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