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We present an ab-initio real-time-based computational approach to studynonlinear optical properties in condensed matter systems that is especiallysuitable for crystalline solids and periodic nanostructures. The equations ofmotion and the coupling of the electrons with the external electric field arederived from the Berry-phase formulation of the dynamical polarization [Souzaet al., Phys. Rev. B 69, 085106 (2004)]. Many-body effects are introduced byadding single-particle operators to the independent-particle Hamiltonian. Weadd a Hartree operator to account for crystal local effects and a scissoroperator to correct the independent particle band structure for quasiparticleeffects. We also discuss the possibility of accurately treating excitoniceffects by adding a screened Hartree-Fock self-energy operator. The approach isvalidated by calculating the second-harmonic generation of SiC and AlAs bulksemiconductors: an excellent agreement is obtained with existing ab initiocalculations from response theory in frequency domain [Luppi et al., Phys. Rev.B 82, 235201 (2010)]. We finally show applications to the second-harmonicgeneration of CdTe and the third-harmonic generation of Si.

physical review. b, condensed matter and materials physics

Nonlinear optics from an ab-initio approach by means of the dynamical  Berry phase: Application to second- and third-harmonic generation in  semiconductors