Nonlinear optical susceptibilities, Raman efficiencies, and electro-optic tensors from first-principles density functional perturbation theory

The nonlinear response of infinite periodic solids to homogenous electric fields and collective atomic displacements is discussed in the framework of density functional perturbation theory. The approach is based on the 2n+1 theorem applied to an electric-field-dependent energy functional. We report the expressions for the calculation of the nonlinear optical susceptibilities, Raman scattering efficiencies, and electro-optic (EO) coefficients. Different formulations of third-order energy derivatives are examined and their convergence with respect to the k-point sampling is discussed. We apply our method to a few simple cases and compare our results to those obtained with distinct techniques. Finally, we discuss the effect of a scissors correction on the EO coefficients and nonlinear optical susceptibilities.

[1]  Mauri,et al.  Wannier and Bloch orbital computation of the nonlinear susceptibility. , 1994, Physical review. B, Condensed matter.

[2]  I. P. Kaminow,et al.  Quantitative Determination of Sources of the Electro-Optic Effect in LiNbO3and LiTaO3 , 1967 .

[3]  N. Marzari,et al.  Maximally localized generalized Wannier functions for composite energy bands , 1997, cond-mat/9707145.

[4]  D. Strauch,et al.  Intrinsic lifetimes and anharmonic frequency shifts of long-wavelength optical phonons in polar crystals , 2004 .

[5]  X. Gonze,et al.  Adiabatic density-functional perturbation theory. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[6]  Richard M. Martin,et al.  Microscopic theory of force constants in the adiabatic approximation , 1970 .

[7]  Gernot Deinzer,et al.  Ab initio calculation of the linewidth of various phonon modes in germanium and silicon , 2003 .

[8]  Xavier Gonze,et al.  Berry-phase treatment of the homogeneous electric field perturbation in insulators , 2001 .

[9]  J. K. Dewhurst,et al.  Linear and second-order optical response of III-V monolayer superlattices , 2003 .

[10]  T. Arias,et al.  Iterative minimization techniques for ab initio total energy calculations: molecular dynamics and co , 1992 .

[11]  Xavier Gonze,et al.  Concentration of small ring structures in vitreous silica from a first-principles analysis of the Raman spectrum. , 2003, Physical review letters.

[12]  D. A. Kleinman,et al.  Nonlinear Dielectric Polarization in Optical Media , 1962 .

[13]  Gonze,et al.  Perturbation expansion of variational principles at arbitrary order. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[14]  First-principles calculation of vibrational Raman spectra in large systems: signature of small rings in crystalline SiO2. , 2002, Physical review letters.

[15]  Günter,et al.  Dielectric, elastic, piezoelectric, electro-optic, and elasto-optic tensors of BaTiO3 crystals. , 1994, Physical review. B, Condensed matter.

[16]  W. D. Johnston.  Nonlinear Optical Coefficients and the Raman Scattering Efficiency of LO and TO Phonons in Acentric Insulating Crystals , 1970 .

[17]  Alfredo Pasquarello,et al.  Raman scattering intensities in α-quartz: A first-principles investigation , 2001 .

[18]  Ronald E. Cohen,et al.  Origin of ferroelectricity in perovskite oxides , 1992, Nature.

[19]  Allan,et al.  Calculation of the nonlinear susceptibility for optical second-harmonic generation in III-V semiconductors. , 1991, Physical review letters.

[20]  David Vanderbilt.  Berry-phase theory of proper piezoelectric response , 1999 .

[21]  Coulomb interaction and ferroelectric instability of BaTiO3 , 1996, mtrl-th/9601001.

[22]  Teter.  Additional condition for transferability in pseudopotentials. , 1993, Physical review. B, Condensed matter.

[23]  Gernot Deinzer,et al.  Raman tensor calculated from the 2n+1 theorem in density-functional theory , 2002 .

[24]  J. Nye.  Physical Properties of Crystals: Their Representation by Tensors and Matrices , 1957 .

[25]  Godby,et al.  Density-Polarization Functional Theory of the Response of a Periodic Insulating Solid to an Electric Field. , 1995, Physical review letters.

[26]  Polarization-dependent density-functional theory and quasiparticle theory: Optical response beyond local-density approximations. , 1996, Physical review. B, Condensed matter.

[27]  Wang,et al.  Accurate and simple analytic representation of the electron-gas correlation energy. , 1992, Physical review. B, Condensed matter.

[28]  D. Vanderbilt,et al.  Theory of polarization of crystalline solids. , 1993, Physical review. B, Condensed matter.

[29]  M. Veithen,et al.  First-principles study of the dielectric and dynamical properties of lithium niobate , 2002 .

[30]  D. Vanderbilt,et al.  Electric polarization as a bulk quantity and its relation to surface charge. , 1993, Physical review. B, Condensed matter.

[31]  Xavier Gonze,et al.  Photoelasticity of alpha-quartz from first principles , 2001 .

[32]  M. Kakihana,et al.  Materials Research Society Symposium - Proceedings , 2000 .

[33]  Martins,et al.  Efficient pseudopotentials for plane-wave calculations. , 1991, Physical review. B, Condensed matter.

[34]  Philippe Ghosez,et al.  First-principles study of the electro-optic effect in ferroelectric oxides. , 2004, Physical review letters.

[35]  Stefano de Gironcoli,et al.  Phonons and related crystal properties from density-functional perturbation theory , 2000, cond-mat/0012092.

[36]  Baroni,et al.  Anharmonic Phonon Lifetimes in Semiconductors from Density-Functional Perturbation Theory. , 1995, Physical review letters.

[37]  Two-phonon infrared absorption spectra of germanium and silicon calculated from first principles , 2004 .

[38]  Pietro Bernasconi,et al.  TEMPERATURE DEPENDENCE AND DISPERSION OF ELECTRO-OPTIC AND ELASTO-OPTIC EFFECT IN PEROVSKITE CRYSTALS , 1995 .

[39]  W. Kohn,et al.  Self-Consistent Equations Including Exchange and Correlation Effects , 1965 .

[40]  Levine.  Optical second-harmonic susceptibilities: Frequency-dependent formulation with results for GaP and GaAs. , 1994, Physical review. B, Condensed matter.

[41]  E. Kaldis.  Current Topics in Materials Science , 1980 .

[42]  Third-order density-functional perturbation theory: A practical implementation with applications to anharmonic couplings in Si , 1994, cond-mat/9406063.

[43]  P. Hohenberg,et al.  Inhomogeneous Electron Gas , 1964 .

[44]  Hari Singh Nalwa,et al.  Handbook of advanced electronic and photonic materials and devices , 2001 .

[45]  Stefano de Gironcoli,et al.  Ab initio calculation of phonon dispersions in semiconductors. , 1991, Physical review. B, Condensed matter.

[46]  Benoît Champagne,et al.  Nonlinear optical properties of quasilinear conjugated oligomers, polymers and organic molecules , 1997 .

[47]  Q. Fang.  Theoretical treatment of the nonlinear anelastic internal friction peaks appearing in the cold-worked Al-based solid solutions , 1997 .

[48]  Baroni,et al.  Ab initio calculation of the low-frequency Raman cross section in silicon. , 1986, Physical review. B, Condensed matter.

[49]  Real-space approach to calculation of electric polarization and dielectric constants. , 1994, Physical review letters.

[50]  A. Debernardi.  PHONON LINEWIDTH IN III-V SEMICONDUCTORS FROM DENSITY-FUNCTIONAL PERTURBATION THEORY , 1998 .

[51]  Grimsditch,et al.  Anharmonicity of the lowest-frequency A1(TO) phonon in PbTiO3. , 1993, Physical review. B, Condensed matter.

[52]  Teter,et al.  Separable dual-space Gaussian pseudopotentials. , 1996, Physical review. B, Condensed matter.

[53]  M. Fontana,et al.  Electro-optic properties in pure LiNbO3 crystals from the congruent to the stoichiometric composition , 1998 .

[54]  Electron localization in the insulating state: Application to crystalline semiconductors , 2001, cond-mat/0101440.

[55]  Allan,et al.  Linear optical response in silicon and germanium including self-energy effects. , 1989, Physical review letters.

[56]  Matthieu Verstraete,et al.  First-principles computation of material properties: the ABINIT software project , 2002 .

[57]  Car,et al.  Generalized-gradient approximations to density-functional theory: A comparative study for atoms and solids. , 1996, Physical review. B, Condensed matter.

[58]  K. Sugiyama,et al.  Production of YbH + by chemical reaction of Yb + in excited states with H 2 gas , 1997 .

[59]  High-order density-matrix perturbation theory , 2003, cond-mat/0307603.

[60]  David Vanderbilt,et al.  First-principles approach to insulators in finite electric fields. , 2002, Physical review letters.

[61]  M. Cardona,et al.  Absolute efficiency and dispersion of Raman scattering by phonons in silicon , 1983 .

[62]  X. Gonze,et al.  Density-functional approach to nonlinear-response coefficients of solids. , 1989, Physical review. B, Condensed matter.