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We present a method to construct an efficient approximation to the bare exchange and screened direct interaction kernels of the Bethe-Salpeter Hamiltonian for periodic solid state systems via the interpolative separable density fitting technique. We show that the cost of constructing the approximate Bethe-Salpeter Hamiltonian scales nearly optimally as $\mathcal{O}(N_k)$ with respect to the number of samples in the Brillouin zone $N_k$. In addition, we show that the cost for applying the Bethe-Salpeter Hamiltonian to a vector scales as $\mathcal{O}(N_k \log N_k)$. Therefore the optical absorption spectrum, as well as selected excitation energies can be efficiently computed via iterative methods such as the Lanczos method. This is a significant reduction from the $\mathcal{O}(N_k^2)$ and $\mathcal{O}(N_k^3)$ scaling associated with a brute force approach for constructing the Hamiltonian and diagonalizing the Hamiltonian respectively. We demonstrate the efficiency and accuracy of this approach with both one-dimensional model problems and three-dimensional real materials (graphene and diamond). For the diamond system with $N_k=2197$, it takes $6$ hours to assemble the Bethe-Salpeter Hamiltonian and $4$ hours to fully diagonalize the Hamiltonian using $169$ cores when the brute force approach is used. The new method takes less than $3$ minutes to set up the Hamiltonian and $24$ minutes to compute the absorption spectrum on a single core.

The zone-center $E_{2g}$ modes play a crucial role in MgB$_2$, controlling the scattering mechanisms in the normal state as well the superconducting pairing. Here, we demonstrate via first-principles quantum-field theory calculations that, due to the anisotropic electron-phonon interaction, a $hot$-$phonon$ regime where the $E_{2g}$ phonons can achieve significantly larger effective populations than other modes, is triggered in MgB$_2$ by the interaction with an ultra-short laser pulse. Spectral signatures of this scenario in ultrafast pump-probe Raman spectroscopy are discussed in detail, revealing also a fundamental role of nonadiabatic processes in the optical features of the $E_{2g}$ mode., Comment: Article as accepted for publication in Physical Review Letters; 6 pages, 3 figures

We present ab initio results for the electron-phonon interaction of the \Gamma-point phonons in the tetragonal high-temperature phase of La2CuO4. Eigenfrequencies and eigenvectors for the symmetry-allowed phonon modes are calculated with the full-potential augmented plane wave+local orbitals method using the frozen phonon approach. It is found that the \Gamma-point phonons with the strongest electron-phonon interaction are the A{2u} modes with 236 cm^{-1}, 131 cm^{-1} and 476 cm^{-1}. To take effect of strong electron on-site interaction into account we use generalized tight-binding method that results in the interaction of phonons with Hubbard fermions forming quasiparticle's band structure. Finally, the matrix elements of Hubbard fermion-phonon interaction and their reduction due to strong electron correlation are obtained., Comment: 7 pages

The methodology used to obtain the values of the spin-orbit couplings from the spin expectation values from perturbation theory was incorrect. As a result Figs. 2 and 3 are incorrect., Comment: This paper has been withdrawn

The electronic band structure of graphene in the presence of spin-orbit coupling and transverse electric field is investigated from first principles using the linearized augmented plane-wave method. The spin-orbit coupling opens a gap at the $K(K')$-point of the magnitude of 24 $\mu$eV (0.28 K). This intrinsic splitting comes 96% from the usually neglected $d$ and higher orbitals. The electric field induces an additional (extrinsic) Bychkov-Rashba-type splitting of 10 $\mu$eV (0.11 K) per V/nm, coming from the $\sigma$-$\pi$ mixing. A 'mini-ripple' configuration with every other atom is shifted out of the sheet by less than 1% differs little from the intrinsic case., Comment: 4 pages, 4 figures

We theoretically investigate inhomogeneity effects on the charges, electric field gradients and site-projected densities of states in HgBa$_2$CuO$_{4+\delta}$. We find pronounced differences in the doping-induced number of holes at different atomic sites. The contributions of these sites to the density of states in the vicinity of the Fermi level are peaked at the same energy, but vary in magnitude by up to 70 percent and have different energy dependence. Due to this energy dependence the role of the intrinsic inhomogeneities for superconductivity strongly depends on the energy and character of the quasiparticle mediating the Cooper pairing. Our results can explain the origin of doping-induced effects observed either by local or macroscopic experimental probes., Comment: 5 pages, 2 figures

A description of non-collinear magnetism in the framework of spin-density functional theory is presented for the exact exchange energy functional which depends explicitly on two-component spinor orbitals. The equations for the effective Kohn-Sham scalar potential and magnetic field are derived within the optimized effective potential (OEP) framework. With the example of a magnetically frustrated Cr monolayer it is shown that the resulting magnetization density exhibits much more non-collinear structure than standard calculations. Furthermore, a time-dependent generalization of the non-collinear OEP method is well suited for an ab-initio description of spin dynamics. We also show that the magnetic moments of solids Fe, Co and Ni are well reproduced., Comment: 4 pages 2 fig accepted in Phys. Rev. Lett. (2007)

Exact exchange (EXX) Kohn-Sham calculations within an all-electron full-potential method are performed on a range of semiconductors and insulators (Ge, GaAs, CdS, Si, ZnS, C, BN, Ne, Ar, Kr and Xe). We find that the band-gaps are not as close to experiment as those obtained from previous pseudopotential EXX calculations. Full-potential band-gaps are also not significantly better for $sp$ semiconductors than for insulators, as had been found for pseudopotentials. The locations of $d$-band states, determined using the full-potential EXX method, are in excellent agreement with experiment, irrespective of whether these states are core, semi-core or valence. We conclude that the inclusion of the core-valence interaction is necessary for accurate determination of EXX Kohn-Sham band structures, indicating a possible deficiency in pseudopotential calculations., Comment: 4 pages 2 figs

The magnetic properties of the intermetallic compound FeAl are investigated using exact exchange density functional theory. This is implemented within a state of the art all-electron full potential method. We find that FeAl is magnetic with a moment of 0.70 $\mu_B$, close to the LSDA result of 0.69 $\mu_B$. A comparison with the non-magnetic density of states with experimental negative binding energy result shows a much better agreement than any previous calculations. We attribute this to the fine details of the exchange field, in particular its asymmetry, which is captured very well with the orbital dependent exchange potential., Comment: 4 pages 4 figs

We investigate the electronic structure and the hole content in the copper-oxygen planes of Hg based high Tc cuprates for one to four CuO2 layers and hydrostatic pressures up to 15 GPa. We find that with the pressure-induced additional number of holes of the order of 0.05e the density of states at the Fermi level changes approximately by a factor of 2. At the same time the saddle point is moved to the Fermi level accompanied by an enhanced k_z dispersion. This finding explains the pressure behavior of Tc and leads to the conclusion that the applicability of the van Hove scenario is restricted. By comparison with experiment, we estimate the coupling constant to be of the order of 1, ruling out the weak coupling limit., Comment: 4 pages, 4 figures

The electronic structure of two V-based ladder compounds, the quarter-filled NaV$_2$O$_5$ in the symmetric phase and the iso-structural half-filled CaV$_2$O$_5$ is investigated by ab initio calculations. Based on the bandstructure we determine the dielectric tensor $\epsilon(\omega)$ of these systems in a wide energy range. The frequencies and eigenvectors of the fully symmetric A$_{g}$ phonon modes and the corresponding electron-phonon and spin-phonon coupling parameters are also calculated from first-principles. We determine the Raman scattering intensities of the A$_g$ phonon modes as a function of polarization and frequency of the exciting light. All results, i.e. shape and magnitude of the dielectric function, phonon frequencies and Raman intensities show very good agreement with available experimental data., Comment: 11 pages, 10 figures

We present a scheme for the calculation of linear optical properties by the all-electron full-potential linearized augmented planewave (LAPW) method. A summary of the theoretical background for the derivation of the dielectric tensor within the random-phase approximation is provided together with symmetry considerations and the relation between the optical constants. The momentum matrix elements are evaluated in detail for the LAPW basis, and the interband as well as the intraband contributions to the dielectric tensor are given. Results are presented for the metals aluminum and gold, where we crosscheck our results by sumrules. We find that the optical spectra can be extremely sensitive to the Brillouin zone sampling. For gold, the influence of relativistic effects on the dielectic function is investigated. It is shown that the scalar-relativistic effect is much more important than spin-orbit coupling. The interpretability of the Kohn-Sham eigenstates in terms of excited states is discussed.

We investigate electronic and optical properties of the V-based ladder compounds NaV2O5, the iso-structural CaV2O5, as well as MgV2O5, which differs from NaV2O5 and CaV2O5 in the c axis stacking. We calculate ab initio the A_g phonon modes in these compounds as a basis for the investigation of the electron-phonon and spin-phonon coupling. The phonon modes together with the dielectric tensors as a function of the corresponding ion displacements are the starting point for the calculation of the A_g Raman scattering., Comment: 4 pages, 5 figures, .bbl file with references included. Accepted for publication in Physica Scripta

We investigate charge ordering in the presence of electron-phonon coupling for quarter-filled ladder systems by using Exact Diagonalization. As an example we consider NaV2O5 using model parameters obtained from first-principles band-structure calculations. The relevant Holstein coupling to the lattice considerably reduces the critical value of the nearest-neighbor Coulomb repulsion at which formation of the zig-zag charge-ordered state occurs, which is then accompanied by a static lattice distortion. Energy and length of a kink-like excitation on the background of the distorted lattice are calculated. Spin and charge spectra on ladders with and without static distortion are obtained, and the charge gap and the effective spin-spin exchange parameter J are extracted. J agrees well with experimental results. Analysis of the dynamical Holstein model, restricted to a small number of phonons, shows that low frequency lattice vibrations increase the charge order, accompanied by dynamically produced zig-zag lattice distortions., Comment: 11 pages, 17 figures, revised version as to appear in Phys. Rev. B

In this work the mechanism of Li insertion/intercalation in the anode materials InSb and Cu$_2$Sb is investigated by means of the first principles total energy calculations. The total charge densities for the lithiated products of the two compounds are presented. Based on these results the change in the bonding character on lithiation is discussed. Further, the isomer shift for InSb and Cu$_2$Sb and there various lithiated products is reported. The average insertion/intercalation voltage and volume expansion for transitions from InSb to Li$_2$InSb and Cu$_2$Sb to Li$_2$CuSb are calculated and found to be in good agreement with the experimental values. These findings help to resolve the controversy regarding the lithiation mechanism in InSb., Comment: 5 pages 3 figures

We present detailed first-principles calculations for the normal state electronic properties of the high T$_C$ superconductor Bi$_2$Sr$_2$CaCu$_2$O$_8$, by means of the linearized augmented plane wave (LAPW) method within the framework of density functional theory (DFT). As a first step, the body centered tetragonal (BCT) cell has been adopted, and optimized regarding its volume, $c/a$ ratio and internal atomic positions by total energy and force minimizations. The full optimization of the BCT cell leads to small but visible changes in the topology of the Fermi surface, rounding the shape of CuO$_2$ barrels, and causing both the BiO bands, responsible for the pockets near the \textit{\=M} 2D symmetry point, to dip below the Fermi level. We have then studied the influence of the distortions in the BiO plane observed in nature by means of a $\sqrt{2}\times\sqrt{2}$ orthorhombic cell (AD-ORTH) with $Bbmb$ space group. Contrary to what has been observed for the Bi-2201 compound, we find that for Bi-2212 the distortion does not sensibly shift the BiO bands which retain their metallic character. As a severe test for the considered structures we present Raman-active phonon frequencies ($q = 0$) and eigenvectors calculated within the frozen-phonon approximation. Focussing on the totally symmetric A$_{g}$ modes, we observe that for a reliable attribution of the peaks observed in Raman experiments, both $c$- and a-axis vibrations must be taken into account, the latter being activated by the in-plane orthorhombic distortion., Comment: 22 pages, 4 figures

We report first-principles calculations of the frequency dependent linear and second-order optical properties of the two probable extended-solid phases of CO$_2$--V, i.e. $I\bar42d$ and $P2_12_12_1$. Compared to the parent $Cmca$ phase the linear optical susceptibility of both phases is much smaller. We find that $I\bar42d$ and $P2_12_12_1$ differ substantially in their linear optical response in the higher energy regime. The nonlinear optical responses of the two possible crystal structures differ by roughly a factor of five. Since the differences in the nonlinear optical spectra are pronounced in the low energy regime, i.e. below the band gap of diamond, measurements with the sample inside the diamond anvil cell are feasible. We therefore suggest optical experiments in comparison with our calculated data as a tool for the unambiguous identification of the high pressure phase of CO$_2$., Comment: 4 pages 2 figs

We present a full formalism for the calculation of the linear and second-order optical response for semiconductors and insulators. The expressions for the optical susceptibilities are derived within perturbation theory. As a starting point a brief background of the single and many particle Hamiltonians and operators is provided. As an example we report calculations of the linear and nonlinear optical properties of the mono-layer InP/GaP (110) superlattice. The features in the linear optical spectra are identified to be coming from various band combinations. The main features in the second-order optical spectra are analyzed in terms of resonances of peaks in linear optical spectra. With the help of the strain corrected effective-medium-model the interface selectivity of the second-order optical properties is highlighted., Comment: 10 pages 4 figures, conference & physica scripta

We report the first fully self-consistent calculations of the nonlinear optical properties of superlattices. The materials investigated are mono-layer superlattices with GaP grown on the the top of InP, AlP and GaAs (110) substrates. We use the full-potential linearized augmented plane wave method within the generalized gradient approximation to obtain the frequency dependent dielectric tensor and the second-harmonic-generation susceptibility. The effect of lattice relaxations on the linear optical properties are studied. Our calculations show that the major anisotropy in the optical properties is the result of strain in GaP. This anisotropy is maximum for the superlattice with maximum lattice mismatch between the constituent materials. In order to differentiate the superlattice features from the bulk-like transitions an improvement over the existing effective medium model is proposed. The superlattice features are found to be more pronounced for the second-order than the linear optical response indicating the need for full supercell calculations in determining the correct second-order response., Comment: 9 pages, 4 figures, submitted to Phy. Rev. B

The lattice dynamical properties of Li$_x$BC are calculated for several values of $x$ using density functional perturbation theory. We find that the electron-phonon coupling parameter $\lambda$ increases monotonically with decreasing $x$ to a maximum value of 1.4 for $x=0.125$ owing to the increasing radius of multiply-nested Fermi surface cylinders. The B-C bond-stretching phonon modes have frequencies which are 28% higher than the equivalent modes in MgB$_2$. This combination results in a $T_c$ of about 65 K for $x=0.5$., Comment: 6 pages, 5 figures

To understand the link between doping and electronic properties in high temperature superconductors, we report first-principles calculations on the oxygen doping effect for the single layer cuprate HgBa$_2$CuO$_{4+\delta}$. The doping effect is studied both by supercell and single cell virtual crystal type approaches. We find ionic behavior of the dopant atom up to an optimal doping concentration of $\delta=0.22$. The excess oxygen attracts electrons from the CuO$_2$ plane leading to an increase of the hole concentration in this building block. The maximum amount of holes is reached when the oxygen $p$-shell is nearly completely filled. As a consequence the density of states at the Fermi level exhibits a pronounced maximum at the optimal oxygen content. The calculated hole content as a function of doping is in accordance with experimental findings., Comment: 4 pages, 4 figures, comments to sule@mfa.kfki.hu

Charge kinks are considered as fundamental excitations in quarter-filled charge-ordered ladders. The strength of the coupling of the kinks to the three-dimensional lattice depends on their energy. The integrated intensity of Raman scattering by kink-antikink pairs is proportional to $\phi ^{5}$ or $\phi ^{4},$ where $\phi $ is the order parameter. The exponent is determined by the system parameters and by the strength of the electron-phonon coupling., Comment: To be published in Phys. Rev.B (june 2001)

The electronic structure of SrBi2Ta2O9 is investigated from first-principles, within the local density approximation, using the full-potential linearized augmented plane wave (LAPW) method. The results show that, besides the large Ta(5d)-O(2p) hybridization which is a common feature of the ferroelectric perovskites, there is an important hybridization between bismuth and oxygen states. The underlying static potential for the ferroelectric distortion and the primary source for ferroelectricity is investigated by a lattice-dynamics study using the Frozen Phonon approach., Comment: 17 pages, 7 figures. Phys. Rev. B, in press

We report first-principles frozen-phonon calculations for the determination of the force-free geometry and the dynamical matrix of the five Raman-active A1g modes in YBa2Cu3O7. To establish the shape of the phonon potentials atomic forces are calculated within the LAPW method. Two different schemes - the local density approximation (LDA) and a generalized gradient approximation (GGA) - are employed for the treatment of electronic exchange and correlation effects. We find that in the case of LDA the resulting phonon frequencies show a deviation from experimental values of approximately -10%. Invoking GGA the frequency values are significantly improved and also the eigenvectors are in very good agreement with experimental findings., Comment: 15 pages