Abstract:
We have performed density functional calculations using a range of local and semi-local as well as hybrid density functional approximations of the structure and elastic constants of 18 semiconductors and insulators. We find that most of the approximations have a very small error in the lattice constants, of the order of 1\%, while the error in the elastic constants and bulk modulus are much larger, at about 10\%. In addition, we find that the error in the elastic constants, $c_{ij}$, are larger compared to the error in the bulk modulus. Depending on the functional and which error estimate that is being used, the difference in the error between the elastic constants and the bulk modulus can be rather large, about a factor of two. According to our study, the overall best performing density functional approximation for determining the structure and elastic properties is the PBEsol, closely followed by the two hybrid functionals PBE0 and HSE, and the AM05 functional.

Abstract:
(Screened) hybrid functionals are being used more and more for solid-state calculations. Usually the fraction alpha of Hartree-Fock exchange is kept fixed during the calculation, however there is no single (universal) value for alpha which systematically leads to satisfying accuracy. Instead, one could use a property of the system under consideration to determine alpha and in this way the functional would be more flexible and potentially more accurate. Recently, it was proposed to use the static dielectric constant epsilon for the calculation of alpha [Shimazaki and Asai, Chem. Phys. Lett. 466, 91 (2008) and Marques et al., Phys. Rev. B 83, 035119 (2011)]. We explore this idea further and propose a scheme where the connection between epsilon and alpha is optimized based on experimental band gaps. epsilon, and thus alpha, is recalculated at each iteration of the self-consistent procedure. We present results for the band gap and lattice constant of various semiconductors and insulators with this procedure. In addition, we show that this approach can also be combined with a non-self-consistent hybrid approximation to speed up the calculations considerably, while retaining an excellent accuracy in most cases.

Abstract:
We present an efficient implementation of the PBE0 hybrid functional within the full-potential linearized augmented-plane-wave (FLAPW) method. The Hartree-Fock exchange term, which is a central ingredient of hybrid functionals, gives rise to a computationally expensive nonlocal potential in the one-particle Schroedinger equation. The matrix elements of this exchange potential are calculated with the help of an auxiliary basis that is constructed from products of FLAPW basis functions. By representing the Coulomb interaction in this basis the nonlocal exchange term becomes a Brillouin-zone (BZ) sum over vector-matrix-vector products. We show that the Coulomb matrix can be made sparse by a suitable unitary transformation of the auxiliary basis, which accelerates the computation of the vector-matrix-vector products considerably. Additionally, we exploit spatial and time-reversal symmetry to identify the nonvanishing exchange matrix elements in advance and to restrict the k summations for the nonlocal potential to an irreducible set of k points. Favorable convergence of the self-consistent-field cycle is achieved by a nested density-only and density-matrix iteration scheme. We discuss the convergence with respect to the parameters of our numerical scheme and show results for a variety of semiconductors and insulators, including oxide materials, where the PBE0 hybrid functional improves the band gaps and the description of localized states in comparison with the PBE functional. Furthermore, we find that in contrast to conventional local exchange-correlation functionals ferromagnetic EuO is correctly predicted to be a semiconductor.

Abstract:
We present an analytical study of the spatial decay rate $\gamma$ of the one-particle density matrix $\rho(\vec r,\vec r')\sim\exp(-\gamma|\vec r-\vec r'|)$ for systems described by single particle orbitals in periodic potentials in arbitrary dimensions. This decay reflects electronic locality in condensed matter systems and is also crucial for O(N) density functional methods. We find that $\gamma$ behaves contrary to the conventional wisdom that generically $\gamma\propto\sqrt{\Delta}$ in insulators and $\gamma\propto\sqrt{T}$ in metals, where $\Delta$ is the direct band gap and $T$ the temperature. Rather, in semiconductors $\gamma\propto\Delta$, and in metals at low temperature $\gamma\propto T$.

Abstract:
Nanoparticles exhibit physical properties distinctively different from that of bulk. They possess a large fraction of surface atoms or ions or molecules in unit volume. The very large surface area provides a huge surface energy. Further, the electronic structures of semiconductor nanocrystals differ from those of bulk materials. Band gap-illumination of semiconductor results in formation of electron-hole pairs; electron in the conduction band (CB) and hole in the valence band (VB) [1]. While most of the electron-hole pairs recombine, some of the charge carriers diffuse to the crystal surface and react with the adsorbed electron donors and acceptors leading to photocatalysis. Here we compare the photocatalytic efficiencies of nanocrystalline semiconductors. Iodide ion is the test substrate taken up for the study. Production of energy bearing chemicals through thermodynamically uphill reactions is the objective of solar energy conversion and storage and iodide ion-oxidation is such a reaction (ΔG° = +51.6 kJ mol-1). In addition, it is well known that degradation of organic molecules involve photogenerated reactive oxygen species (ROS) and the major active oxidizing species is hydroxyl radical [2]. The capacity to photogenerate hydroxyl radical is also taken as a measure of the photocatalytic activity of photocatalyst [3]. More importantly, the photocatalytic mineralization of organics is complicated by the formation of a number of stable intermediates. But the iodide ion oxidation is a simple electron transfer process [4-7]. Further, unlike iodide ion the organic molecules such as phenols and dyes may have chemical affinity to the oxide surface and enter into some sort of bond formation with the oxides. These factors led to the selection of iodide ion as the test substrate for this investigation. The present photocatalytic results on iodide ion oxidation show that some of the nanocrystalline semiconductors are less efficient photocatalysts than insulators such as Al2O

Abstract:
We report the discovery of weak topological insulators by ab initio calculations in a honeycomb lattice. We propose a structure with an odd number of layers in the primitive unit-cell as a prerequisite for forming weak topological insulators. Here, the single-layered KHgSb is the most suitable candidate for its large bulk energy gap of 0.24 eV. Its side surface hosts metallic surface states, forming two anisotropic Dirac cones. Though the stacking of even-layered structures leads to trivial insulators, the structures can host a quantum spin Hall layer with a large bulk gap, if an additional single layer exists as a stacking fault in the crystal. The reported honeycomb compounds can serve as prototypes to aid in the finding of new weak topological insulators in layered small-gap semiconductors.

Abstract:
We present in this work the electronic structure and transition energies (both thermodynamic and optical) of Cl vacancies in NaCl by hybrid density functionals. The underestimated transition energies by the semi-local functional inherited from the band gap problem are recovered by the PBE0 hybrid functional through the non-local exact exchange, whose amount is adjusted to reproduce the experimental band gap. The hybrid functional also gives a better account of the lattice relaxation for the defect systems arising from the reduced self-interaction. On the other hand, the quantitative agreement with experimental vertical transition energy cannot be achieved with hybrid functionals due to the inaccurate descriptions of the ionization energies of the localized defect and the positions of the band edges.

Abstract:
To investigate ferromagnetic semiconductors and insulators, such as the famous EuO, EuS, or CrBr$_3$, we propose a hybridized Kondo-lattice model, where, in addition to the conduction electrons, localized moments (e.g., the $4f$-electrons) are modeled as a strongly correlated band system. The quasi-empty conduction band is weakly filled due to the hybridization term. This activates the intraatomic exchange coupling between conduction and localized electrons. Temperature-dependent phase diagrams and quasiparticle densities of states are presented for various coupling and hybridization strengths. Moreover, the influence of the one-particle energy of the localized electrons $E_f$ is discussed. A comparison with mean field calculations is given at the end of this work.

Abstract:
We present an implementation of the Heyd-Scuseria-Ernzerhof (HSE) hybrid functional within the full-potential linearized augmented-plane-wave (FLAPW) method. Pivotal to the HSE functional is the screened electron-electron interaction, which we separate into the bare Coulomb interaction and the remainder, a slowly varying function in real space. Both terms give rise to exchange potentials, which sum up to the screened nonlocal exchange potential of HSE. We evaluate the former with the help of an auxiliary basis, defined in such a way that the bare Coulomb matrix becomes sparse. The latter is computed in reciprocal space, exploiting its fast convergence behavior in reciprocal space. This approach is general and can be applied to a whole class of screened hybrid functionals. We obtain excellent agreement of band gaps and lattice constants for prototypical semiconductors and insulators with electronic-structure calculations using plane-wave or Gaussian basis sets. We apply the HSE hybrid functional to examine the ground-state properties of rocksalt GdN, which have been controversially discussed in literature. Our results indicate that there is a half-metal to insulator transition occurring between the theoretically optimized lattice constant at 0 K and the experimental lattice constant at room temperature. Overall, we attain good agreement with experimental data for band transitions, magnetic moments, and the Curie temperature.

Abstract:
The renormalization of electronic eigenenergies due to electron-phonon coupling is sizable in many materials with light atoms. This effect, often neglected in ab-initio calculations, can be computed using the perturbation-based Allen-Heine-Cardona theory in the adiabatic or non-adiabatic harmonic approximation. After a short description of the numerous recent progresses in this field, and a brief overview of the theory, we focus on the issue of phonon wavevector sampling convergence, until now poorly understood. Indeed, the renormalization is obtained numerically through a q-point sampling inside the BZ. For q-points close to G, we show that a divergence due to non-zero Born effective charge appears in the electron-phonon matrix elements, leading to a divergence of the integral over the BZ for band extrema. Although it should vanish for non-polar materials, unphysical residual Born effective charges are usually present in ab-initio calculations. Here, we propose a solution that improves the coupled q-point convergence dramatically. For polar materials, the problem is more severe: the divergence of the integral does not disappear in the adiabatic harmonic approximation, but only in the non-adiabatic harmonic approximation. In all cases, we study in detail the convergence behavior of the renormalization as the q-point sampling goes to infinity and the imaginary broadening parameter goes to zero. This allows extrapolation, thus enabling a systematic way to converge the renormalization for both polar and non-polar materials. Finally, the adiabatic and non-adiabatic theory, with corrections for the divergence problem, are applied to the study of five semiconductors and insulators: a-AlN, b-AlN, BN, diamond and silicon. For these five materials, we present the zero-point renormalization, temperature dependence, phonon-induced lifetime broadening and the renormalized electronic bandstructure.