The relationship between crystal structure and related material properties is discussed for the common 3C, 6H, 4H, and 2H polytypes of SiC. The theoretical results are derived in the framework of well converged density‐functional calculations within the local‐density approximation and the pseudopotential‐plane‐wave approach. In the case of electronic excitations additionally quasiparticle corrections are included. The lattice‐dynamical properties of the noncubic polytypes are described within a bond‐charge model. We focus our attention on the actual atomic structures, the accompanying lattice vibrations, thermodynamical properties, properties of layered combinations of polytypes, optical spectra, and surface equilibrium structures. On the one hand, the influence of the polytype on the material properties is considered. On the other hand, indications for driving forces of the polytypism are extracted.

We report numerical calculations of the frequency-dependent dielectric function for different gauges of the electromagnetic field in the optical transition operator. Comparing the results, we draw conclusions about the importance of different nonlocality effects entering the calculations. Apart from the spatial inhomogeneity related to the atomic structure of matter, they are due to nonlocal pseudopotentials, quasiparticle self-energies, and the incompleteness of the basis functions. Besides their influence on optical spectra, their effect on the validity of the f -sum rule and the magnitude of the resulting dielectric constants is also discussed. We present results for optical spectra where the many-body quasiparticle effect is included beyond the scissors-operator approximation. The group-IV materials Si, SiC, and C are considered as model substances.

The inclusion of dynamical quasiparticle effects lifts the underestimation of band gaps in semiconductors and insulators derived within density-functional theory. Simultaneously, they give rise to a remarkable reduction of the strengths of the quasiparticle peaks that is not observed in optical spectra. We show that dynamical contributions to the vertex corrections widely compensate the peak renormalization due to the dynamics in the quasiparticle formation. The slight reduction of the absorption spectrum yields an improvement of the computed f-sum rule. [S0031-9007(97)02512-X] PACS numbers: 71.35.Cc, 71.45.Gm, 78.20.Bh The recent major advances in the quantitative computation of ground-state properties of solids are essentially related to the development of density-functional theory (DFT) in local-density approximation (LDA) [1]. However, spectroscopic properties, as optical spectra, are not accessible in this theory, since its single-particle eigenvalues or differences of them cannot be directly identifed with electronic excitation energies. For instance, energy gaps of semiconductors and insulators are remarkably underestimated within DFT-LDA [2]. Instead, quasiparticle (QP) energies have to be computed. The basic approach to quasiparticles is Hedin's GW approximation [3], in which the spatially nonlocal and energy-dependent exchange-correlation (XC) self-energy S is approximated by a convolution of single-particle Green function G and dynamically screened Coulomb interaction W. Vertex corrections are neglected. Full numerical calculations of the single-particle excitations can now be performed on real crystals starting from the DFT-LDA results [4,5]. The effect of the XC self-energy is not restricted to shift the single-particle energy from the DFT-LDA value for a certain band n and Bloch wave vector k to the QP position´n͑k͒. Rather, the energy dependence of the self-energy, b n ͑k͒ 2≠S͑ ͑ ͑nk,´n͑k͒͒ ͒ ͒͞≠´n͑k͒, gives rise to a considerable reduction of the spectral strength ͓1 2 b n ͑k͔͒ of the main QP peak by about 25% and to the simultaneous appearance of satellite structures in the single-QP spectral function. The strongest satellites appear around the plasmon energy of the system and its replicas [6]. Applying the QP results to optical spectra, the question arises if the oscillator strength of a certain direct electronic transition from a valence band y to a conduction band c at the wave vector k in the Brillouin zone (BZ) has to be reduced by a factor ͓1 2 b cy ͑k͔͒ with b cy ͑k͒ b c ͑k͒ 1 b y ͑k͒, i.e., by about 50%. A recent calculation by Del Sole and Girlanda [7] has shown that this is indeed the result, if the polarizability is calculated according to the strict GW-RPA method, namely, neglecting vertex corrections but including dynamicalself-energy effects. Since dynamical effects worsen the agreement between theory and experiment, they are usually neglected in calculating the dielectric function of a system within the independent QP approximation (i.e., neglecting excitonic effects) [8-10], al...

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A method to study the low-temperature conductivity in the Coulomb glass, i.e. , a disordered system with many electrons subject to long-range electron-electron interaction, is introduced. After determining the lowlying many-electron states of the system we calculate the transition matrix between these states, including one-electron hopping as well as many-electron hopping processes. The conductivity is then obtained by an examination of that eigenvector of the transition matrix which describes the stationary state. The results demonstrate that the low-temperature conductivity in interacting systems is strongly influenced by manyelectron hopping processes.