During past decades, concepts about the electrostatics of infinite systems have been a challenge for theoretical physicists. In particular, the question of whether the absolute macroscopic polarization or the difference between the polarizations of two states of an insulating crystal is a well-defined bulk property has remained a controversial one. Recently, King-Smith and Vanderbilt, and Resta have provided an approach in terms of the geometric Berrys phase of electronic orbitals in an independent-particle approximation. Here we extend the derivation of Niu and Thouless for quantized charge transport to the case where the quantum adiabatic evolution is noncyclic, and we show how this polarization difference can be written in terms of a Berrys phase for a system with many-body interactions. We also discuss the origin and magnitude of the ‘‘quantum uncertainty’’ that appears when a path-independent gauge is used to compute those geometric quantum phases. This geometric viewpoint not only helps us understand the issues raised above but provides a mathematical method to compute polarizations in a many-body framework.

State-of-the-art electronic-structure calculations based on the local-density approximation (LDA) to the density functional fail to reproduce the insulating antiferromagnetic ground state in the parent compounds of the high-temperature oxide superconductors. Similar problems have been observed earlier in classical transition-metal oxides such as FeO, CoO, and NiO. In this work we present the method which delivers the correct insulating antiferromagnet ground state in the correlated oxides preserving other properties as well as the efficiency of the standard LDA. The method embeds the relevant (for a given system of electrons) part of the Hubbard Hamiltonian into the Kohn-Sham LDA equation. The resulting Hamiltonian attempts to fix two intrinsic problems of the LDA: the deficiency in forming localized (atomiclike) moments and the lack of discontinuity of the effective one-particle potential when going from occupied to unoccupied states. We present the detailed study of ${\mathrm{La}}_2$${\mathrm{CuO}}_4$ and ${\mathrm{LaCuO}}_3$. In the case of ${\mathrm{La}}_2$${\mathrm{CuO}}_4$ the energy gap and the value of the localized magnetic moment in the stable insulating antiferromagnetic solution are in good agreement with experiment. We compare our results with standard local spin density approximation calculation and multiband Hubbard model calculations, as well as with results of spectroscopy: inverse photoemission, valence photoemission, and x-ray absorption at the K edge of oxygen. In the case of ${\mathrm{LaCuO}}_3$ such an extensive comparison is limited due to the limited data available for this compound. We discuss, however, the electric and magnetic properties and the insulator-metal-insulator transitions upon increase of oxygen deficiency.

We present the results of the LMTO-CPA-LDA calculations of the electronic structure and thermodynamic properties of random Al-Li alloys. In order to take into account the charge-transfer and local-environment effects, we use a simple and physically transparent model for the Madelung potential and energy in the single-site coherent-potential approximation. As a result, all calculated ground-state properties are in good agreement with experimental data. The use of the high-temperature relation between Poisson’s ratio and the Grüneisen constant allows us to calculate the thermal and elastic properties of random Al-Li alloys without any adjustable parameters on the basis of the binding-energy curves at 0 K.

We report x-ray-absorption spectra at the oxygen K edge for ${\mathrm{LaNi}}_{1\mathrm{-}\mathit{x}}$${\mathit{M}}_{\mathit{x}}$${\mathrm{O}}_3$ (M=Mn, Fe, and Co) for values of x spanning the entire composition range which exhibit metal-insulator transitions at critical values of x. This study clearly shows that the metal-insulator transition in the homovalent substituted series is achieved by transferring hole states from near ${\mathit{E}}_{\mathit{F}}$ to an energy position above ${\mathit{E}}_{\mathit{F}}$ due to the potential of the substituent. This is in strong contrast to hole doping, e.g., as in ${\mathrm{La}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{MnO}}_3$, where states are formed within the band gap of the underlying electronic structure. The sensitivity of the O K-edge spectra to substitution confirms the large oxygen 2p admixture to states at the Fermi level due to a substantial hopping interaction strength between the transition-metal 3d and oxygen 2p derived states in these perovskite oxides. The present results suggest that the electronic structures of these perovskite oxides are dominated by local interactions.

The piezomodulated and photomodulated reflectivity spectra of monoisotopic Ge ${(}^{70}$Ge, ${}_{}{}^{73}{}_{}{}^{}\mathrm{Ge}$, ${}_{}{}^{74}{}_{}{}^{}\mathrm{Ge}$, ${}_{}{}^{76}{}_{}{}^{}\mathrm{Ge}$) and natural Ge measured at T=6 K show clear signatures of the ${\mathit{E}}_0$ and the ${\mathit{E}}_0$+${\mathrm{\Delta }}_0$ transitions; their energies increase with increasing isotopic mass. From a comparison of the phonon-assisted indirect transition energies obtained from electromodulated and wavelength-modulated transmission and photoluminescence, the isotopic mass dependence of both the indirect gap and the relevant zone-boundary phonons are deduced. The isotopic-mass dependence of the energy gaps is interpreted in the context of the electron-phonon interaction and the volume expansion of the crystal lattice.

We present ab initio quantum-mechanical molecular-dynamics simulations of the liquid-metal–amorphous-semiconductor transition in Ge. Our simulations are based on (a) finite-temperature density-functional theory of the one-electron states, (b) exact energy minimization and hence calculation of the exact Hellmann-Feynman forces after each molecular-dynamics step using preconditioned conjugate-gradient techniques, (c) accurate nonlocal pseudopotentials, and (d) Nosé dynamics for generating a canonical ensemble. This method gives perfect control of the adiabaticity of the electron-ion ensemble and allows us to perform simulations over more than 30 ps. The computer-generated ensemble describes the structural, dynamic, and electronic properties of liquid and amorphous Ge in very good agreement with experiment. The simulation allows us to study in detail the changes in the structure-property relationship through the metal-semiconductor transition. We report a detailed analysis of the local structural properties and their changes induced by an annealing process. The geometrical, bonding, and spectral properties of defects in the disordered tetrahedral network are investigated and compared with experiment.

The Zeeman behavior of shallow donors in silicon has been investigated within the framework of the effective-mass theory. A numerical approach has been used to calculate the wave functions on a discrete radial mesh by the Lanzcos method. The Zeeman Hamiltonian has been evaluated in a limited basis set of zero-field wave functions resulting in an accurate description of the lowest excited states up to fields of about 6 T. In order to describe the Zeeman behavior of the higher excited states, magnetic-field-dependent wave functions have been calculated and used as a basis for the residual coupling terms in the Zeeman Hamiltonian. The results of our calculations are compared with experimental data on magnesium- and phosphorus-doped silicon.

The microstructure of ${\mathrm{SnO}}_2$, prepared by the sol-gel method, was studied by scanning electron microscopy, transmission electron microscopy, high-resolution electron microscopy, and x-ray diffraction. A nanosponge structure was observed. There is much surface and interface structure. The interfaces vary in type from amorphous to crystalline. The high density of defects greatly influences the physical and chemical properties of this material.

Ga vacancies are believed to mediate self-diffusion of Ga and diffusion of substitutional impurities residing on the Ga sublattice in GaAs. We present results of first-principles calculations for the vacancy-mediated diffusion of Si and Ga. We show that a DX-like mechanism facilitates the migration of lattice site atoms into the interstitial region and that the dangling bonds of a second-nearest-neighbor vacancy assist migration through the interstitial region. Due to these two mechanisms vacancy-assisted diffusion of both Ga and Si occurs with a low-energy barrier.

Small-polaron formation is studied for a disordered multidimensional version of Holstein’s molecular-crystal model (MCM). The MCM is appropriate for the study of polaronic effects in covalent semiconductors, where the electron-lattice interactions are short ranged. Our considerations focus on the ‘‘adiabatic’’ regime since it prevails in most semiconductors. In this domain the near-neighbor electronic-transfer energies are much greater than the characteristic phonon energy. We consider a situation in which the characteristic near-neighbor electronic-transfer energy ${\mathit{t}}_0$ and the small-polaron binding energy ${\mathit{E}}_{\mathit{b}}$ are such that the stable carriers in a crystal would be quasifree rather than small polarons: ${\mathit{zt}}_0$>${\mathit{E}}_{\mathit{b}}$, where z is the number of nearest neighbors. We then address how disordering of the transfer energies affects small-polaron formation. In particular, disorder is taken to replace ${\mathit{t}}_0$ with a distribution of electronic-transfer energies. Small electronic-transfer energies about some sites by themselves stabilize small-polaron formations at these sites. Moreover, stabilization of a small polaron at a site is found to foster the stabilization of a small polaron at sites adjacent to it. This effect enhances the effectiveness with which disorder can trigger the collapse of a steady-state carrier from being quasifree to being a small polaron. That is, disorder reduces the strength of the electron-lattice coupling needed to stabilize global small-polaron formation. With the stabilization of small-polaronic carriers, the electronic transport changes from being that of quasifree carriers (that may occasionally be trapped at small-polaronic sites) to small-polaron hopping.

On the basis of the line-shape theory introduced by the isolation-projection technique, we calculate the cyclotron-resonance half-linewidths for intravalley-deformation-potential scattering in the quantum limit. For comparison of the theoretical values with the experimental data, the effective deformation-potential constant (${\mathit{E}}_1$) is chosen as the fitting parameter, as in the works of Bagguley, Flaxen, and Stradling [Phys. Lett. 1, 111 (1962)], Stradling and Zhukov [Proc. Phys. Soc. 87, 263 (1966)], Ito, Kawamura, and Fukai [Phys. Lett. 13, 26 (1964)], and Murase, Enjouji, and Otsuka [J. Phys. Soc. Jpn. 29, 1248 (1970)]. In the best fitting, we obtain ${\mathit{E}}_1$=12.7 eV for Ge and ${\mathit{E}}_1$=7.90 eV for Si, which are similar to the values obtained by the other authors. In the quantum limit, the half-linewidths in Ge and Si are in good agreement with the experimental data of Kobori, Ohyama, and Otsuka [J. Phys. Soc. Jpn. 59, 2141 (1990)], except for the extremely low-temperature region.

The recombination processes of excitonic complexes in undoped and Ni-activated CdS crystals are investigated by means of time-resolved photoluminescence spectroscopy at liquid-He temperatures. The free-exciton recombination is found to be dominated by trapping at impurities, making the free-exciton lifetime a sensitive measure of crystal purity. Bound-exciton lifetimes in the ps region are observed which increase with increasing binding energy of the complex and are altered by the Ni doping. Calculations on the basis of the model of Rashba and Gurgenishvili show that competing nonradiative Auger-recombination processes can be neglected in undoped CdS. In Ni-doped samples a pronounced reduction of the excitonic lifetimes is found and attributed to energy-transfer processes. The deep Ni center offers an additional nonradiative recombination channel for bound-exciton complexes, which is assigned to ‘‘deep-center Auger processes’’ exciting charge-transfer transitions of Ni. Additionally, a bound-exciton complex with a binding energy of 13 meV is found to be related to the Ni doping. This complex is attributed to an exciton bound to a Ni-related neutral acceptor formed by the deep substitutional Ni acceptor paired with a shallow donor. The results demonstrate the possibility of the formation of shallow bound-exciton complexes at transition-metal centers.

The tight-binding theory of defects by Hjalmarson et al. [Phys. Rev. Lett. 44, 810 (1980)] is used to calculate the wave function of an electron localized near the ${\mathrm{P}}_{\mathrm{Ga}}$ antisite in GaP. The effect of the defect potential is extended to the nearest-neighbor sites, including the effects of lattice relaxation around the antisite phosphorous. From the calculated wave function, the hyperfine interaction of an electron with a P or a Ga nucleus near the defect is obtained and compared with electron-spin-resonance data and optically detected magnetic-resonance data. Good agreement is obtained for antisite phosphorus and nearest-neighbor atoms. The effects of lattice relaxation on the defect energy level, the wave function, and the hyperfine-interaction constants are discussed. The outward relaxation of nearest-neighbor atoms was determined to be 21% of the bond length.

A detailed study of the implantation-induced damage in Si on sapphire, carried out by optical-absorption measurements extending from energies above the band gap down to energies far into the subgap region of Si, is presented. The changes induced in the optical band gap, band-edge slopes, and in the subgap features of the spectra are carefully described. The various stages of formation and quenching of divacancies were monitored as a function of implantation conditions and annealing cycles through their 1.8-μm absorption band. It is shown that the divacancies strongly affect the population of band-tail states and the annealing studies revealed that the progressive quenching of the divacancy band is followed by the appearance of another absorption band, characteristic of some intrinsic secondary defect, whose annealing behavior is similar to the one observed for the five-vacancy electron-paramagnetic-resonance spectrum. The study of the structural relaxation process in implanted a-Si gave indications that the process is indeed associated with annihilation of defects as well as average strain reduction in the material, in agreement with earlier indications. Finally, some common features, such as band-edge inverse-logarithmic slope values and subgap features, are found in annealed implanted crystalline and a-Si.

The perturbed-angular-correlation (PAC) technique has been applied to the study of the internal electric-field gradients (EFG) in Yb, Y, and Dy sesquioxides. The ${}_{}{}^{181}{}_{}{}^{}\mathrm{Ta}$ PAC probes were introduced in the oxide lattices by means of ${}_{}{}^{181}{}_{}{}^{}\mathrm{Hf}$ implantation, which decays to the Ta impurity by β emission. The tracer ${}_{}{}^{181}{}_{}{}^{}\mathrm{Ta}$ was used and the results were compared to those obtained in bixbyite structure compounds using ${}_{}{}^{111}{}_{}{}^{}\mathrm{Cd}$ as a probe. The measured EFG are essentially independent from the probe, reflecting the structure characteristics of both crystalline sites in these compounds. In the case of ${}_{}{}^{181}{}_{}{}^{}\mathrm{Hf}_{}^{4+}{}_{}{}^{}$ and ${}_{}{}^{181}{}_{}{}^{}\mathrm{Ta}_{}^{5+}{}_{}{}^{}$, charge compensation (the cations are 3+) seems to be accomplished through a uniform distribution of the probe’s extra electrons in the neighboring oxygen anions. Comparisons of the results to point-charge model predictions are also discussed.

Spontaneous ordering of III-V alloys is known to cause a band-gap reduction ‖Δ${\mathit{E}}_{\mathit{g}}$‖ and a splitting Δ${\mathit{E}}_{12}$ of the valence-band maximum. Strain also leads to a valence-band splitting and, depending on the sign of the strain ε, to an increase (for ε<0) or decrease (for ε>0) in the band gap. We present a general theory explaining how the strain produced by lattice mismatch with the substrate interacts with ordering effects. We find for (001) strain and (111) ‘‘CuPt’’ ordering that (i) atomic ordering removes the cusp in the band gap vs strain curve of random alloys; (ii) epitaxial strain always leads to an increase in the ordering-induced valence-band splitting Δ${\mathit{E}}_{12}$; (iii) atomic ordering reduces the slope of Δ${\mathit{E}}_{12}$ vs strain; (iv) while (a) strain, (b) ordering, and (c) clustering can all lead to a band-gap reduction, we show here that the three effects can be partially distinguished on the basis of a Δ${\mathit{E}}_{12}$ vs ‖Δ${\mathit{E}}_{\mathit{g}}$‖ plot; (v) the wave-function type at the valence-band maximum (VBM) (and, hence, the cause of the splitting) can be further determined by measuring the polarization dependence of the intensities of the transitions between the VBM split components and the conduction-band minimum; (vi) we predict that ordering can significantly enhance the degree of spin polarization of photoelectrons emitted from the VBM. Ordered III-V alloys can thus be used as a good polarized electron source. These general results open avenues of band-gap engineering by combining epitaxial strain with atomic ordering. Specific experimentally testable predictions are presented.

A general treatment for finding the energy levels of electrons and holes in a system with slowly varying inhomogeneous strain is given in the envelope-function approximation. An eight-band model is derived, then block diagonalized to 2×2 and 6×6 for the conduction and valence bands, respectively. To first order, i.e., in the so-called effective-mass approximation, the gradient of the strain tensor does not appear in the Hamiltonian; in the second-order approximation, both the strain variation of the effective masses and the gradients of the strain tensor appear. The second-order effect can be significant within the range of applicability of the theory when the strain is not sufficiently small and its variation is not sufficiently slow. The general theory is first applied to the case of homogeneous strain (for the conduction band), which gives the strain dependence of the band structure, with comparison to previous work. The theory is then applied to laterally strain-confined quantum wells, with the first-order approximation. In the strain-confined system, the valence band is treated by four simultaneous envelope-function equations. Under certain conditions, they can be reduced to a pair of independent equations. Numerical results for the energy levels in a specific quantum wire are given. In the strain-confined system, the conditions under which the second-order effect could be significant are discussed.

Excitonic properties of ZnSe/${\mathrm{ZnS}}_{0.18}$${\mathrm{Se}}_{0.82}$ strained-layer superlattices have been investigated by means of one- and two-photon absorption spectroscopy. Heavy- and light-hole excitons associated with n=1,2 subbands have been observed and experimental evidence of 2s states in these systems has been obtained. Experimental exciton transition energies have been found to be in good agreement with theoretical predictions considering strain and confinement effects. The different selection rules governing linear and nonlinear absorption processes have been verified and some violations of them have been observed. Furthermore, exciton binding energy has been measured and compared with the result of a recent theoretical model.

The symmetry properties of surface second-harmonic generation (SHG) have been studied for compound semiconductor materials, such as GaAs, in which the nonlinear susceptibility of the bulk does not vanish. The rotation-angle dependence (anisotropy) of the intensity of surface-reflection SHG for singular as well as vicinal surfaces, with and without surface tensor components, was examined and compared with the existing experimental results.

The dependence of optical four-wave-mixing (FWM) signals in semiconductors on carrier density and laser-field polarization is investigated. The theoretical and experimental analysis reveals the importance of the excitation-induced dephasing processes for the understanding of numerous published results on polarization selections rules in FWM signals. Even apparently contradictory earlier findings can be explained with this theoretical model.