Showing papers in "Physical Review B in 1988"

Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density

Abstract: A correlation-energy formula due to Colle and Salvetti [Theor. Chim. Acta 37, 329 (1975)], in which the correlation energy density is expressed in terms of the electron density and a Laplacian of the second-order Hartree-Fock density matrix, is restated as a formula involving the density and local kinetic-energy density. On insertion of gradient expansions for the local kinetic-energy density, density-functional formulas for the correlation energy and correlation potential are then obtained. Through numerical calculations on a number of atoms, positive ions, and molecules, of both open- and closed-shell type, it is demonstrated that these formulas, like the original Colle-Salvetti formulas, give correlation energies within a few percent.

New empirical approach for the structure and energy of covalent systems

Abstract: Empirical interatomic potentials permit the calculation of structural properties and energetics of complex systems. A new approach for constructing such potentials, by explicitly incorporating the dependence of bond order on local environment, permits an improved description of covalent materials. In particular, a new potential for silicon is presented, along with results of extensive tests which suggest that this potential provides a rather realistic description of silicon. The limitations of the potential are discussed in detail.

Effective Hamiltonian for the superconducting Cu oxides

Abstract: Although assuming that doping creates holes primarily on oxygen sites, we derive explicitly a single-band effective Hamiltonian for the high-${T}_{c}$ Cu-oxide superconductors. Cu-O hybridization strongly binds a hole on each square of O atoms to the central ${\mathrm{Cu}}^{2+}$ ion to form a local singlet. This moves through the lattice in a similar way as a hole in the single-band effective Hamiltonian of the strongly interacting Hubbard model.

X-ray and neutron scattering from rough surfaces

Abstract: The scattering of x rays and neutrons from rough surfaces is calculated. It is split into specular reflection and diffuse scattering terms. These are calculated in the first Born approximation, and explicit expressions are given for surfaces whose roughness can be described as self-affine over finite length scales. Expressions are also given for scattering from liquid surfaces, where it is shown that ``specular'' reflections only exist by virtue of a finite length cutoff to the mean-square height fluctuations. Expressions are also given for the scattering from randomly oriented surfaces, as studied in a typical small-angle scattering experiment. It is shown how various well-known asymptotic power laws in S(q) are obtained from the above theory. The distorted-wave Born approximation is next used to treat the case where the scattering is large (e.g., near the critical angle for total external reflection), and its limits of validity are discussed. Finally, the theory is compared with experimental results on x-ray scattering from a polished Pyrex glass surface.

Microscopic structure of the SiO 2 /Si interface

Abstract: The bonding of Si atoms at the SiO2/Si interface is determined via high-resolution core level spectroscopy with synchrotron radiation. For oxides grown in pure O2, the SiO2/Si interface is found to contain Si atoms in intermediate oxidation states with a density of 1.5 ± 0.5 × 1015 cm−2. From the density and distribution of intermediate oxidation states, models of the interface structure are obtained. The interface is not abrupt, as evidenced by the non-ideal distribution of intermediate oxidation states and their high density (about 2 monolayers of Si). The finite width of the interface is explained by the bond density mismatch between SiO2 and Si. Annealing in H2 is found to influence the electrical parameters by removing the Pb centers that pin the Fermi level. The distribution of intermediate oxidation states is not affected.

Electronic structure of Cu2O and CuO

Abstract: The electronic structure of copper oxides has been investigated by photoelectron (x-ray photoemission, ultraviolet photoemission), Auger electron, and bremsstrahlung isochromat spectroscopies. The experimental results are compared with one-electron band-structure calculations as well as with a cluster configuration interaction model. It is demonstrated that the results for ${\mathrm{Cu}}_{2}$O agree well with band theory, whereas those for CuO clearly show strong deviations which we argue are due to electron-correlation effects in the open-shell $d$ bands. From the comparison to cluster calculations we extract values for the $\mathrm{Cu} d\ensuremath{-}d$ and $\mathrm{O} p\ensuremath{-}p$ Coulomb interactions, the O to Cu charge transfer energy, and the degree of $\mathrm{Cu} d\ensuremath{-}\mathrm{O} 2p$ hybridization. From this we demonstrate that CuO is a charge-transfer gap insulator.

Empirical interatomic potential for silicon with improved elastic properties.

Abstract: An alternative parametrization is given for a previous empirical interatomic potential for silicon. The new potential is designed to more accurately reproduce the elastic properties of silicon, which were poorly described in the earlier potential. The properties of liquid Si are also improved, but energies of surfaces are less accurate. Detailed tests of the new potential are described.

Absence of backscattering in the quantum Hall effect in multiprobe conductors

Abstract: Under certain conditions, high magnetic fields in a two-dimensional conductor lead to a suppression of both elastic and inelastic backscattering. This, together with the formation of edge states, is used to develop a picture of the integer quantum Hall effect in open multiprobe conductors. We consider both ideal contacts without elastic scattering and also disordered contacts. Ideal contacts populate edge states equally whereas disordered contacts lead to an initial nonequilibrium population of the edge states. In Hall samples much larger than an inelastic length, and in the presence of disordered contacts, the sample edges become equipotential lines only an inelastic scattering length away from the current source and current drain contacts. Samples so small that the carriers can travel from one contact to the other without inelastic relaxation do not exhibit exact quantization if the contacts are disordered. In all cases we find that the quantum Hall effect occurs only if the sample exhibits at least two sets of equilibrated edge states which do not interact via elastic or inelastic scattering. The onset of interaction between the two sets of edge states leads to deviations from exact quantization and eventually to a breakdown of the quantum Hall effect.

Quantum-size effects of interacting electrons and holes in semiconductor microcrystals with spherical shape

Abstract: Quantum-size effects of an electron-hole system confined in microcrystals of semiconductors are studied theoretically with the spherical-dielectric continuum model. An extensive numerical calculation for the eigenvalue problem is carried out by Ritz's variational technique. The motional state of the lowest level is classified into three regimes: the regime of exciton confinement for R/${a}_{B}^{\mathrm{*}}$\ensuremath{\gtrsim}4, the regime of individual particle confinement for R/${a}_{B}^{\mathrm{*}}$\ensuremath{\lesssim}2, and the intermediate regime for 2\ensuremath{\lesssim}R/${a}_{B}^{\mathrm{*}}$\ensuremath{\lesssim}4, where R is the radius of the quantum well and ${a}_{B}^{\mathrm{*}}$ is the exciton Bohr radius. In the region R/${a}_{B}^{\mathrm{*}}$\ensuremath{\gtrsim}4, the high-energy shift of the lowest exciton state is described by the rigid-sphere model of the exciton quite well, which takes into account the spatial extension of the relative motion of the electron and the hole. The oscillator strength of the interband optical transition changes dramatically across the region 2\ensuremath{\lesssim}R/${a}_{B}^{\mathrm{*}}$\ensuremath{\lesssim}4. The metamorphosis of the absorption spectrum is shown as a function of R/${a}_{B}^{\mathrm{*}}$ and compared with the experimental data.

Self-energy operators and exchange-correlation potentials in semiconductors

Abstract: We show how the density-functional theory (DFT) exchange-correlation potential ${V}_{\mathrm{xc}(\mathrm{r}}$) of a semiconductor is calculated from the self-energy operator \ensuremath{\Sigma}(r,r',\ensuremath{\omega}), and how \ensuremath{\Sigma} is obtained using the one-particle Green's function and the screened Coulomb interaction (the GW approximation). We discuss the nature of ${V}_{\mathrm{xc}}$ and the self-energy in real space, and investigate features and trends found in Si, GaAs, AlAs, and diamond. In each case the calculated quasiparticle band structure is in good agreement with experiment, while the DFT band structure is surprisingly similar to that with the common local-density approximation (LDA); in particular, about 80% of the severe LDA band-gap error is shown to be inherent in DFT calculations, being accounted for by the discontinuity \ensuremath{\Delta} in ${V}_{\mathrm{xc}}$ upon addition of an electron. The relationship of the calculated ${V}_{\mathrm{xc}}$ to the LDA and its extensions is also examined.

Monte carlo analysis of electron transport in small semiconductor devices including band-structure and space-charge effects

Abstract: The physics of electron transport in Si and GaAs is investigated with use of a Monte Carlo technique which improves the "state-of-the-art" treatment of high-energy carrier dynamics. (1) The semiconductor is modeled beyond the effective-mass approximation by using the band structure obtained from empirical-pseudopotential calculations. (2) The electron-phonon, electron-impurity, and electron-electron scattering rates are computed in a way consistent with the full band structure of the solid, thus accounting for density-of-states and matrix-element effects more accurately than previous transport formulations. (3) The long-range carrier-carrier interaction and space-charge effects are included by coupling the Monte Carlo simulation to a self-consistent two-dimensional Poisson solution updated at a frequency large enough to resolve the plasma oscillations in highly doped regions. The technique is employed to study experimental submicrometer Si field-effect transistors with channel lengths as small as 60 nm operating at 77 and 300 K. Velocity overshoot and highly nonlocal, off-equilibrium phenomena are investigated together with the role of electron-electron interaction in these ultrasmall structures. In the systems considered, the inclusion of the full band structure has the effect of reducing the amount of velocity overshoot via electron transfer to upper conduction valleys, particularly at large biases and low temperatures. The reasonableness of the physical picture is supported by the close agreement of the results of the simulation to available experimental data.

Band-gap tailoring of ZnO by means of heavy Al doping

Abstract: Films of ZnO:Al were produced by weakly reactive dual-target magnetron sputtering. Optical band gaps, evaluated from spectrophotometric data, were widened in proportion to the Al doping. The widening could be quantitatively reconciled with an effective-mass model for n-doped semiconductors, provided the polar character of ZnO was accounted for.

Large- n limit of the Heisenberg-Hubbard model: Implications for high- T c superconductors

Abstract: The Heisenberg-Hubbard model is solved in the large-n limit to gain insight into its relevance to the coppper-oxide materials. A gapless disordered ground state is found for the Heisenberg model. Electronically induced orthorhombic-tetragonal symmetry breaking is observed as a function of doping, with the greatest tendency towards superconductivity occurring in the orthorhombic phase.

Structural and physical properties of the metal (M) substituted YBa2Cu3-xMxO7-y perovskite.

Abstract: The mixed ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{M}}_{\mathrm{x}}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{y}}$ (M=Ni, Zn, Fe, Co, and Al) phases have been characterized for their structural, magnetic, and superconducting properties. The oxygen content in these phases is dependent on the nature and the amount of doping, especially for Co and Fe. The material remains orthorhombic when Cu is replaced by Ni or Zn whereas it evolves to tetragonal symmetry for the Fe-, Co-, and Al-doped compounds when x exceeds 0.05. Evidence for the major substitution of Co in the Cu-O chains only is obtained by means of thermogravimetric analysis and neutron diffraction measurements. The room-temperature M\"ossbauer spectra of the Fe-doped compounds consist of three doublets; their site assignments are proposed. dc resistance and ac susceptibility have shown that both magnetic and diamagnetic ions destroy ${T}_{c}$ in a similar manner. At x=0.2 the Fe and Co compounds are tetragonal, superconduct at 50 K, and show a Curie-type magnetic behavior associated with a magnetic moment of 3.4${\ensuremath{\mu}}_{B}$ per doping atom. The origin of the orthorhombic-tetragonal transition and the importance of the Cu-O chains for superconductivity is discussed. The behavior of these materials with respect to magnetic impurities is apparently different from conventional Bardeen-Cooper-Schrieffer-type superconductors, and we believe that any new mechanism proposed must be mostly sensitive to local structural disorder.

Calculated thermal properties of metals.

Abstract: The thermal properties of the 14 nonmagnetic cubic metals through the 4d transition series are derived from first-principles electronic-structure calculations coupled with a Debye treatment of the vibrating lattice. Debye temperatures and Gr\"uneisen constants are derived from an analysis of the compressional characteristics of rigid-lattice binding curves and are used to define the contribution of the lattice vibrations to the free energy. A minimization of the resulting free energy with respect to volume yields temperature-dependent lattice separations and coefficients of thermal expansion. Theoretical values of cohesive energies, equilibrium lattice separations, bulk moduli, Debye temperatures, Gr\"uneisen constants, and coefficients of thermal expansion are derived directly from computed electronic-structure results. Good agreement with experiment is found for all computed quantities.

Quantitative analysis of the effect of disorder-induced mode coupling on infrared absorption in silica.

Abstract: The infrared-absorption spectrum of a-${\mathrm{SiO}}_{2}$ is analyzed in terms of its transverse-optic (TO) and longitudinal-optic (LO) vibrational modes. It is shown that the independent-oscillator model for the a-${\mathrm{SiO}}_{2}$ dielectric function fails to yield a consistent value of mode strength for the optically active oxygen asymmetric stretch (${\mathrm{AS}}_{1}$) TO mode at 1076 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ (in-phase motion of adjacent oxygen atoms) when different but equivalent methods of measurement and analysis are used. This inconsistency is resolved by introducing disorder-induced mechanical coupling between the ${\mathrm{AS}}_{1}$ mode and the relatively optically inactive oxygen asymmetric stretch (${\mathrm{AS}}_{2}$) mode (out-of-phase motion of adjacent oxygen atoms) into the oscillator model. Coupled ${\mathrm{AS}}_{1}$- and ${\mathrm{AS}}_{2}$-mode LO-TO frequency pairs are experimentally observed as peaks at approximately 1256--1076 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ and 1160--1200 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, respectively, in oblique-incidence p-polarized absorption spectra of thin a-${\mathrm{SiO}}_{2}$ films grown thermally on c-Si wafers.Additionally, two other LO-TO-mode pairs are observed in these spectra as absorption peaks at approximately 820--810 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ and 507--457 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. The simplest form of the coupled-mode model consistent with experiment is found to be one in which the ${\mathrm{AS}}_{1}$-mode LO-TO frequency splitting is due to the ${\mathrm{AS}}_{1}$ transverse effective charge and the ${\mathrm{AS}}_{2}$-mode LO-TO splitting is due to the mechanical coupling between these two modes and not to the ${\mathrm{AS}}_{2}$ transverse effective charge, which is negligibly small. The ${\mathrm{AS}}_{2}$ TO and the ${\mathrm{AS}}_{1}$ LO modes found at approximately 1200 and 1256 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, respectively, are shown to be consistent with experimental mode strengths and with the analytic requirements that all LO and TO modes be interspersed and that, as a result of lying between the ${\mathrm{AS}}_{1}$-mode LO-TO pair frequencies, the ${\mathrm{AS}}_{2}$-mode LO-TO frequency splitting be inverted. Comparison of these experimental LO-TO-mode pair frequencies with the vibrational density of states (VDOS) spectrum of a-${\mathrm{SiO}}_{2}$ shows that the TO absorption peaks correspond quite well with the VDOS spectral peaks, whereas the LO absorption peaks do not appear to exhibit any such correspondence.

Nonequilibrium dynamics of spin glasses.

Abstract: We consider the nonequilibrium behavior of the spin-glass ordered phase within the droplet scaling theory introduced previously. The fundamental long-time nonequilibrium process is assumed to be the thermally activated growth of spin-glass ordered domains. The remanent magnetization, m(t), in zero field is found to decay at long times as m(t)\ensuremath{\sim}${R}_{t}^{\mathrm{\ensuremath{-}}\ensuremath{\lambda}}$, where ${R}_{t}$\ensuremath{\sim}(lnt${)}^{1/\ensuremath{\psi}}$ is the linear domain size, \ensuremath{\psi} is the previously introduced barrier exponent describing the growth of activation-barrier heights with length scale, and \ensuremath{\lambda} is a new nonequilibrium dynamic exponent, satisfying the relation \ensuremath{\lambda}\ensuremath{\ge}d/2 for d-dimensional systems. The effects of waiting for partial equilibration before making a measurement are studied in various regimes. The effects of quenching first to one temperature and then to another are also examined. Such experiments can, in principle, be used to obtain information about the relative rate of dynamic evolution as well as the overlap between the equilibrium states at different temperatures. In particular, the length scale ${L}_{\ensuremath{\Delta}T}$, below which equilibrium correlations at temperatures T and T+\ensuremath{\Delta}T are similar, plays an important role. The decay of m(t) and the growth of spin-glass order after a quench are examined in Monte Carlo simulations of the Sherrington-Kirkpatrick model.

Analytic nearest-neighbor model for fcc metals

Abstract: The implications of the mathematical format of the embedded-atom method of computer modeling of metals have been studied with use of a simple nearest-neighbor analytic model for the fcc lattice. The physical inputs into the model are the atomic volume, the cohesive energy, the bulk modulus, the average shear modulus, the vacancy-formation energy, and the slope at the nearest-neighbor distance of the spherically averaged free-atom electron density calculated with Hartree-Fock theory. The model employs an exponential repulsion between nearest-neighboring atoms, an exponentially decreasing function for the free-atom electron density, and a universal equation relating the crystal energy and the lattice constant. The anisotropy ratio of the cubic shear moduli is constrained to be 2 with this model. The dependence of the energies for unrelaxed configurations for vacancy formation, divacancy binding, and low-index plane surfaces on the model parameters has been analyzed. The average shear modulus plays a dominant role in determining these energies relative to the bulk modulus or the cohesive energy because the slope of the embedding function at the equilibrium electron density is linear in the average shear modulus. Embedding functions are not uniquely determined in specific models, and it is shown that the embedding functions used inmore » several models are essentially equivalent.« less

Size effect on the ferroelectric phase transition in PbTiO3 ultrafine particles.

Abstract: We report a size effect on the ferroelectric phase transition in ${\mathrm{PbTiO}}_{3}$ ultrafine particles. The samples were synthesized by an alkoxide method. The size was determined by x-ray analysis with the aid of Scherrer's equation. When the particle size is less than 50 nm, the transition temperature ${T}_{c}$, determined by Raman scattering, decreases from its bulk value (500 \ifmmode^\circ\else\textdegree\fi{}C) as the size decreases. The temperature ${T}_{c}$ is described by an empirical expression, ${T}_{c}$=500-588.5/(D-12.6) (\ifmmode^\circ\else\textdegree\fi{}C), where D is the average particle size (nm).

Anderson localization and interactions in one-dimensional metals.

Abstract: A one-dimensional interacting electron gas in a random potential exhibits a localized-delocalized transition for increasingly attractive interactions. We develop here a renormalization-group approach to study this transition. Our treatment allows us to obtain the phase diagram and the exponents of the correlation functions in the delocalized regime. The boundary between the two regimes is found to depend both on disorder and the strength of the interactions. For (nearly) spin-isotropic interactions the delocalized phase is dominated by superconducting fluctuations of either singlet or triplet type. The temperature dependence of the conductivity in the delocalized phase is also obtained and a nonuniversal power-law behavior is found. A description of the crossover towards the localized phase is given and the localization length is computed. An analogous description is developed for the localized-superfluid transition of a one-dimensional boson gas. In this case the transition to the localized regime occurs for increasingly repulsive interactions. We suggest a phase diagram with two different localized phases. Finally, we discuss some possible implications of our model for real quasi-one-dimensional metals.

Crystal substructure and physical properties of the superconducting phase Bi4(Sr,Cr)6Cu4O16+x.

Abstract: We have isolated a high-T/sub c/ phase in the Bi-Sr-Ca-Cu-O system of composition Bi/sub 4/(Sr,Ca)/sub 6/Cu/sub 4/O/sub 16/..mu../sub x/. The crystal substructure has a tetragonal unit cell (a = 3.817 A, c = 30.6 A) with similarities to both the oxygen-defect perovskites YBa/sub 2/Cu/sub 3/O/sub 7/..sqrt../sub x/ and the K/sub 2/NiF/sub 4/ structure of La/sub 2/CuO/sub 4/. The oxygen content, determined by titration and thermogravimetric analysis (TGA) experiments, corresponds to a formal oxidation state Cu(2.15). Oxygen can be reversibly depleted in an argon ambient in an amount corresponding to the reduction of the Cu(III) into Cu(II). The compound has a metalliclike resistance above its T/sub c/ near 85 K. Processing this precursor compound by heating to temperatures near its melting point (885 /sup 0/C) produces a sharp resistivity drop near 110 K that we show by ac susceptibility and Meissner effect is due to a superconducting transition.

Very large optical nonlinearity of semiconductor microcrystallites

Abstract: We analyze theoretically the oscillator strength and the third-order optical polarizability X 13, due to excitons in semiconductor microcrystallites. The nonlinear optical polarizability is shown to be greatly enhanced for an assembly of such microcrystallites as the exciton is quantized due to the confinement effect and the excitons in a single microcrystallite interact strongly enough to make the excitons deviate from ideal harmonic oscillators.

First-principles study of the atomic reconstructions and energies of Ga- and As-stabilized GaAs(100) surfaces

Abstract: We have carried out ab initio total-energy density-functional calculations to study the reconstructions of GaAs(100) surfaces as a function of Ga and As surface coverage. Equilibrium atomic geometries and energies for Ga- and As-stabilized 1\ifmmode\times\else\texttimes\fi{}1, 2\ifmmode\times\else\texttimes\fi{}1, 1\ifmmode\times\else\texttimes\fi{}2, and 2\ifmmode\times\else\texttimes\fi{}2 surfaces consisting of various combinations of dimers and vacancies were determined. Dimerization of Ga (As) surface atoms is calculated to lower the energy by 1.7 eV (0.7 eV) per dimer and to lead to the most stable atomic configurations. For half-monolayer coverages, relaxation energies are very large, and nondimerized structures are only slightly (0.03--0.05 eV per 1\ifmmode\times\else\texttimes\fi{}1 cell) higher in energy. Asymmetric dimers were tested for As surfaces and found to be higher in energy than symmetric dimers. The stability of surfaces in equilibrium with Ga and As sources is considered and it is shown that the chemical potentials are restricted within limits set by the free energies of the elemental bulk phases of Ga and As. Ab initio calculations of these bulk energies at T=0 K determine the limiting chemical potentials and also the heat of formation, which we find to be 0.73 eV per GaAs pair, compared with the experimental value of 0.74 eV. Our calculations indicate that with excess bulk As available, a full monolayer coverage of As is energetically more favorable than a half-monolayer coverage, whereas with excess Ga available, the surface energy of full and half-monolayer coverages are nearly the same. To examine the effects of larger unit-cell dimensions on total energies, we rely on results from tight-binding calculations. For half-monolayer coverages, 2\ifmmode\times\else\texttimes\fi{}4 unit cells are found to have a significantly lower energy than 2\ifmmode\times\else\texttimes\fi{}2 cells not because of a greater lattice relaxation but because of orbital rehybridization effects which are not possible in a smaller cell. The results of the ab initio and tight-binding calculations indicate that the optimal surface coverage for Ga- and As-terminated surfaces is less than a full monolayer.

Structure and physical properties of single crystals of the 84-K superconductor Bi 2.2 Sr 2 Ca 0.8 Cu 2 O 8+δ

Abstract: Single crystal sof the 84-K superconductor ${\mathrm{Bi}}_{2.2}{\mathrm{Sr}}_{2}{\mathrm{Ca}}_{0.8}{\mathrm{Cu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ were characterized by x-ray diffraction, dc magnetic susceptibility, electrical resistivity, and microwave absorption. The structure has ${[\mathrm{Cu}{\mathrm{O}}_{2}]}_{\ensuremath{\infty}}$ planes separated by calcium atoms, edge-shared bismuth oxide double layers, and an incommensurate superlattice along $b$ with a period of 4.76. The in-plane resistivity above ${T}_{c}$ is linear in $T$, with ${\ensuremath{\rho}}_{\mathrm{RT}}=130$ \ensuremath{\mu}\ensuremath{\Omega} cm. Initial results on Pb substitution yielding ${T}_{c}'\mathrm{s}$ of 107 K are reported.

Three-dimensional vortex dynamics in superfluid He 4 : Homogeneous superfluid turbulence

Abstract: The behavior of a tangle of quantized vortex lines subject to uniform superfluid and normal-fluid driving velocities is investigated. The dynamical equation of the quantized vortices in the local approximation is supplemented by the assumption that when two such singularities cross, they undergo a reconnection. The properties of the dynamical equation, when combined with the assumption of homogeneity, imply numerous scaling relations, which are in fact observed experimentally. The primitive dynamical rules are utilized to perform extensive numerical simulations of the vortex tangle, using not only periodic, but also smooth-wall and rough-wall boundary conditions. All lead to the same homogeneous vortex-tangle state, although the case of periodic boundary conditions requires an additional trick to eliminate artificial features. The quantitative results obtained from these simulations are found to be in excellent absolute agreement with a large variety of experiments, including recent studies of the vortex-tangle anisotropy.

Functional integral theories of low-dimensional quantum Heisenberg models

Abstract: We investigate the low-temperature properties of the quantum Heisenberg models, both ferromagnetic and antiferromagnetic, in one and two dimensions. We study two different large-N formulations, using Schwinger bosons and S=(1/2 fermions, and solve for their low-order thermodynamic properties. Comparison with exact solutions in one dimension demonstrates the applicability of this expansion to the physical models at N=2. For the square lattice, we find at the mean-field level a low-temperature correlation length which behaves as \ensuremath{\xi}\ensuremath{\propto}exp(A/T), where A asymptotically approaches 2\ensuremath{\pi}${S}^{2}$ for large spin S, but ${A}_{S=1/2}$\ensuremath{\simeq}1.16 and ${A}_{S=1}$\ensuremath{\simeq}5.46. We mention the relevance of our results to recent experiments in ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$.

Melt-textured growth of polycrystalline YBa2Cu3O7- delta with high transport Jc at 77 K.

Abstract: The progress toward major applications of ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$-type high-${T}_{c}$ superconductors has been hindered by low critical current densities (${J}_{c}$) and their significant deterioration in weak magnetic fields. The present work demonstrates that these problems can successfully be overcome through proper microstructural control using molten oxide processing. Melt-textured growth of ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ from a supercooled melt created an essentially 100% dense structure consisting of locally aligned, long, needle-shaped grains (typically 40--600 \ensuremath{\mu}m in length). The needles appear to have their long axes parallel to the conduction plane (basal plane) of the orthorhombic structure, with a low-angle orientation change between adjacent grains. This new microstructure, which completely replaces the previous granular and random structure of the sintered precursor, exhibits a dramatically higher transport ${J}_{c}$ (7400 A/${\mathrm{cm}}^{2}$ at 77 K) than the typical sintered materials (${J}_{c}$=150--600 A/${\mathrm{cm}}^{2}$). Even more significant is the much reduced field dependence of ${J}_{c}$(\ensuremath{\approxeq}1000 A/${\mathrm{cm}}^{2}$ at H=1 T as compared to \ensuremath{\approxeq}1 A/${\mathrm{cm}}^{2}$ in the sintered structure), indicating that the coupling between grains is much stronger in the new structure. The mechanism responsible for the suppressed weak-link behavior in the melt-textured material is inferred to be the combined effects of the densification, alignment of crystals, and formation of cleaner grain boundaries.

Modified Broyden’s method for accelerating convergence in self-consistent calculations

Abstract: A modification to Broyden's method for obtaining stable and computationally efficient convergence in self-consistent calculations is developed and discussed. The method incorporates the advantages of two schemes proposed by Srivastava and by Vanderbilt and Louie without any increase in complexity. Its improvement over their methods is discussed. The present method is compared with two other widely used convergence methods, simple mixing and Anderson's method, for the case of the disordered binary alloy ${\mathrm{Ni}}_{0.35}$${\mathrm{Fe}}_{0.65}$ on the verge of a magnetic instability and is shown to be much improved in stability and rate of convergence.

Effective Bloch equations for semiconductors

Abstract: Generalized Bloch equations for laser-excited semiconductors are derived applying quantum-mechanical projection-operator techniques. The equations include phase-space filling and the many-body Coulomb effects. The coherent part of the equations is evaluated for the regime of ultrafast-pump-probe excitation and shown to reduce to the inhomogeneously broadened two-level Bloch equations for the different momentum states if the proper Coulomb enhancement in the density of states is taken into account. For the high-excitation quasithermal regime a generalization of the Elliott formula for the absorption spectrum is derived which is valid not only for bulk semiconductors, but also for quantum-well structures and other systems with reduced spatial dimensions.