Showing papers in "Physical Review B in 1992"

Accurate and simple analytic representation of the electron-gas correlation energy

Abstract: We propose a simple analytic representation of the correlation energy ${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{c}}$ for a uniform electron gas, as a function of density parameter ${\mathit{r}}_{\mathit{s}}$ and relative spin polarization \ensuremath{\zeta}. Within the random-phase approximation (RPA), this representation allows for the ${\mathit{r}}_{\mathit{s}}^{\mathrm{\ensuremath{-}}3/4}$ behavior as ${\mathit{r}}_{\mathit{s}}$\ensuremath{\rightarrow}\ensuremath{\infty}. Close agreement with numerical RPA values for ${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{c}}$(${\mathit{r}}_{\mathit{s}}$,0), ${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{c}}$(${\mathit{r}}_{\mathit{s}}$,1), and the spin stiffness ${\mathrm{\ensuremath{\alpha}}}_{\mathit{c}}$(${\mathit{r}}_{\mathit{s}}$)=${\mathrm{\ensuremath{\partial}}}^{2}$${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{c}}$(${\mathit{r}}_{\mathit{s}}$, \ensuremath{\zeta}=0)/\ensuremath{\delta}${\mathrm{\ensuremath{\zeta}}}^{2}$, and recovery of the correct ${\mathit{r}}_{\mathit{s}}$ln${\mathit{r}}_{\mathit{s}}$ term for ${\mathit{r}}_{\mathit{s}}$\ensuremath{\rightarrow}0, indicate the appropriateness of the chosen analytic form. Beyond RPA, different parameters for the same analytic form are found by fitting to the Green's-function Monte Carlo data of Ceperley and Alder [Phys. Rev. Lett. 45, 566 (1980)], taking into account data uncertainties that have been ignored in earlier fits by Vosko, Wilk, and Nusair (VWN) [Can. J. Phys. 58, 1200 (1980)] or by Perdew and Zunger (PZ) [Phys. Rev. B 23, 5048 (1981)]. While we confirm the practical accuracy of the VWN and PZ representations, we eliminate some minor problems with these forms. We study the \ensuremath{\zeta}-dependent coefficients in the high- and low-density expansions, and the ${\mathit{r}}_{\mathit{s}}$-dependent spin susceptibility. We also present a conjecture for the exact low-density limit. The correlation potential ${\mathrm{\ensuremath{\mu}}}_{\mathit{c}}^{\mathrm{\ensuremath{\sigma}}}$(${\mathit{r}}_{\mathit{s}}$,\ensuremath{\zeta}) is evaluated for use in self-consistent density-functional calculations.

Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation.

Abstract: Generalized gradient approximations (GGA's) seek to improve upon the accuracy of the local-spin-density (LSD) approximation in electronic-structure calculations. Perdew and Wang have developed a GGA based on real-space cutoff of the spurious long-range components of the second-order gradient expansion for the exchange-correlation hole. We have found that this density functional performs well in numerical tests for a variety of systems: (1) Total energies of 30 atoms are highly accurate. (2) Ionization energies and electron affinities are improved in a statistical sense, although significant interconfigurational and interterm errors remain. (3) Accurate atomization energies are found for seven hydrocarbon molecules, with a rms error per bond of 0.1 eV, compared with 0.7 eV for the LSD approximation and 2.4 eV for the Hartree-Fock approximation. (4) For atoms and molecules, there is a cancellation of error between density functionals for exchange and correlation, which is most striking whenever the Hartree-Fock result is furthest from experiment. (5) The surprising LSD underestimation of the lattice constants of Li and Na by 3--4 % is corrected, and the magnetic ground state of solid Fe is restored. (6) The work function, surface energy (neglecting the long-range contribution), and curvature energy of a metallic surface are all slightly reduced in comparison with LSD. Taking account of the positive long-range contribution, we find surface and curvature energies in good agreement with experimental or exact values. Finally, a way is found to visualize and understand the nonlocality of exchange and correlation, its origins, and its physical effects.

Adsorbate-substrate and adsorbate-adsorbate interactions of Na and K adlayers on Al(111)

Abstract: We present total-energy, force, and electronic-structure calculations for Na and K adsorbed in various geometries on an Al(111) surface. The calculations apply density-functional theory together with the local-density approximation and the ab initio pseudopotential formalism. Two adsorbate meshes, namely, (\ensuremath{\surd}3 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}3 )R30\ifmmode^\circ\else\textdegree\fi{} and (2\ifmmode\times\else\texttimes\fi{}2), are considered and for each of them the geometry of the adlayer relative to the substrate is varied over a wide range of possibilities. By total-energy minimization we determine stable and metastable geometries. For Na we find for both adsorbate meshes that the ordering of the calculated binding energies per adatom is such that the substitutional geometry, where each Na atom replaces a surface Al atom, is most favorable and the on-top position is most unfavorable. The (\ensuremath{\surd}3 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}3 )R30\ifmmode^\circ\else\textdegree\fi{} structure has a lower energy than the (2\ifmmode\times\else\texttimes\fi{}2) structure. This is shown to be a substrate effect and not an effect of the adsorbate-adsorbate interaction. In contrast to the results for Na, we find for the (\ensuremath{\surd}3 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}3 )R30\ifmmode^\circ\else\textdegree\fi{} K adsorption that the calculated adsorption energies for the on-top, threefold hollow, and substitutional sites are equal within the accuracy of our calculation, which is \ifmmode\pm\else\textpm\fi{}0.03 eV. The similarity of the energies of the on-surface adsorption sites is explained as a consequence of the bigger size of K which implies that the adatom experiences a rather small substrate electron-density corrugation. Therefore for potassium the on-top and hollow sites are close in energy already for the unrelaxed Al(111) substrate. Because the relaxation energy of the on-top site is larger than that of the threefold hollow site both sites receive practically the same adsorption energy. The unexpected possibility of surface-substitutional sites is explained as a consequence of the ionic nature of the bonding which, at higher coverages, can develop strongest when the adatom can dive into the substrate as deep as possible. The interesting result of the studied systems is that the difference in bond strengths between the ``normal'' and substitutional geometries is sufficiently large to kick out a surface Al atom.

Lower limit to the thermal conductivity of disordered crystals

Abstract: Measurements of the thermal conductivity above 30 K of mixed crystals with controlled disorder, (KBr${)}_{1\mathrm{\ensuremath{-}}\mathit{x}}$(KCN${)}_{\mathit{x}}$, (NaCl${)}_{1\mathrm{\ensuremath{-}}\mathit{x}}$, (NaCn${)}_{\mathit{x}}$ ${\mathrm{Zr}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Y}}_{\mathit{x}}$${\mathrm{O}}_{2\mathrm{\ensuremath{-}}\mathit{x}/2}$, and ${\mathrm{Ba}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{La}}_{\mathit{x}}$${\mathrm{F}}_{2+\mathit{x}}$, support the idea of a lower limit to the thermal conductivity of disordered solids. In each case, as x is increased, the data approach the calculated minimum conductivity based on a model originally due to Einstein. These measurements support the claim that the lattice vibrations of these disordered crystals are essentially the same as those of an amorphous solid.

Modified embedded-atom potentials for cubic materials and impurities

Abstract: In a comprehensive study, the modified embedded-atom method is extended to a variety of cubic materials and impurities. In this extension, all functions are analytic and computationally simple. The basic equations of the method are developed and applied to 26 elements: ten fcc, ten bcc, three diamond cubic, and three gaseous materials. The materials modeled include metals, semiconductors, and diatomic gases, all of which exhibit different types of bonding. Properties of these materials, including equation of state, elastic moduli, structural energies and lattice constants, simple defects, and surfaces, are calculated. The formalism for applying the method to combinations of these elements is developed and applied to the calculation of dilute heats of solution. In all cases, comparison is made to experiment or higher-level calculations when possible.

Electron transport at metal-semiconductor interfaces : general theory

Abstract: A dipole-layer approach is presented, which leads to analytic solutions to the potential and the electronic transport at metal-semiconductor interfaces with arbitrary Schottky-barrier-height profiles. The presence of inhomogeneities in the Schottky-barrier height is shown to lead to a coherent explanation of many anomalies in the experimental results. These results suggest that the formation mechanism of the Schottky barrier is locally nonuniform at common, polycrystalline, metal-semiconductor interfaces.

Electronic structure of graphene tubules based on C 60

Abstract: The electronic structures of some possible carbon fibers nucleated from the hemisphere of a ${\mathrm{C}}_{60}$ molecule are presented. A one-dimensional electronic band-structure model of such carbon fibers, having not only rotational symmetry but also screw axes, is derived by folding the two-dimensional energy bands of graphite. A simple tight-binding model shows that some fibers are metallic and are stable against perturbations of the one-dimensional energy bands and the mixing of \ensuremath{\sigma} and \ensuremath{\pi} bands due to the curvature of the circumference of the fiber.

Surface energy and work function of elemental metals.

Abstract: We have performed an ab initio study of the surface energy and the work function for six close-packed surfaces of 40 elemental metals by means of a Green's-function technique, based on the linear-muffin-tin-orbitals method within the tight-binding and atomic-sphere approximations. The results are in excellent agreement with a recent full-potential, all-electron, slab-supercell calculation of surface energies and work functions for the 4d metals. The present calculations explain the trend exhibited by the surface energies of the alkali, alkaline earth, divalent rare-earth, 3d, 4d, and 5d transition and noble metals, as derived from the surface tension of liquid metals. In addition, they give work functions which agree with the limited experimental data obtained from single crystals to within 15%, and explain the smooth behavior of the experimental work functions of polycrystalline samples as a function of atomic number. It is argued that the surface energies and work functions calculated by present day ab initio methods are at least as accurate as the experimental values.

Theory of the quantum confinement effect on excitons in quantum dots of indirect-gap materials

Abstract: The quantum confinement effect on excitons in quantum dots of indirect-gap materials is investigated and a mechanism that induces an indirect-to-direct conversion of the character of the optical transition is clarified. The exciton transition energy and the exciton binding energy are calculated and found to be in good agreement with experimental results on Si and Ge nanostructures. The large exciton binding energy in Si and Ge quantum dots suggests that the photoluminescence from these nanostructures is of excitonic origin even at room temperature. The estimated radiative lifetime of excitons is strongly size dependent and varies from nanosecond to millisecond corresponding to the diameter from \ensuremath{\sim}10 to \ensuremath{\sim}30 \AA{}. These theoretical results suggest strongly the importance of the quantum confinement effect in the luminescence processes of porous Si.

Zinc-blende-wurtzite polytypism in semiconductors.

Abstract: The zinc-blende (ZB) and wurtzite (W) structures are the most common crystal forms of binary octet semiconductors. In this work we have developed a simple scaling that systematizes the T=0 energy difference \ensuremath{\Delta}${\mathit{E}}_{\mathrm{W}\mathrm{\ensuremath{-}}\mathrm{ZB}}$ between W and ZB for all simple binary semiconductors. We have first calculated the energy difference \ensuremath{\Delta}${\mathit{E}}_{\mathrm{W}\mathrm{\ensuremath{-}}\mathrm{ZB}}^{\mathrm{LDF}}$(AB) for AlN, GaN, InN, AlP, AlAs, GaP, GaAs, ZnS, ZnSe, ZnTe, CdS, C, and Si using a numerically precise implementation of the first-principles local-density formalism (LDF), including structural relaxations. We then find a linear scaling between \ensuremath{\Delta}${\mathit{E}}_{\mathrm{W}\mathrm{\ensuremath{-}}\mathrm{ZB}}^{\mathrm{LDF}}$(AB) and an atomistic orbital-radii coordinate R\ifmmode \tilde{}\else \~{}\fi{}(A,B) that depends only on the properties of the free atoms A and B making up the binary compound AB. Unlike classical structural coordinates (electronegativity, atomic sizes, electron count), R\ifmmode \tilde{}\else \~{}\fi{} is an orbital-dependent quantity; it is calculated from atomic pseudopotentials. The good linear fit found between \ensuremath{\Delta}${\mathit{E}}_{\mathrm{W}\mathrm{\ensuremath{-}}\mathrm{ZB}}$ and R\ifmmode \tilde{}\else \~{}\fi{} (rms error of \ensuremath{\sim}3 meV/atom) permits predictions of the W-ZB energy difference for many more AB compounds than the 13 used in establishing this fit. We use this model to identify chemical trends in \ensuremath{\Delta}${\mathit{E}}_{\mathrm{W}\mathrm{\ensuremath{-}}\mathrm{ZB}}$ in the IV-IV, III-V, II-VI, and I-VII octet compounds as either the anion or the cation are varied. We further find that the ground state of MgTe is the NiAs structure and that CdSe and HgSe are stable in the ZB form. These compounds were previously thought to be stable in the W structures.

Transmission through barriers and resonant tunneling in an interacting one-dimensional electron gas.

Abstract: We study theoretically transport of a one-dimensional single-channel interacting electron gas through barriers or constrictions. We find that electrons with repulsive interactions, incident upon a single barrier, are completely reflected at zero temperature. At finite temperature (T), the conductance is shown to vanish as a power of T, and at zero temperature, power-law current-voltage characteristics are predicted. For attractive interactions, we predict perfect transmission at zero temperature, with similar power-law corrections. We also study resonant tunneling through a double-barrier structure and related effects associated with the Coulomb blockade. Resonant peaks in the transmission are possible, provided the interactions are not too strongly repulsive. However, in contrast to resonant tunneling in a noninteracting electron gas, we find that in the presence of interactions the width of the resonance vanishes, as a power of temperature, in the zero-temperature limit. Moreover, the resonance line shapes are shown to be described by a universal scaling function, which has power law, but non-Lorentzian tails. For a particular choice of interaction strengths, we present an exact solution of our model, which verifies the scaling assumptions and provides an explicit expression for the scaling function. We also consider the role played by the electron-spin degree of freedom in modifying the trasnsmission through barriers. With spin, there are four possible phases corresponding to perfect transmission or perfect reflection of charge and spin. We present phase diagrams for these different behaviors and analyze the nontrivial transitions between them. At these transitions we find that the conductance or transmission is universal---depending only on the dimensionless conductance of the leads and not on the details of the barriers. In the case of resonant tunneling with spin, we discuss the ``Kondo'' resonance, which occurs when there is a spin degeneracy for electrons between the two barriers. Many of the predictions should be directly testable in gated GaAs wires.

Excitation-power dependence of the near-band-edge photoluminescence of semiconductors.

Abstract: We present a model calculation for the dependence of the near-band-edge photoluminescence (NBEPL) on the power of the exciting laser light. Our model explains all features of the NBEPL power dependence that were previously observed in experiment: (i) the variation of the excitonic photoluminescence intensity I with ${\mathit{L}}^{\mathit{k}}$, where L is the excitation power and k is an exponent between 1 and 2, (ii) deviations from the I\ensuremath{\sim}${\mathit{L}}^{\mathit{k}}$ law as L is varied by more than two orders of magnitude, and (iii) the variation of k for exciton emission lines when the wavelength of the exciting laser radiation is varied. Furthermore, our model relates the k values of the free exciton, bound exciton, and the free-to-bound transitions. The results are in excellent agreement with experimental data.

Energetics of Nanoscale Graphitic Tubules

Abstract: Using both empirical potentials and first-principles total-energy methods, we have examined the energetics and elastic properties of all possible graphitic tubules with radii less than 9 \AA{}. We find that the strain energy per carbon atom relative to an unstrained graphite sheet varies as 1/${\mathit{R}}^{2}$ (where R is the tubule radius) and is insensitive to other aspects of the lattice structure, indicating that relationships derivable from continuum elastic theory persist well into the small-radius limit. We also predict that this strain energy is much smaller than that in highly symmetric fullerene clusters with similar radii, suggesting a possible thermodynamic preference for tubular structures rather than cage structures. The empirical potentials further predict that the elastic constants along the tubule axis generally soften with decreasing tubule radius, although with a distinct dependence on helical conformation.

Hubbard model in infinite dimensions

Abstract: We present an exact mapping of the Hubbard model in infinite dimensions onto a single-impurity Anderson (or Wolff) model supplemented by a self-consistency condition. This provides a mean-field picture of strongly corrrelated systems, which becomes exact as d\ensuremath{\rightarrow}\ensuremath{\infty}. We point out a special integrable case of the mean-field equations, and study the general case using a perturbative renormalization group around the atomic limit. Three distinct Fermi-liquid regimes arise, corresponding to the Kondo, mixed-valence, and empty-orbitals regimes of the single-impurity problem. The Kondo resonance and the satellite peaks of the single-impurity model correspond to the quasiparticle and Hubbard-bands features of the Hubbard model, respectively.

Systematic study of insulator-metal transitions in perovskites RNiO3 (R=Pr,Nd,Sm,Eu) due to closing of charge-transfer gap.

Abstract: The detailed behavior of the phase transitions was mapped out for the series R${\mathrm{NiO}}_{3}$ as a function of the rare earth (R). A sharp insulator-metal transition is observed, which depends strongly on R.Forsmall$R it occurs at a higher temperature than the antiferromagnetic ordering (measured by muon-spin relaxation). By increasing either the temperature or the size of R, an insulator-metal transition is observed, most probably caused by the closing of the charge-transfer gap, induced by increase in the electronic bandwidth.

Theory for displacive excitation of coherent phonons.

Abstract: We report femtosecond time-resolved pump-probe reflection experiments in semimetals and semiconductors that show large-amplitude oscillations with periods characteristic of lattice vibrations. Only ${\mathit{A}}_{1}$ modes are detected, although modes with other symmetries are observed with comparable intensity in Raman scattering. We present a theory of the excitation process in this class of materials, which we refer to as displacive excitation of coherent phonons (DECP). In DECP, after excitation by a pump pulse, the electronically excited system rapidly comes to quasiequilibrium in a time short compared to nuclear response times. In materials with ${\mathit{A}}_{1}$ vibrational modes, the quasiequilibrium nuclear ${\mathit{A}}_{1}$ coordinates are displaced with no change in lattice symmetry, giving rise to a coherent vibration of ${\mathit{A}}_{1}$ symmetry about the displaced quasiequilibrium coordinates. One important prediction of the DECP mechanism is the excitation of only modes with ${\mathit{A}}_{1}$ symmetry. Furthermore, the oscillations in the reflectivity R are excited with a cos(${\mathrm{\ensuremath{\omega}}}_{0}$t) dependence, where t=0 is the time of arrival of the pump pulse peak, and ${\mathrm{\ensuremath{\omega}}}_{0}$ is the vibrational frequency of the ${\mathit{A}}_{1}$ mode. These predictions agree well with our observations in Bi, Sb, Te, and ${\mathrm{Ti}}_{2}$${\mathrm{O}}_{3}$. The fit of the experimental \ensuremath{\Delta}R(t)/R(0) data to the theory is excellent.

Pair-distribution function and its coupling-constant average for the spin-polarized electron gas

Abstract: The pair-distribution function g describes physical correlations between electrons, while its average g\ifmmode\bar\else\textasciimacron\fi{} over coupling constant generates the exchange-correlation energy. The former is found from the latter by g=(1-${\mathit{a}}_{0}$\ensuremath{\partial}/\ensuremath{\partial}${\mathit{a}}_{0}$)g\ifmmode\bar\else\textasciimacron\fi{}, where ${\mathit{a}}_{0}$ is the Bohr radius. We present an analytic representation of g\ifmmode\bar\else\textasciimacron\fi{} (and hence g) in real space for a uniform electron gas with density parameter ${\mathit{r}}_{\mathit{s}}$ and spin polarization \ensuremath{\zeta}. This expression has the following attractive features: (1) The exchange-only contribution is treated exactly, apart from oscillations we prefer to ignore. (2) The correlation contribution is correct in the high-density (${\mathit{r}}_{\mathit{s}}$\ensuremath{\rightarrow}0) and nonoscillatory long-range (R\ensuremath{\rightarrow}\ensuremath{\infty}) limits. (3) The value and cusp are properly described in the short-range (R\ensuremath{\rightarrow}0) limit. (4) The normalization and energy integrals are respected. The result is found to agree with the pair-distribution function g from Ceperley's quantum Monte Carlo calculation. Estimates are also given for the separate contributions from parallel and antiparallel spin correlations, and for the long-range oscillations at a high finite density.

Electrostatics of edge channels.

Abstract: We propose a quantitative electrostatic theory of the gate-induced confinement of two-dimensional electron gas (2DEG) in the quantum Hall regime. The self-consistent electrostatic potential in the region occupied by 2DEG changes in a steplike manner due to the formation of alternating strips of compressible and incompressible electron liquids. We obtain the dependence of positions and widths of these strips on the filling factor. Incompressible strips are shown to be much more narrow than the compressible ones. The relationship between the widths of the adjacent compressible and incompressible strips is found to be universal: It does not depend on the strip number, magnetic field, or gate voltage. Our theory enables us to explain results obtained in experimental studies of edge-state equilibration.

Transient thermal process after a high-energy heavy-ion irradiation of amorphous metals and semiconductors

Abstract: Following a description used to explain a phase transformation observed after pulsed femtosecond laser irradiation, a transient thermal process is used to describe latent-track formation after high electronic excitation induced by energetic (GeV) heavy ions. The transient thermal calculation is restricted to the amorphous materials a-Ge, a-Si, and a-${\mathrm{Fe}}_{85}$${\mathrm{B}}_{15}$, for which nearly all latent-track radii and/or macroscopic thermodynamic properties are known. The heat-flow equation is solved numerically in cylindrical geometry. The time-dependent heat-generation term is assumed to be due to the electron-atom interaction. The characteristic length \ensuremath{\lambda} of the energy transport by secondary electrons is taken as the only free parameter and the maximum diameter of the cylinder of liquid matter is considered as the diameter of the observed latent track. Using the single value \ensuremath{\lambda}=14 nm, we have been able to calculate these diameters in a-Si and a-Ge in reasonable agreement with experimental track diameters, taking into account the large differences between the macroscopic thermodynamic parameters of both materials. This \ensuremath{\lambda} value is less than that for the crystalline state. In the case of a-${\mathrm{Fe}}_{85}$${\mathrm{B}}_{15}$, the diameters calculated with use of \ensuremath{\lambda}=19 nm are in agreement with the ones determined recently by electrical-resistivity change.

Dielectric confinement effect on excitons in PbI4-based layered semiconductors.

Abstract: By varying the dielectric environment in new ${\mathrm{PbI}}_{4}$-based layer-type perovskite compounds, we have demonstrated directly the contribution by dielectric confinement to the exciton binding energy in three such ``natural-quantum-well'' semiconductors. With different dielectric environment, exciton binding energies of 320, 220, and 170 meV have been observed, dominated by the dielectric confinement. In terms of the conventional size-related electronic confinement, two of the materials represent monolayer ${\mathrm{PbI}}_{4}$ quantum wells while the third corresponds to a bilayer case, with a corresponding reduction in the electronic confinement. From theory, including the dielectric confinement effect, the effective mass of the exciton in a ${\mathrm{PbI}}_{4}$-based dielectric quantum well has been determined to be 0.09${\mathit{m}}_{\mathit{e}}$; the corresponding quasi-two-dimensional exciton Bohr radii were 15.5, 17.0, and 20.5 \AA{} for the three cases, respectively.

Scattering theory of current and intensity noise correlations in conductors and wave guides.

Abstract: The low-frequency current-fluctuation spectra of phase-coherent electron conductors are related to the scattering matrix of the conductor. Each contact of the conductor is connected to a thermal equilibrium electron reservoir. The current-current correlations of the conductor are compared with the intensity-intensity correlations of a photon wave guide with all its ports connected to blackbody radiation sources. Only two sources of noise are considered: (a) Fluctuations in the occupation numbers of the incident channels that reflect the thermal equilibrium fluctuations of the reservoir states and (b) a shot noise (or partition noise) that originates if a carrier can be scattered into more than one final state and is present even at zero temperature. The theory uses single-particle scattering states to build up multiparticle states with the proper symmetry. Second quantization provides an elegant treatment of this problem if annihilation and creation operators for both the input and output channels of the wave guide are introduced. At equilibrium, in the absence of transport, the correlations of flux fluctuations measured at two different contacts are negative for both fermions and bosons. Away from equilibrium, in the presence of a net flux, the fluctuations are related to transport coefficients which invoke products of four scattering matrices.The transport portion of the correlation of the flux fluctuations at two different contacts is negative for fermions but is positive for bosons. The transport portion (shot noise) is very sensitive to the transmission behavior of the wave guide. Both for fermions and for bosons completely open transmission channels give no contribution. In addition to two-terminal conductors, we consider four-probe conductors in high magnetic fields which have the property that carriers transmitted and reflected at a barrier reach separate contacts. We discuss a four-terminal experiment which explicitly shows that the correlation function in the presence of two particle sources is not an incoherent sum of correlations generated by particles originating in one of the sources but contains exchange terms due to the indistinguishability of identical particles. We discuss the conditions for such exchange terms to be sensitive to a quantum-mechanical phase and the possibility to tune this phase with the help of an Aharonov-Bohm flux.

Structural refinement of superlattices from x-ray diffraction.

Abstract: We present a general procedure for quantitative structural refinement of superlattice structures. To analyze a wide range of superlattices, we derived a general kinematical diffraction formula that includes random, continuous, and discrete fluctuations from the average structure. We show that only the structure factor of one single layer of each material has to be averaged over the random variables and prove that this relation is equivalent to earlier, less general models. Implementing a nonlinear-fitting algorithm to fit the entire x-ray-diffraction profile, refined parameters that describe the average superlattice structure and deviations from this average are obtained. We compare the results of structural refinement to results obtained independently from other measurements. The roughness introduced artificially during growth in Mo/Ni and Nb/Cu superlattices is accurately reproduced by the refinement. The lattice parameters of Ag/Mn obtained from this refinement procedure are in very good agreement with the values obtained from independent extended x-ray-absorption fine-structure and x-ray photoelectron diffraction studies. The relative thicknesses of the layers can be accurately determined, as proved for Cu/Ni in comparison with chemical analysis, for W/Ni compared to the calibrated sputtering rate, and for Mo/Ni compared to the low-angle profile.

Infrared absorption strength and hydrogen content of hydrogenated amorphous silicon.

Abstract: We have used infrared transmission and nuclear-reaction analysis to determine the ir absorption strength of the Si-H wagging and stretching modes in hydrogenated amorphous silicon (a-Si:H). The films were deposited by plasma-assisted chemical vapor deposition and reactive magnetron sputtering. We show that the widely used ir-data-analysis method of Brodsky, Cardona, and Cuomo can lead to significant errors in determining the absorption coefficients, particularly for films less than \ensuremath{\sim}1 \ensuremath{\mu}m thick. To eliminate these errors we explicitly take into account the effects of optical interference to analyze our data. We show that the hydrogen content can be determined from the stretching modes at \ensuremath{\omega}=2000 and 2100 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ as well as the wagging mode at \ensuremath{\omega}=640 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. By assigning different oscillator strengths to the 2000- and 2100-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ modes, we show that the absorption strength of the stretching modes does not depend on the details of sample preparation, contrary to hypotheses previously invoked to explain experimental data. We obtain ${\mathit{A}}_{640}$=(2.1\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}${10}^{19}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$, ${\mathit{A}}_{2000}$=(9.0\ifmmode\pm\else\textpm\fi{}1.0)\ifmmode\times\else\texttimes\fi{}${10}^{19}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$, and ${\mathit{A}}_{2100}$=(2.2\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}${10}^{20}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$ for the proportionality constants between the hydrogen concentration and the integrated absorbance of the wagging and stretching modes. The value of ${\mathit{A}}_{640}$ is \ensuremath{\sim}30% larger than the generally used value. We show that previously published data for both the wagging and stretching modes are consistent with the proportionality factors determined in the present study.

Compositional dependence of Judd-Ofelt parameters of Er3+ ions in alkali-metal borate glasses.

Abstract: The Judd-Ofelt intensity parameters, ${\mathrm{\ensuremath{\Omega}}}_{\mathit{t}}$ (t=2,4,6) for f-f transitions of ${\mathrm{Er}}^{3+}$ ions doped in ${\mathrm{B}}_{2}$${\mathrm{O}}_{3}$-${\mathit{R}}_{2}$O (R=Na,K) glasses were determined from optical-absorption measurements, and their compositional dependence was investigated systematically. The values of ${\mathrm{\ensuremath{\Omega}}}_{2}$ exhibited a maximum around 25 mol % ${\mathit{R}}_{2}$O, while those of ${\mathrm{\ensuremath{\Omega}}}_{4}$ and ${\mathrm{\ensuremath{\Omega}}}_{6}$ decreased monotonically with an increase in ${\mathit{R}}_{2}$O content. The compositional dependences of ${\mathrm{\ensuremath{\Omega}}}_{4,6}$ were consistent with those of the isomer shift in $^{151}\mathrm{Eu}$ M\"ossbauer spectroscopy, which gives information about the 6s-electron density of ${\mathrm{Eu}}^{3+}$ ions. The variation of ${\mathrm{\ensuremath{\Omega}}}_{2}$ against ${\mathit{R}}_{2}$O content was related to the change in asymmetry of the rare-earth ligand due to the structural mixing of borate groups, while those of ${\mathrm{\ensuremath{\Omega}}}_{4,6}$ were related to the local basicity of rare-earth sites in the glass.

Controlled-valence properties of La1-xSrxFeO3 and La1-xSrxMnO3 studied by soft-x-ray absorption spectroscopy.

Abstract: The controlled-valence properties of ${\mathrm{La}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{FeO}}_{3}$ and ${\mathrm{La}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{MnO}}_{3}$ are studied by means of soft-x-ray absorption spectroscopy. A comparison between the transition-metal 2p spectra and atomic-multiplet calculations is used to determine the 3d count. The O 1s spectrum is used to characterize changes in unoccupied states that contain oxygen p character. The results indicate that the holes induced by substitution for both series are located in states of mixed metal 3d--oxygen 2p character. The ground state of ${\mathrm{LaFeO}}_{3}$ is mainly 3${\mathit{d}}^{5}$ and becomes 3${\mathit{d}}^{5}$L (where L denotes a ligand hole) in the ${\mathrm{La}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{FeO}}_{3}$ series for low Sr concentration. The main component of the ground state of ${\mathrm{LaMnO}}_{3}$ is 3${\mathit{d}}^{4}$ and becomes a mixture of 3${\mathit{d}}^{3}$ and 3${\mathit{d}}^{4}$L in the ${\mathrm{La}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{MnO}}_{3}$ series. The trends in controlled- valence properties of similar oxides across the transition-metal series can be rationalized within the framework of the Zaanen-Sawatzky-Allen model.

Kagomé- and triangular-lattice Heisenberg antiferromagnets: Ordering from quantum fluctuations and quantum-disordered ground states with unconfined bosonic spinons.

Abstract: The kagome\ifmmode\acute\else\textasciiacute\fi{}-lattice quantum Heisenberg antiferromagnet is studied by a large-N expansion based upon groups with symplectic Sp(N) symmetry. Two distinct types of ground states are found. (i) for large values of the ``spin'' the ground state has long-range magnetic order with the spins ordered in a \ensuremath{\surd}3 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}3 structure with 9 sites per unit cell. Quantum fluctutions are explicitly shown to select this structure from the large number of classically degenerate states. The only zero-energy excitations about the magnetically ordered state are shown to be the physical, infinite-wavelength, Goldstone spin waves; in contrast the naive semiclassical theory has zero-energy spin waves at all wave vectors. (ii) For small values of the ``spin,'' the ordered moment disappears and we obtain a quantum-disordered ground state with no broken symmetries. As in previous work on frustrated square-lattice antiferromagnets, this state is argued to possess unconfined, spin-1/2, bosonic, spinon excitations for all values of the underlying lattice spin. A similar, small-``spin'' quantum-disordered ground state with unconfined bosonic spinons is studied in the triangular-lattice quantum Heisenberg antiferromagnet by extending earlier results. A large N, Sp(N) theory of the classical kagome\ifmmode\acute\else\textasciiacute\fi{} Heisenberg antiferromagnet at finite temperature is also presented: fluctuations of the \ensuremath{\surd}3 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}3 structure dominate, with a correlation length which diverges exponentially in the zero-temperature limit. The significance of these results for experimental kagome\ifmmode\acute\else\textasciiacute\fi{}-lattice systems is discussed.

Raman scattering and x-ray-absorption spectroscopy in gallium nitride under high pressure.

Abstract: Gallium nitride was studied by Raman scattering and x-ray-absorption spectroscopy up to 60 GPa. A high-pressure structural phase transition was observed in gallium nitride at 47 GPa by means of Raman scattering and x-ray-absorption spectroscopy. We also report the direct determination of the bulk modulus ${\mathit{B}}_{0}$ of this compound (245 GPa). Gr\"uneisen parameters of the four observed phonon modes were established. The transition pressure is compared with existing calculations.

Superconductivity in ladders and coupled planes

Abstract: We discuss an electronic model consisting of two chains or planes, each described by a t-J model, coupled by t'-J' interactions between them. For J'\ensuremath{\sim}J or larger we show the presence of a spin-gap and hole-pair formation upon doping. The model exhibits superconducting pairing correlations away from half filling. We support our claims by numerical studies of the spin gap, the binding energy of holes, and the pairing correlations on finite clusters. The hole-pairing operator is a spin singlet with one member of the pair in each chain or plane. Our model belongs to the universality class of the U0 Hubbard model with \ensuremath{\Vert}U\ensuremath{\Vert}\ensuremath{\gg}t. We argue that this model may be physically realized by doping the orthorhombic compound (VO${)}_{2}$${\mathrm{P}}_{2}$${\mathrm{O}}_{7}$.

Deviation from Curie-Weiss behavior in relaxor ferroelectrics.

Abstract: The deviation from Cure-Weiss behavior has been investigated in lead magnesium niobate relaxor ferroelectrics. At high temperatures, the susceptibility was found to follow the Curie-Weiss relationship. A Curie constant and temperature of 1.2\ifmmode\times\else\texttimes\fi{}${10}^{5}$ and 398 K, respectively, were obtained. With decreasing temperature the deviation was found to increase. It is proposed that this deviation arises due to short-range correlations between polar regions, and that these correlations at high temperatures are the precursor to a freezing of the polarization fluctuations into a glassy state. A local (glassy) order parameter was calculated from the susceptibility by analogy to spin glasses [D. Sherrington and S. Kirkpatrick, Phys. Rev. Lett. 35, 1972 (1975)]. These results are compared to the rms polarization [G. Burns and F. Dacol, Solid State Commun. 48, 853 (1983)] and to the measured remanent polarization. The frequency and field dependence has also been investigated.

Electron thermalization in gold.

Abstract: We report the direct observation of the thermalization of electrons in gold following 180 fs optical pulse excitation. The evolution of the electron energy distribution from the nascent (as photoexcited) to a hot Fermi-Dirac distribution was measured by time-resolved photoemission spectroscopy. Depending on the excitation density, thermalization times as long as \ensuremath{\approxeq}1 ps were observed. A model incorporating both electron-electron and electron-phonon scattering, and using Fermi-liquid theory to properly account for screening is found to reproduce the main features of the experiment.