Showing papers in "Physical Review B in 1994"

Projector augmented-wave method

Abstract: An approach for electronic structure calculations is described that generalizes both the pseudopotential method and the linear augmented-plane-wave (LAPW) method in a natural way. The method allows high-quality first-principles molecular-dynamics calculations to be performed using the original fictitious Lagrangian approach of Car and Parrinello. Like the LAPW method it can be used to treat first-row and transition-metal elements with affordable effort and provides access to the full wave function. The augmentation procedure is generalized in that partial-wave expansions are not determined by the value and the derivative of the envelope function at some muffin-tin radius, but rather by the overlap with localized projector functions. The pseudopotential approach based on generalized separable pseudopotentials can be regained by a simple approximation.

Ab initio molecular-dynamics simulation of the liquid-metal-amorphous-semiconductor transition in germanium.

Abstract: 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) Nos\'e 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.

Improved tetrahedron method for Brillouin-zone integrations

Abstract: Several improvements of the tetrahedron method for Brillouin-zone integrations are presented. (1) A translational grid of k points and tetrahedra is suggested that renders the results for insulators identical to those obtained with special-point methods with the same number of k points. (2) A simple correction formula goes beyond the linear approximation of matrix elements within the tetrahedra and also improves the results for metals significantly. For a required accuracy this reduces the number of k points by orders of magnitude. (3) Irreducible k points and tetrahedra are selected by a fully automated procedure, requiring as input only the space-group operations. (4) The integration is formulated as a weighted sum over irreducible k points with integration weights calculated using the tetrahedron method once for a given band structure. This allows an efficient use of the tetrahedron method also in plane-wave-based electronic-structure methods.

Time-dependent transport in interacting and noninteracting resonant-tunneling systems

Abstract: We consider a mesoscopic region coupled to two leads under the influence of external timedependent voltages. The time dependence is coupled to source and drain contacts, the gates controlling the tunnel-barrier heights, or to the gates that define the mesoscopic region. We derive, with the Keldysh nonequilibrium-Green-function technique, a formal expression for the fully nonlinear, time-dependent current through the system. The analysis admits arbitary interactions in the mesoscopic region, but the leads are treated as noninteracting. For proportionate coupling to the leads, the time-averaged current is simply the integral between the chemical potentials of the time-averaged density of states, weighted by the coupling to the leads, in close analogy to the time-independent result of Meir and Wingreen [Phys. Rev. Lett. 68, 2512 (1992)]. Analytical and numerical results for the exactly solvable noninteracting resonant-tunneling system are presented. Due to the coherence between the leads and the resonant site, the current does not follow the driving signal adiabatically: a "ringing" current is found as a response to a voltage pulse, and a complex time dependence results in the case of harmonic driving voltages. We also establish a connection to recent linear-response calculations, and to earlier studies of electron-phonon scattering effects in resonant tunneling.

Theory of graphitic boron nitride nanotubes

Abstract: Based upon the similarities in properties between carbon- and BN-based (BN=boron nitride) materials, we propose that BN-based nanotubes can be stable and study their electronic structure. A simple Slater-Koster tight-binding scheme has been applied. All the BN nanotubes are found to be semiconducting materials. The band gaps are larger than 2 eV for most tubes. Depending on the helicity, the calculated band gap can be direct at [Gamma] or indirect. In general, the larger the diameter of the nanotube the larger the band gap, with a saturation value corresponding to the calculated local-density-approximation band gap of hexagonal BN. The higher ionicity of BN is important in explaining the electronic differences between these tubes and similar carbon nanotubes.

Magnetoelectric effect in composites of piezoelectric and piezomagnetic phases

Abstract: The magnetoelectric effect in composites of piezoelectric and piezomagnetic phases is investigated theoretically. The magnetoelectric effect is totally absent in these two constituent phases, and so it is a new property of the composites. A generalized theoretical framework based on a Green's function method and perturbation theory is proposed to treat the coupled magnetoelectric behavior in the composites. Explicit relations for determining the effective magnetoelectric effect in the composites are derived, and the different approximate expressions for the magnetoelectric coefficient of the fibrous composites with 1-3 or 3-1 connectivity of phases are given. To illustrate the technique, numerical calculations of the magnetoelectric coefficients of the BaTiO3-CoFe2O4 composites for various phase compositions and particle shapes are performed. The theoretical estimates are shown to be in agreement with available experimental results, and also show the interesting magnetoelectric behavior of the composites.

Theoretical possibility of stage corrugation in Si and Ge analogs of graphite

Abstract: The planarity of the aromatic stage of two-dimensional Si and Ge layers are theoretically investigated by first-principles total-energy calculations. While a C atom prefers to form the flat aromatic stage, i.e., graphite, Si and Ge prefer to form the corrugated aromatic stage. Si can be said to be the critical element by which the corrugated stage is formed.

Implementation of gradient-corrected exchange-correlation potentials in car-parrinello total-energy calculations

Abstract: The application of gradient-corrected exchange-correlation functionals in total-energy calculations using a plane-wave basis set is discussed. The usual form of the exchange-correlation potential includes gradients whose calculation requires the use of a high-quality representation of the density which is computationally expensive in both memory and time. These problems may be overcome by defining an exchange-correlation potential for the discrete set of grid points consistent with the discretized form of the exchange-correlation energy that is used in Car-Parrinello-type total-energy calculations. This potential can be calculated exactly on the minimum fast-Fourier-transform grid and gives improved convergence and stability as well as computational efficiency.

Critical layer thickness for self-assembled InAs islands on GaAs.

Abstract: Using atomic force microscopy (AFM), we have directly observed the progression of surface morphology of InAs deposited by molecular-beam epitaxy on GaAs(100). InAs self-assembled dots (coherent) or relaxed InAs islands (incoherent) are formed depending on the InAs coverage. The InAs coverage was varied continuously and AFM was used to monitor in detail the nucleation and resulting size and shape transition of the InAs self-assembled dots. Dots of uniform size were observed only at the initial stages of this Stranski-Krastanow growth-mode transition. The self-assembled dot density increased very abruptly with total deposited amount of InAs. Treating this InAs growth-mode transition as a first-order phase transition with InAs total coverage as the critical parameter, we extract a critical thickness for surface elastic relaxation of 1.50 ML.

Governing equations for the coupled electromagnetics and acoustics of porous media

Abstract: The macroscopic governing equations controlling the coupled electromagnetics and acoustics of porous media are derived here from first principles. The porous material is assumed to consist of a packing of solid grains that is saturated by an electrolyte. A sedimentary rock is an example of such a material. The approach is to volume average the equations known to apply in the fluid and solid phases while allowing for the boundary conditions that exist on the fluid-solid interface. The coupling is due to a layer of excess charge adsorbed to the sufaces of the solid grains that is balanced by mobile ions in the fluid electrolyte; i.e., the coupling is electrokinetic in nature. The derived equations have the form of Maxwell's equations coupled to Biot's equations with coupling occurring in the flux-force (or transport) relations. The frequency-dependent macroscopic-transport coefficients are explicitly obtained and related to each other. Onsager reciprocity is derived and is not simply postulated.

Theory of acoustic band structure of periodic elastic composites.

Abstract: We study an elastic composite described by the position-dependent mass density \ensuremath{\rho}(r), the longitudinal speed of sound ${\mathit{c}}_{\mathit{l}}$(r), and the transverse speed of sound ${\mathit{c}}_{\mathit{t}}$(r). For a spatially periodic composite---a ``phononic crystal''---we derive the eigenvalue equation for the frequencies ${\mathrm{\ensuremath{\omega}}}_{\mathit{n}}$(K), where n is the serial number of the band and K is the Bloch wave vector. This is applied to the special case of a binary composite and, further, to the case of infinite cylinders that form a two-dimensional lattice. For this configuration (and no wave-vector component parallel to the cylinders) there are two independent modes of vibration. The elastic displacement u(r) is parallel to the cylinders for one of them---the transverse polarization mode. The other one is a mixed (longitudinal-transverse) polarization mode with u(r) perpendicular to the cylinders. Specifically we consider circular cylinders that form a square lattice. We compute the band structures for the transverse modes of nickel alloy cylinders in an aluminum alloy host, and vice versa. In both situations we find band gaps which extend throughout the Brillouin zone. Within these gaps the transverse vibrations, sound, and phonons are forbidden. We also investigate the dependence of the band gap on the filling fraction and on the material parameters.

Vibrational analysis of polyaniline: A comparative study of leucoemeraldine, emeraldine, and pernigraniline bases

Abstract: We present a comparative vibrational study of leucoemeraldine, emeraldine, and pernigraniline bases: fully reduced, half oxidized, and fully oxidized forms of polyaniline, respectively. By performing a general vibrational calculation based on the symmetrized dynamical matrix, we determine the force constants, the potential-energy distribution, and the Cartesian displacements for the three forms of polyaniline and associated model compounds. We discuss the assignment of the fundamental Raman and ir vibrational modes of the polymers. The modifications of the frequencies and consequently of the main force constants observed from one compound to the other are analyzed by considering the quinoid and aromatic characters along the chain. In this way, we determine a force field with physical significance which may be used to interpret the electronic modification between neutral and protonated as well as photoexcited emeraldine forms. This comparative analysis demonstrates the important changes of the electronic distribution around the nitrogen atom, which plays a major role in the conduction mechanism in this class of conducting polymers.

Atomic geometry and electronic structure of native defects in GaN

Abstract: We have studied the electronic structure, atomic geometry, and formation energies of native defects in GaN using first-principles total-energy calculations. Our results reveal the vacancies to be the dominant defects in GaN, whereas antisites and interstitials are energetically less favorable. In p-type GaN the nitrogen vacancy (a donor) has the lowest formation energy, in n-type GaN the gallium vacancy (an acceptor). Our results show that the vacancies may be important for compensation. However, isolated point defects and particularly the nitrogen vacancy can be excluded as the source for the n-type conductivity in as-grown GaN, contrary to the generally accepted picture.

Femtosecond-tunable measurement of electron thermalization in gold

Abstract: Femtosecond electron thermalization in metals was investigated using transient thermomodulation transmissivity and reflectivity. Studies were performed using a tunable multiple-wavelength femtosecond pump-probe technique in optically thin gold films in the low perturbation limit. An IR pump beam is used to heat the electron distribution and changes in electron temperature are measured with a visible probe beam at the d band to Fermi-surface transition. We show that the subpicosecond optical response of gold is dominated by delayed thermalization of the electron gas. This effect is particularly important far off the spectral peak of the reflectivity or transmissivity changes, permitting a direct and sensitive access to the internal thermalization of the electron gas. Using a simple rate-equation model, line-shape analysis of the transient reflectivity and transmissivity indicates a thermalization time of the order of 500 fs. At energies close to the Fermi surface, longer thermalization times \ensuremath{\sim}1--2 ps are observed. These results are in agreement with a more sophisticated model based on calculations of the electron-thermalization dynamics by numerical solutions of the Boltzmann equation. This model quantitatively describes the measured transient optical response during the full thermalization time of electron gas, of the order of 1.5 ps, and gives new insight into electron thermalization in metals.

Corrected atomic limit in the local-density approximation and the electronic structure of d impurities in rb

Abstract: We propose an energy functional for localized electron systems that corresponds to the constrained-local-density approximation (LDA) but includes some corrections for spin and orbital polarization to take Hund's first and second rules into account. The discontinuity of the one-electron potential known for an exact density functional can be easily incorporated in LDA in the scope of our formalism. Applications of the method to the electronic structure and configurational stability of d impurities in Rb are presented.

Intrinsic Josephson effects in high-Tc superconductors.

Abstract: We have investigated the coupling between ${\mathrm{CuO}}_{2}$ layers in high-${\mathit{T}}_{\mathit{c}}$ superconductors by direct measurements of all dc and ac Josephson effects with current flow in the c-axis direction. The measurements have been performed on small single crystals of ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{8}$, (${\mathrm{Pb}}_{\mathit{y}}$${\mathrm{Bi}}_{1\mathrm{\ensuremath{-}}\mathit{y}}$${)}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{8}$, ${\mathrm{Tl}}_{2}$${\mathrm{Ba}}_{2}$${\mathrm{Ca}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{10}$, and ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathit{x}}$ and on a-axis-oriented ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{2}$${\mathrm{O}}_{7}$ thin films. The results clearly show that all materials behave like stacks of superconductor-insulator-superconductor Josephson junctions. The current-voltage characteristics exhibit large hystereses and multiple branches, which can be explained by a series connection of highly capacitive junctions. From the modulation of the critical current in a magnetic field parallel to the layers, we infer a junction thickness of approximately 15 \AA{}. In our microwave emission experiments we were able to prove explicitly that every pair of ${\mathrm{CuO}}_{2}$ double or triple layers forms a working Josephson contact. An exception is ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$, where only flux-flow behavior has been observed.

Superconductivity up to 164 K in HgBa2Cam-1CumO2m+2+ delta (m=1, 2, and 3) under quasihydrostatic pressures.

Abstract: The superconducting transition temperatures (${\mathit{T}}_{\mathit{c}}$'s) of optimally doped ${\mathrm{HgBa}}_{2}$${\mathrm{Ca}}_{\mathit{m}\mathrm{\ensuremath{-}}1}$${\mathrm{Cu}}_{\mathit{m}}$${\mathrm{O}}_{2\mathit{m}+2+\mathrm{\ensuremath{\delta}}}$ (Hg 1:2:m-1:m) with m=1, 2, and 3 and ${\mathrm{Hg}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Pb}}_{\mathit{x}}$${\mathrm{Ba}}_{2}$${\mathrm{Ca}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{8+\mathrm{\ensuremath{\delta}}}$ [Hg(xPb) 1:2:2:3] have been investigated resistively under quasihydrostatic pressures up to 45 GPa. There seems to be a universal upward shift of ${\mathit{T}}_{\mathit{c}}$ under pressure, regardless of m, for all Hg 1:2:m-1:m, implying a common origin for all compounds. Record high ${\mathit{T}}_{\mathit{c}}$'s of 164, 154, and 118 K were reached for the optimally doped Hg 1:2:m-1:m with m=3, 2, and 1, respectively. However, the ${\mathit{T}}_{\mathit{c}}$ enhancement is suppressed by Pb substitution, suggesting the possibility that Hg plays an important role in these compounds.

Local-density functional and on-site correlations: The electronic structure of La2CuO4 and LaCuO3

Abstract: 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 antiferromagnetic 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 La2CuO4 and LaCuO3. In the case of La2CuO4 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 the 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 LaCuO3 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.

First-principles calculations of the energetics of stoichiometric TiO2 surfaces.

Abstract: We present self-consistent ab initio total-energy calculations of the equilibrium relaxed structures and surface energies of the stoichiometric (1\ifmmode\times\else\texttimes\fi{}1) (110), (100), (001), and (011) surfaces of ${\mathrm{TiO}}_{2}$. The relaxations of atoms on these surfaces are found to be substantial, and are responsible for a large reduction of the calculated surface energies. A Wulff construction is used to display the relative energetics of these surfaces. The (100) surface is found to be stable with respect to forming macroscpic (110) facets, while the (001) surface is nearly unstable with respect to forming macroscopic (1\ifmmode\times\else\texttimes\fi{}1) (011) facets. These results shed light on published experimental results on the structures of these surfaces.

Optical and structural properties of III-V nitrides under pressure

Abstract: Self-consistent linear muffin-tin-orbital band-structure calculations are used to investigate the optical and structural properties of III-V semiconducting nitrides under hydrostatic pressure. The pressure behavior of the energy band structures is discussed in the context of the postulated chemical trends in III-V semiconductors. The regions in k space of dominant interband contributions to the elements of structure in the dielectric functions are identified. The total-energy calculations suggest that all the nitrides under pressure transform to the semiconducting rocksalt phase. The calculated transition pressures are 21.6 GPA (InN), 51.8 GPa (GaN), 16.6 GPa (AlN), and 850 GPa (BN). Experimental values that agree well with this have been found for the first three compounds. The fact that GaN and AlN have such different transition pressures in spite of their very similar ionicities is explained by the presence of 3d states on Ga.

Stability of the wurtzite-type structure under high pressure: GaN and InN.

Abstract: High-pressure in situ x-ray-diffraction studies on GaN and InN have been carried out using an imaging-plate technique and a diamond-anvil cell up to about 60 GPa. The two compounds crystallize in the wurtzite-type structure at ambient conditions. The axial ratio c/a of GaN remains unchanged from the ambient value of 1.626 whereas c/a of InN is considerably decreased from 1.613 to 1.597 with increasing pressure to about 15 GPa. Equation-of-state data obtained for the wurtzite phase have yielded the bulk modulus of GaN to be 237(31) GPa and that of InN to be 125.5(4.6) GPa. Structural phase transition into the rocksalt-type structure takes place in GaN at 52.2 GPa and in InN at 12.1 GPa. The trend in the transition pressures of the III-V nitrides is discussed in terms of various ionicity scales.

First-principles investigation of ferroelectricity in perovskite compounds

Abstract: We have used a first-principles ultra-soft-pseudopotential method in conjunction with an efficient preconditioned conjugate-gradient scheme to investigate the properties of a series of eight cubic perovskite compounds. The materials considered in this study are ${\mathrm{BaTiO}}_{3}$, ${\mathrm{SrTiO}}_{3}$, ${\mathrm{CaTiO}}_{3}$, ${\mathrm{KNbO}}_{3}$, ${\mathrm{NaNbO}}_{3}$ ${\mathrm{PbTiO}}_{3}$ , ${\mathrm{PbZrO}}_{3}$, and ${\mathrm{BaZrO}}_{3}$. We computed the total-energy surface for zone-center distortions correct to fourth order in the soft-mode displacement, including renormalizations due to strain coupling. Quantities calculated for each material include lattice constants, elastic constants, zone-center phonon frequencies, Gr\"uneisen parameters, and band structures. Our calculations correctly predict the symmetry of the ground-state structures of all compounds whose observed low-temperature structure retains a primitive five-atom unit cell. The database of results we have generated shows a number of trends which can be understood using simple chemical ideas based on the sizes of ions, and the frustration inherent in the cubic perovskite structure.

Remanence and coercivity in isotropic nanocrystalline permanent magnets.

Abstract: Numerical micromagnetic calculations rigorously describe the correlation between the microstructure and the magnetic properties of nanocrystalline permanent magnets. In isotropic nanocrystalline permanent magnets exchange interactions override the anisotropy of the individual grains. Therefore the spontaneous magnetic polarization deviates from the easy axes in a region along the grain boundaries. For a fine grain structure with a mean grain size d20 nm the remanence is considerably enhanced, since the volume fraction of the boundary regions where the spontaneous magnetic polarization points towards the direction of the applied field becomes significantly high. The inhomogeneous ground state, however, favors the nucleation of reversed domains leading to a reduction of the coercive field with decreasing grain size. A uniform grain structure with a very small range in grain size avoids large demagnetizing fields and thus preserves a high coercivity. For a grain size of 10 nm isotropic two-phase permanent magnets based on ${\mathrm{Fe}}_{14}$${\mathrm{Nd}}_{2}$B and \ensuremath{\alpha}-Fe show remarkable high-energy products, because the volume fraction of the magnetically soft phase can be increased up to 50% without a significant loss of coercivity.

Thermal conductivity of a -Si:H thin films

Abstract: The thermal conductivity of sputtered a-Si:H thin films for a hydrogen content of 1--20 % and a film thickness of 0.2--1.5 \ensuremath{\mu}m is determined in the temperature range 80--400 K using an extension of the 3\ensuremath{\omega} measurement technique. The reliability of the method is demonstrated on 1-\ensuremath{\mu}m-thick a-${\mathrm{SiO}}_{2}$ thermally grown on Si. Scattering of phonons at the interface between the a-Si:H film and the substrate places a simple upper limit on the heat transport by long-wavelength phonons and facilitates the comparison of the experimental data to recent numerical solutions of a Kubo formula using harmonic vibrations.

Electronic structure of

Abstract: Please format your submission as a single PDF file according to the instructions in the syllabus and submit it on UBlearns before 11:59 pm on Sunday, April 6. 1. (17 points) A variational calculation of the ground state energy of the Hydrogen atom is discussed in Thijssen Section 3.2.2. Review this section and the lecture notes to understand the method. Write a code, or use the hydrogen codes, to do the Programming Exercise on page 36: Check 1 Fortunately, we again have an exact answer for the ground state energy: this should be equal to −0.5 hartree = 13.6058 eV, and, if your program contains no errors, you should find −0.499278 hartree, which is amazingly good if you realize that only four functions have been taken into account. Check 2 The soution of the eigenvalue problem not only yields the eigenvalues (energies) but also the eigenvectors. Use these to draw the variational ground state wave function and compare with the exact form ψ(r) = 2 a 3/2 0 e −r/a0. 2. (17 points) The Kronig-Penney model of a periodic potential in one dimension is discussed in Thijssen Problem 6.2 on pages 164-165. Write a code, or use the kronig-penney codes, also studied in PHY 410-505 last semester, to compute a plot a band structure diagram for the model.

Integer quantum Hall transition: An alternative approach and exact results

Abstract: We introduce and analyze a class of model systems to study transitions in the integer quantum Hall effect (IQHE). Even without disorder our model exhibits an IQHE transition as a control parameter is varied. We find that the transition is in the two-dimensional Ising universality class and compute all associated exponents and critical transport properties. The fixed point has time-reversal, particle-hole, and parity invariance. We then consider the effect of quenched disorder on the IQHE transition and find the following. (i) Randomness in the control parameter (which breaks all the above symmetries) translates into bond randomness in the Ising model and is hence marginally irrelevant. The transition may equally well be viewed as a quantum percolation of edge states localized on equipotentials. The absence of random-phase factors for the edge states is responsible for the nongeneric (Ising) critical properties. (ii) For a random magnetic field (which preserves particle-hole symmetry in every realization) the model exhibits an exactly solvable fixed line, described in terms of a product of a Luttinger liquid and an SU(n) spin chain. While exponents vary continuously along the fixed line, the longitudinal conductivity is constant due to a general conformal sum rule for Kac-Moody algebras (derived here), and is computed exactly. We also obtain a closed expression for the extended zero-energy wave function for every realization of disorder and compute its exact multifractal spectrum f(\ensuremath{\alpha}) and the exponents of all participation ratios. One point on the fixed line corresponds to a recently proposed model by Gade and Wegner. (iii) The model in the presence of a random on-site potential scales to a strong disorder regime, which is argued to be described by a symplectic nonlinear-sigma-model fixed point. (iv) We find a plausible global phase diagram in which all forms of disorder are simultaneously considered. In this generic case, the presence of random-phase factors in the edge-state description indicates that the transition is described by a Chalker-Coddington model, with a so far analytically inaccessible fixed point.

Space-charge relaxation in perovskites.

Abstract: We report a dielectric anomaly in several perovskites at intermediate frequencies 10\ensuremath{\le}f\ensuremath{\le}${10}^{7}$ Hz in the temperature range 400 \ifmmode^\circ\else\textdegree\fi{}C \ensuremath{\le}T\ensuremath{\le}800 \ifmmode^\circ\else\textdegree\fi{}C. We have found this dielectric maximum in more than 100 samples of various shapes and textures. This anomaly is shown to arise from a Debye dielectric dispersion that slows down following an Arrhenius law. We have established a link between this dielectric relaxation and the conductivity. We propose that it can be achieved through a space-charge model that quantitatively agrees with the experimental results in the lower temperature range.

Magnetization and transport currents in thin superconducting films.

Abstract: The critical-state behavior of an infinitely long type-II superconducting thin-film strip is theoretically analyzed for an arbitrary sequence of applied transport currents and perpendicular magnetic fields. Included are solutions for applied field only, transport current only, transport current applied to a sample initially in the remanent critical state, ac applied field, ac transport current, and simultaneously applied field and transport current. The results are compared side by side with corresponding solutions for the more famililar slab geometry; there are striking differences in behavior.

Hot-electron effects in metals.

Abstract: When sufficient electrical power P is dissipated in a thin metal film at millikelvin temperatures, the electrons can be driven far out of thermal equilibrium with the phonons. For uniform power dissipation in a volume \ensuremath{\Omega} we show that the electrons attain a steady-state temperature ${\mathit{T}}_{\mathit{e}}$=(P/\ensuremath{\Sigma}\ensuremath{\Omega}+${\mathit{T}}_{\mathit{p}}^{5}$${)}^{1/5}$, where ${\mathit{T}}_{\mathit{p}}$ is the phonon temperature and \ensuremath{\Sigma} is a parameter involving the electron-phonon coupling. We have used a sensitive ammeter based on a dc superconducting quantum interference device (SQUID) to measure the Nyquist current noise in thin films of AuCu as a function of P, and thus inferred ${\mathit{T}}_{\mathit{e}}$. We fitted our data to the theory with the single parameter \ensuremath{\Sigma}, and found good agreement for \ensuremath{\Sigma}=(2.4\ifmmode\pm\else\textpm\fi{}0.6)\ifmmode\times\else\texttimes\fi{}${10}^{9}$ ${\mathrm{Wm}}^{\mathrm{\ensuremath{-}}3}$ ${\mathrm{K}}^{\mathrm{\ensuremath{-}}5}$. When we increased the volume of the resistor by attaching a thin-film cooling fin, there was a much smaller increase in ${\mathit{T}}_{\mathit{e}}$ for a given power dissipation in the resistor, in qualitative agreement with a simple model for nonuniform heating. We also measured the flux noise in dc SQUIDs at low temperatures, and found that the white noise was limited by heating of the electrons in the resistive shunts of the Josephson junctions. We were able to reduce these effects substantially by attaching cooling fins to the shunts.

Dielectric, elastic, piezoelectric, electro-optic, and elasto-optic tensors of BaTiO 3 crystals

Abstract: The complete set of material parameters of a top-seeded solution-grown ${\mathrm{BaTiO}}_{3}$ crystal has been determined by numerically evaluating available measurements and using additional measurements presented in this work. The parameters were determined at room temperature and consist of the low-frequency clamped dielectric constants ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{i}\mathit{j}}^{\mathit{S}}$, elastic stiffness constants at constant electric field ${\mathit{c}}_{\mathit{i}\mathit{j}\mathit{k}\mathit{l}}^{\mathit{E}}$, piezoelectric stress coefficients ${\mathit{e}}_{\mathit{i}\mathit{j}\mathit{k}}$, elasto-optic tensor at constant electric field ${\mathit{p}}_{\mathit{i}\mathit{j}\mathit{k}\mathit{l}}^{\mathit{E}}$, and clamped electro-optic coefficients ${\mathit{r}}_{\mathit{i}\mathit{j}\mathit{k}}^{\mathit{S}}$.