Jan R. Engelbrecht

Microscopic electronic inhomogeneity in the high-Tc superconductor Bi2Sr2CaCu2O8+x.

The parent compounds of the copper oxide high-transition-temperature (high-Tc) superconductors are unusual insulators (so-called Mott insulators). Superconductivity arises when they are ‘doped’ away from stoichiometry. For the compound Bi2Sr2CaCu2O8+x, doping is achieved by adding extra oxygen atoms, which introduce positive charge carriers (‘holes’) into the CuO2 planes where the superconductivity is believed to originate. Aside from providing the charge carriers, the role of the oxygen dopants is not well understood, nor is it clear how the charge carriers are distributed on the planes. Many models of high-Tc superconductivity accordingly assume that the introduced carriers are distributed uniformly, leading to an electronically homogeneous system as in ordinary metals. Here we report the presence of an electronic inhomogeneity in Bi2Sr2CaCu2O8+x, on the basis of observations using scanning tunnelling microscopy and spectroscopy. The inhomogeneity is manifested as spatial variations in both the local density of states spectrum and the superconducting energy gap. These variations are correlated spatially and vary on the surprisingly short length scale of ∼14 Å. Our analysis suggests that this inhomogeneity is a consequence of proximity to a Mott insulator resulting in poor screening of the charge potentials associated with the oxygen ions left in the BiO plane after doping, and is indicative of the local nature of the superconducting state.

Inhomogeneous d-wave superconducting state of a doped Mott insulator

Recent atomic resolution scanning tunneling microscope (STM) measurements discovered remarkable electronic inhomogeneity, i.e., nanoscale spatial variations of the local density of states (LDOS) and the superconducting energy gap, in the high-T-c superconductor Bi2Sr2CaCu2O8 + x. Based on the experimental findings, we conjectured that the inhomogeneity arises from variations in local oxygen doping level and may be generic of doped Mott insulators. In this paper, we provide theoretical support for this picture, We study a doped Mott insulator within a generalized t-J model, where doping is accompanied by ionic Coulomb potentials centered in the BiO plane located a distance d(s) away from the CuO2 plane. We solve, at the mean-field level, a set of spatially unrestricted Bogoliubov-de Gennes equations self-consistently to obtain the distributions of the hole concentration, the valence bond, and the pairing order parameters for different nominal/average doping concentrations. We calculate the LDOS spectrum, the integrated LDOS, and the local superconducting gap as those measured by STM, make detailed comparisons to experiments, and find remarkable agreement with the experimental data. We emphasize the unconventional screening of the ionic potential in a doped Mott insulator and show that nonlinear screening dominates on nanometer scales, comparable to the short coherence length of the superconductor. which is the origin of the electronic inhomogeneity. It leads to strong inhomogeneous redistribution of the local hole density and promotes the notion of local doping concentration (LDC). We find that the inhomogeneity structure manifests itself at all energy scales in the STM tunneling differential conductance. and elucidate the similarity and the differences between the data obtained in the constant tunneling current mode and the same data normalized to reflect constant tip-to-sample distance. We also discuss the underdoped case where nonlinear screening of the ionic potential turns the spatial electronic structure into a percolative mixture of patches with smaller pairing gaps embedded in a background with larger gaps to single particle excitations.

PSEUDOGAP ABOVE TC IN A MODEL WITH DX2-Y2 PAIRING

We study the anomalous normal state properties of a simple two-dimensional model whose ground state is a d-wave superconductor. Using a self-consistent, conserving formulation, we show that pairing correlations above T_c lead to the appearance of a highly anisotropic pseudogap in the electronic spectral function and the destruction of the Fermi surface. We discuss the similarities and differences between our results and ARPES experiments on underdoped cuprates.

Effect of Ferromagnetic Spin Correlations on Superconductivity in Ferromagnetic Metals

We study the renormalization of quasiparticle properties in weak ferromagnetic metals due to spin fluctuations, away from the quantum critical point for small magnetic moment. We explain the origin of the s -wave superconducting instability in the ferromagnetic phase and find that the vertex corrections are small and that Migdal{close_quote}s theorem is satisfied away from the quantum critical point. {copyright} {ital 1998} {ital The American Physical Society}

Polyhedral object recognition using Hough-space features

Abstract We propose a new technique for three-dimensional (3-D) polyhedral object recognition on the basis of a single two-dimensional (2-D) view of a 3-D scene. The binary gradient image of the captured scene is converted into the Hough-space domain. The cluster patterns originating from straight-line features of the image are explored by reasoning in Hough space. This yields an attributed graph representation of the object to be recognized which is compared to similar representations of CAD-designed wire frame model objects by means of a new attributed subgraph isomorphism algorithm. Simulation experiments illustrate this promising new approach.

S -wave superconductivity in weak ferromagnetic metals

We investigate the behaviour of weak ferromagnetic metals close to the ferromagnetic critical point. We show that in the limit of small magnetic moment the low temperature metallic phase is rigorously described by a local ferromagnetic Fermi liquid that has a momentum-independent self-energy. Whereas, non-Fermi liquid features develop at higher temperatures. Furthermore, we find that an instability towards s -wave superconductivity is possible when the exchange splitting is comparable to the superconducting gap.

Fermi gas descriptions of nuclear level densities

Abstract In this paper the derivation of nuclear level densities from a Fermi gas treatment of the nucleons is surveyed. In fact, there are three classes of Fermi gas models: the infinite, in which an unlimited number of fermions are available for excitation, the finite, in which this number is finite but the single-particle spectrum is unbounded, and the truncated Fermi gas (TFG), where this spectrum consists of a finite number of levels. Exact calculations within the TFG are possible by means of combinatorial methods, while the finite model may be analysed by assuming that the assumptions of statistical mechanics apply to the numbers of nucleons in a nucleus and then using a saddle point approximation. The standard Bethe formulae actually correspond to the infinite model and apply to the other models only in the low-energy limit. Furthermore, at very low energies they do not approximate any of the models with high accuracy and should there be corrected, as indicated in the text. For high-energy or high-temperature applications, it is essential to take into account the effects of truncation. The TFG is constructed here in a way which accommodates the two main features in which the results for real interacting nucleons should differ from the Fermi gas picture. In order to make the TFG results accessible for practical applications without having to perform the cumbersome combinatorial calculations for each case of interest, simple approximations are presented for the nuclear level densities, as well as the closely related canonical partition functions, as obtained by means of calculations using the truncated Fermi gas model.

Robustness of a local Fermi liquid against ferromagnetism and phase separation

We study the properties of Fermi liquids with the microscopic constraint of a local self-energy. In this case the forward scattering sum rule imposes strong limitations on the Fermi-liquid parameters, which rule out any Pomeranchek instabilities---both ferromagnetism and phase separation are suppressed. Superconductivity is possible in an {ital s}-wave channel only. We also study the approach to the metal-insulator transition, and find a Wilson ratio approaching 2. This ratio and other properties of Sr{sub 1{minus}{ital x}}La{sub {ital x}}TiO{sub 3} are all consistent with the local Fermi-liquid scenario.

Classification of attractors for systems of identical coupled Kuramoto oscillators

We present a complete classification of attractors for networks of coupled identical Kuramoto oscillators. In such networks, each oscillator is driven by the same first-order trigonometric function, with coefficients given by symmetric functions of the entire oscillator ensemble. For [Formula: see text] oscillators, there are four possible types of attractors: completely synchronized fixed points or limit cycles, and fixed points or limit cycles where all but one of the oscillators are synchronized. The case N = 3 is exceptional; systems of three identical Kuramoto oscillators can also posses attracting fixed points or limit cycles with all three oscillators out of sync, as well as chaotic attractors. Our results rely heavily on the invariance of the flow for such systems under the action of the three-dimensional group of Möbius transformations, which preserve the unit disc, and the analysis of the possible limiting configurations for this group action.

Dynamical phase transitions in periodically driven model neurons

We explore the dynamics of an integrate-and-fire neuron with an oscillatory stimulus. The frustration due to the competition between the neuron’s natural firing period and that of the oscillatory rhythm, leads to a rich structure of asymptotic phase locking patterns and ordering dynamics. The phase transitions between these states can be classified as either tangent or discontinuous bifurcations, each with its own characteristic scaling laws. The discontinuous bifurcations exhibit a new kind of phase transition that may be viewed as intermediate between continuous and first order, while tangent bifurcations behave like continuous transitions with a diverging coherence scale.