Tunneling conductance of a Bi2Sr2CaCu2O8-SnO2 junction along the c-axis

fine structure was observed in the conductance curve of a tunneling junction composed of a single crystalline Bi2212 and an evaporated SnO₂ film. It is similar to those of Bi2212-GaAs mechanical junctions and there is a certain correspondence between the structure and the phonon density of states. Thus the previous conclusion that the structure is due to phonons has been complemented by this work. The energy gap 2 was 57 meV at 13 K and T _c was 78 K. 2(0)/k _B T _c is then 8.3. (T) showed the BCS-like temperature dependence.     

The analysis of tunneling characteristics measured on Bi2Sr2CaCu2O8 surface

Cleaved in air a-b surface of Bi₂Sr₂CaCu₂O₈ (BSCCO-2212) was measured by means of STM and STS at 4.2 K in liquid hellium bath. From fitting experimental conductivity curves by Dynes' function two superconductivity parameters (gap value) and (smearing parameter) were obtained. The shape of gap structure superimposed on dI/dV characteristics depends on tip-sample distance, what is expressed by the increase of and decrease of with shortening of s. The phenomenon of becoming gap structure more distinct when approaching the tunneling tip to the surface is explained by us as the non-vacuum tunneling, where the surface contamination layer on non-metallic BiO top-surface layer strongly influences the tunneling process. Only for s short enough tunneling electrons penetrate to deeper situated CuO layers and reflect their superconducting behaviour. Non-vacuum STM images are therefore sensitive to the tip-sample distance adjustment. The dependence of gap parameters on lateral position of the tip above the sample can also occur. In such cases STS enables to state which elements of the image belong to the topography of the surface and which to its electron density of states.     

Tunneling and point-contact spectroscopy of high-T c superconductors M−Ba2Cu3O7 (M=Y,La, Eu)

Tunneling and point-contact measurements have been performed on different high-T _c superconductors M–Ba₂Cu₃O₇ with M=Y, La, Eu. The average energy gaps deduced from the tunneling spectra are about 2=33 meV for the Y- and La-type samples and about 2=38 meV for the Eu-type samples, which give ratios 2/k _B T _c in the range from 4 to 6. The point-contact characteristics show a distinct minimum in the differential resistance about zero bias and additional sharp spikes up to 40 mV. From these pointcontacts we can give an estimate of the critical current, yielding values in the range from 0.2 to 3 mA.     

Determination of the electron phonon coupling and the superconducting gap in β-(BEDT-TTF)2X crystals (X=I3, IAuI)

We performed point-contact and tunneling measurements on the organic superconductors -(BEDT-TTF)₂I₃ and -(BEDT-TTF)₂IAuI, in the normal and superconducting states. The point-contact measurement in the normal state provides the Eliashberg function ²()F (). This function has maxima at 4 and 15 mV, as well as a sharp peak at 1 mV which seems to indicate a very soft phonon strongly coupled to the electrons. The measurements in the superconducting state provide the superconducting gap, which for the tunneling measurements has a value 2/k_B T_c4, just slightly above the BCS value.     

Tunneling experiments on amorphous and crystalline superconducting tantalum films

The energy gap and the transition temperature of amorphous and crystalline superconducting Ta films are measured by tunneling experiments. The following values are obtained: 2(0)=0,65 meV,T _c=2,11 K for the amorphous state after quenched condensation and 2(0)=1,24 meV,T _c=4,06 K for the crystalline state after annealing at room temperature. The reduced energy gap 2(0)/kT _c=3,58 demonstrates that amorphous Ta films are weak-coupling superconductors. The crystallization of the amorphous Ta films takes place at 250 K.     

Long-range order in the XXZ model

The existence of long-range order is proved under certain conditions for the antiferromagnetic quantum spin system with anisotropic interactions (XXZ model) on the simple cubic or the square lattice. In three dimensions (the simple cubic lattice), finite long-range order exists at sufficiently low temperatures for any anisotropy(0) ifS1, and for 0<0.29 (XY-like) or>1.19 (Ising-like) ifS=1/2. In two dimensions (the square lattice), ground-state long-range order exists under the following conditions: for any anisotropy (0) ifS3/2; 0<0.032 (XY-like) or 0.67<<1.34 (almost isotropic) or>1.80 (Ising-like) ifS=1;>1.93 (Ising-like) ifS=1/2. We conjecture that the two-dimensional spin-1/2XY model (=0) has finite ground-state long-range order. Numerical evidence supporting this conjecture is given.     

Far-infrared spectroscopy of the supreconductor YBa2Cu4O8

The frequencies of allB _1u (z) phonon modes predicted by a group-theoretical analysis were measured and found to agree well with recent lattice dynamical calculations for this compound. We report also the determination of two superconducting gap values in YBa₂Cu₄O₈ through phonon self-energy effects in the normal and superconducting conducting state. The gap-to-T _c ratios obtained from an analysis of these effects are 2 ₁/kT _c 2.5 and 5.82 ₂/kT _c 9.2. This coincides with previous results of both phononic and electronic Raman scattering where values of 2.1 and 6.3 were found. We further find anomalous softenings of two phonon modes 40 Kabove T _c , which correlate with an observed deviation from the linear temperature dependence of the average plasma frequency _p (T).     

On the failure of the time-energy uncertainty principle

We establish, for the quantum system made up of a single free particle, the formula E t(v/c) , where E is the precision to whichE can be ascertained in time t. The measurement can be carried out with zero disturbance inE itself.     

Wavevector scaling,surface critical behavior,and wetting in the 2-d, 3-state chiral clock model

The controversial 2-d, 3-state chiral Potts model is studied using transfer matrix finite size scaling. at =0, we find dq _N/dN ^–4/5, whereq is the wavevector, the chiral field, andN the strip width (N=4–10). The result is consistent with den Nijs's crossover exponent =1/6. With surface fields on the infinite free boundaries, exponents associated with bulk magnetizationy _H, surface magnetizationy _H, and surface susceptibility are computed vs. ; results are similar for or to the infinite direction. Preliminary results are given for the bulk specific heat critical amplitudes, to test the universality of amplitude ratios. The interface wetting line is located for 01/4 using simple transfer matrix calculations of surface tensions in the solid-on-solid approximation. Overhangs or bubbles seem relatively unimportant at all temperatures.     

Ab initio study for the intermolecular interaction potential surface of Ar-N2 complex

The intermolecular interaction potentials of van der Waals Ar-N2 complex have been studied by ab initio calculations using the single and double excitation coupled cluster [CCSD(T)] theory with perturbative triples correction. The full counterpoise method is applied to correct the basis set superposition error (BSSE). It is found that the T-shaped structure is the most stable conformation with the well depth De of 12.40 meV at the minimum distance Rm of 3.70 Å. The calculated anisotropic values for Rm, R0 and De are 0.56 Å, 0.54 Å and 2.68 meV, respectively. Compared with those obtained by others, our calculated PES seems to be in better agreement with experiments.     

Unstable Particles, Gauge Invariance and the Δ++ Resonance Parameters

The elastic and radiative ⁺ p scattering are studied in the framework of an effective Lagrangian model for the ⁺⁺ resonance and its interactions. The finite width effects of this spin-3/2 resonance are introduced in the scattering amplitudes through a complex mass scheme to respect electromagnetic gauge invariance. The resonant pole ( ⁺⁺) and background contributions ( ⁰, , , and neutron states) are separated according to the principles of the analytic S-matrix theory. The mass and width parameters of the ⁺⁺ obtained from a fit to experimental data on the total cross section are in agreement with the results of a model-independent analysis based on the analytic S-matrix approach. The magnetic dipole moment determined from the radiative ⁺ p scattering is nuclear magnetons.     

Scaling of the energy gap withT c in Bi2Sr2CaCu2O8+δ

The results of a high-resolution photoemission study using synchrotron radiation of two single crystals of Bi₂Sr₂CaCu₂O₈₊, with different critical temperaturesT _c due to a variation in oxygen stoichiometry are reported. Within experimental accuracy, the energy gap 2 is found to scale withT _c , amounting to a reduced gap parameter of 2/k _BT_c7.4. Employing resonant photoemission at the O–2s and Cu–3p thresholds, two spectral peaks at binding energies of 180 meV and 320 meV were identified as predominantly O–2p-and Cu–3d 4s-derived states, respectively.     

Representations of state space transformations by Markov kernels

Every convex subset of a locally convex Hausdorff space (X, ) is equipped with the (-algebra generated by its-relatively open subsets. Within the set () of probability measures on two particular convex subsets are considered: (a) the set ^s () of probability measures with a separable support, and (b) the set ^c () of probability measures with a compact convex support. If is the base of a cone inX, then there exists an affine barycenter map from ^c () onto whose composition with the natural embedding of in ^c () yields the identity map on , and every-continuous affine transformation of can be represented by an affine transformation of ^c () that is induced by a Markov kernel. If (X, ) is a Banach space and is a closed, bounded, generating cone base inX that is contained in a hyperplane, then analogous results are obtained with respect to ^s (). Since the state spaces considered in noncommutative measure theory are cone bases and every change in time of an empirical system can be thought of as an affine transformation of the associated state space (Schrödinger picture), the existence of these representation theorems implies that the time evolution of general empirical systems can be described by dynamical concepts borrowed from classical probability theory.     

Temperature dependence and input optical power tolerance of an InGaAsP electroabsorption modulator module

We report the temperature dependence and input optical power tolerance of an InGaAsP electroabsorption (EA) modulator module. Thermal stability of the module was found to be very high. The optimum E _g at 20°C has been estimated to be 48–55 meV. At E _g of 53 meV, the insertion loss was almost independent of the temperature, while the driving voltage was strongly dependent on the temperature. The breakdown phenomena were investigated in detail; these occurred under conditions of very high input power and/or high bias voltage. Input power for breakdown was smaller for higher bias voltage or smaller E _g. Allowable maximum input optical power has a large margin (>5 dB) for the conventional input level in practical systems.     

Symmetries and half-sided modular inclusions of von Neumann algebras

LetN, be a von Neumann algebras on a Hilbert space , a common cyclic and separating vector. Assume to be cyclic and also separating forN . Denote by , _N , _N the modular operators to (, ), (N, ), resp (N , ). Assume now ^-it N ^it N for allt 0. (Such type of inclusions ((N U, ) , ) are called half-sided modular.) Then the modular groups ^it , _N ^ir , _N ^is ,t, r, s generate a unitary representation of the group S1(2, )/Z ₂ of positive energy.Another result is related to two half-sided modular inclusions (₁ , ) and (₂ , ). Under proper conditions the three modular groups ^it , ₁ ^ir , ₂ ^is ,t, r, s generate the three-dimensional subgroup of O(2, 1) of two commuting translations and the Lorentz transformation.Partly supported by the DFG, SFB 288 Differentialgeometrie und Quantenphysik.     

Additional raising of the degeneracy of CEF-split Ho3+ ions by antiferromagnetic spin-waves in Ho0.1Y0.9Ba2Cu3O6.13

Inelastic neutron scattering has been employed to study in detail the low-energy crystal-field (CEF) excitations of Ho³⁺ in tetragonal antiferromagnetic (AF) Ho_0.1Y_0.9Ba₂Cu₃O_6.13. We observe a splitting of the lowest excited ₅ doublet atT=1.5 K. This splitting is explained as resulting from the exchange interaction with the AF subsystem of copper spins. The corresponding susceptibility at the Ho³⁺ site has a symmetry lower than the tetragonal one of the CEF potential and, as a result, produces the splitting. The value of the coupling between Ho³⁺ and Cu²⁺ ionsJ _ex=2.4 meV is derived from the experimentally observed value of the splitting E=0.1 meV and parameters of the AF subsystem, known from the neutron scattering experiments. Some possible consequences of the rare-earth (RE)-copper exchange are discussed, including the interaction between RE ions via the virtual exchange by spin waves.     

Optimum profiles for dispersive multimode fibres

A simple closed-form expression is given for the index profile of multimode fibres with arbitrary dispersion providing transmission capacities as large as 1.6/ ² Mbit/s km, wheren/n. Our result reduces to a previous result of Marcatili for the special case of circularly symmetric fibres. A transmission capacity of 150 Mbit/s over a 10 km long fibre appears possible with LED sources operating at optimum wavelengths for the medium.     

Group actions on C*-algebras, 3-cocycles and quantum field theory

We study group extensions , where acts on a C^*-algebraA. Given a twisted covariant representation ,V of the pairA, we construct 3-cocycles on with values in the centre of the group generated byV(). These 3-cocycles are obstructions to the existence of an extension of byV() which acts onA compatibly with . The main theorems of the paper introduce a subsidiary invariant which classifies actions of onV() and in terms of which a necessary and sufficient condition for the the cohomology class of the 3-cocycle to be non-trivial may be formulated. Examples are provided which show how non-trivial 3-cocycles may be realised. The framework we choose to exhibit these essentially mathematical results is influenced by anomalous gauge field theories. We show how to interpret our results in that setting in two ways, one motivated by an algebraic approach to constrained dynamics and the other by the descent equation approach to constructing cocycles on gauge groups. In order to make comparisons with the usual approach to cohomology in gauge theory we conclude with a Lie algebra version of the invariant and the 3-cocycle.     

Dependence of the steepness of the exponential absorption tail on the chemical composition of materials

The quantity characterizing the steepness of the exponential tail of the fundamental absorption edge is studied. It is shown, that the magnitude of of binary compounds can be roughly estimated from their chemical composition in a way described in this paper.Boní II, Praha 4, Czechoslovakia.The author thanks Ing. D. Leal, CSc for his valuable discussions concerning this work.     

Transition temperature and gap anisotropy of pure and impure superconductors

The algebraic structure of linearized Eliashberg theory atT=T _c is exploited to derive expressions for the anisotropic gap(k, i _n ) and theT _c-enhancement. These formulas are exact to second order in the anisotropy, and require as input the isotropic gap(k, i _n ), the anisotropic spectral function ² F(k, ), and the impurity scattering rate 1/ _k . Approximate formulas based on a square well model are also given. The formulas for impurity effects are new and very simple.