Table of contents

The stationary localized states of light fluxes propagating in periodic systems of plane-parallel nonlinear waveguides are investigated. It is shown that the problem is reducible to that of a model of connected anharmonic oscillators. All of the parameters of such an oscillator model are found exactly from the microscopic description of the problem. The solution for an optical beam localized perpendicularly to the direction of its propagation is analytically derived.

Luttinger liquids are characterized by the critical exponent Θ of the momentum distribution around the Fermi momentum k_F. Typically Θ⩽1/2, signalling a singularity characterizing a residual Fermi surface. Results of photoemission experiments can be interpreted in terms strongly interacting Luttinger liquids with Θ⩾1 with the residual Fermi surface disappearing. We construct integrable models with such behaviour - models given by the SU(ν) t-J interaction with a hard-core repulsive potential between electrons at distances less than or equal to Δ. The models exhibit both weakly and strongly interacting Luttinger behaviours with Θ varying continuously in the range 0⩽Θ⩽½(1 + Δ-1/[ν(1 + Δ)])² depending on the electron density. In the extreme high-density limit the model exhibits a Mott-Hubbard gap and reduces to an isotropic Heisenberg chain with a new spacing parameter Δ + 1.

Although quasi-two-dimensional organic superconductors such as κ-(BEDT-TTF)₂Cu(NCS)₂ (BEDT-TTF≡bis(ethylene-dithio)tetrathiafulvalene) seem to be very clean systems, with apparent quasiparticle mean free paths of several thousand ångströms, the superconducting transition is intrinsically broad (e.g. ~1 K wide for T_c≈10 K). We propose that this is due to the extreme anisotropy of these materials, which greatly exacerbates the statistical effects of spatial variations in the potential experienced by the quasiparticles. Using a statistical model, we are able to account for the experimental observations. A parameter , which characterizes the spatial potential variations, may be derived from Shubnikov-de Haas oscillation experiments. Using this value, we are able to predict a transition width which is in good agreement with that observed in megahertz penetration-depth measurements on the same sample.

We report measurements of the pressure-dependent superconducting transition temperature T_c and electrical resistivity of the heavy-fermion compound CeCoIn₅. Pressure moves CeCoIn₅ away from its proximity to a quantum-critical point at atmospheric pressure. Experimental results are qualitatively consistent with theoretical predictions for strong-coupled, d-wave superconductivity in an anisotropic three-dimensional superconductor.

We report on the photoluminescence (PL) of anatase TiO₂ thin films caused by the addition of ZnFe₂O₄ nanoparticles prepared by the radio-frequency sputtering method. X-ray diffraction and PL analyses illustrate that there is a very strong band of PL from the anatase TiO₂ thin films caused by the addition of ZnFe₂O₄ at both room and low temperatures; the anatase TiO₂ thin films without this addition show no PL. There is a very weak band of PL from rutile TiO₂ thin films. The strong PL band for the anatase TiO₂ thin films with the addition of ZnFe₂O₄ may be due to increased localization of impurity- and defect-trapped excitons.

The surface structure of RbI(001) was determined directly by means of medium-energy ion scattering (MEIS) with a monolayer depth resolution. The rumpled surface structure determined here was compared with semi-classical shell-model calculations. On the basis of a simple model regarding the lattice site ion as a point charge accompanied by a dipole moment, we evaluated the dipole moments of the top- and second-layer I^- and Rb⁺ ions self-consistently from the relaxed lattice positions determined by means of MEIS and from the polarizabilities estimated systematically from experimental refraction data. The balance between a short-range force and a long-range coulombic one determined the equilibrium positions of the top- and second-layer ions; these are consistent with those derived by means of MEIS within the experimental uncertainties of 0.02 Å. This indicates that the polarizablities derived from the refraction data and the interatomic (short-range) potentials of the Born-Mayer type are applicable.

The reflection anisotropy (RA) spectra from clean Ni(110), Na/Ni(110)(1×2), and CO/Ni(110) surfaces have been measured between 1.5 eV and 4.0 eV. Electronic transitions involving exchange-split d bands to an unoccupied surface state contribute a broad structure to the RA profile of Ni(110). The Na-induced surface reconstruction gives rise to a change in the RA profile that is related to changes in the unoccupied surface state. RA spectroscopy is found to be sensitive to the exposure of Ni(110) to CO.

The local structure of ultrathin a-Si:H sublayers embedded in a-Si:H/a-SiN_x:H multilayers before and after thermal annealing is investigated by Raman scattering spectroscopy. It is found that the confinement of the interfaces leads to a higher temperature being needed for crystallization of the multilayer with thinner a-Si sublayers. The local structure of a-Si becomes more disordered in the uncrystallized multilayer upon thermal annealing due to H-atom expulsion. The transverse optical mode of the residual a-Si shows a shift to high frequencies in peak position with a sharpening of the peak for the nc-Si/a-SiN_x multilayers with increasing annealing temperature, which means that the network of a-Si tends to become more ordered. This tendency is not induced by the stress created during the thermal annealing but caused by the relaxation of the a-Si network.

Linear magneto-optical Kerr effect (MOKE) microscopy and magnetization-induced second-harmonic-generation (MSHG) magnetometry and imaging were used as two complementary optical techniques to measure the magnetic hysteresis loops and to visualize the domain structure in Pt/Co/Pt thin films with a weak uniaxial in-plane magnetic anisotropy. While the MOKE is used to probe the magnetization over the full thickness of the Co layer, MSHG is used to check the Co/Pt interfaces selectively. When the magnetic field H is not applied along the easy axis a, longitudinal MOKE and MSHG hysteresis loops exhibit different shapes. The differences between the longitudinal MOKE and MSHG magnetic pattern images for H∥a are only found in domain wall regions. All of these results are interpreted by considering transverse components of the non-linear optical polarization.

The electronic structure of the layered compound 2H-TaSe₂ has been studied using angle-resolved photoemission before and after in situ intercalation with Na and Cs. Core level spectra verified that Na and Cs both intercalate easily at room temperature, with only small amounts remaining on the surface. Valence band spectra revealed changes in the electronic band structure which were much more extensive than predicted by the rigid band model, but which were in reasonable agreement with theoretical bands calculated by the LAPW method. Some discrepancies between the experimental and calculated results are probably due to intercalation induced changes in the stacking of host layers. A general similarity with results from transition metal dichalcogenides with 1T structure indicates that the intercalation properties are not critically dependent on the internal structure of the host layers.

The growth of Co on Cu(111) with Pb as a surfactant is found to be accompanied by a considerable surface reconstruction of (4 × 4) symmetry induced by the surfactant. Its crystallography was investigated by quantitative low-energy electron diffraction (LEED) for an initial and later stage of growth with deposition of 1.3 monolayer (ML) and 7 ML Co, respectively. In the low coverage case the surface reconstruction is rather similar to that of Pb/Cu investigated earlier. It extends deep into the substrate with simultaneous minimization of the Pb layer buckling. The structure seems to be controlled by dominating fcc-stacking characteristic of this early stage of growth. With further cobalt deposition the type of reconstruction changes. For the 7 ML Co film it is restricted to the Pb and top Co layer only with the buckling of the surfactant layer considerably increased. We discuss that this may be attributed to the slightly different lattice parameters of Cu and Co, though the influences of the different stacking involved cannot be ruled out. The top film layer is always reconstructed during the whole growth which might be responsible for the easy exchange processes which take place during the growth and are essential for the layer-by-layer growth as found earlier.

X-ray structure analysis of single crystals of the Cu_xTiS₂, which were prepared by the iodine transport and the electrochemical methods, has been performed at room temperature. The structure of the samples prepared by the electrochemical method remains that of the mother crystal TiS₂, i.e. a layered compound. The other samples prepared by the iodine transport method have a spinel structure without a layered structure. Cu atoms in the Cu_xTiS₂ made by this method tend to occupy tetragonal sites. This means that the electrochemical method is an effective method for the preparation of the layered compounds Cu_xTiS₂. The electron density distributions for the layered compounds by the maximum entropy method reveal that covalent bonding exists between the Ti and S atoms. On the other hand, no covalent electrons are found between Cu and S atoms. It is understood that Cu atoms show ionic character in these layered compounds.

(TaSe₄)₂I is a quasi-one-dimensional (1D) electrical conductor. It exhibits a phase transition at T_CDW = 263 K towards a charge-density-wave (CDW) state at low temperatures. We report a full structure refinement of the incommensurately modulated structure in the CDW state at T = 110 K against synchrotron radiation, single-crystal x-ray diffraction data. At room temperature the crystal structure has tetragonal symmetry with space group I422. In the CDW state each main reflection in the x-ray scattering is surrounded by eight incommensurate satellites at (±0.064,±0.064,±0.151). The CDW state is found to comprise four domains, and it is characterized by one modulation wavevector. With respect to a √2×√2×1 supercell it has the symmetry of the superspace group F2(0,β,γ) with β = 0.128 and γ = 0.151. The first part of the modulation is found to be a transverse acoustic wave, involving amplitudes of similar magnitudes of about 0.13 Å on all atoms. The second part of the modulation involves displacements of the Ta atoms of about 0.03 Å, that are parallel to the 1D chains. These are interpreted as reflecting the CDW. A Landau free-energy model is developed, that shows that symmetry arguments allow the phase transition to be second order.

The electronic properties of a Σ = 13 32.2° [0001] tilt grain boundary in ZnO have been investigated using first-principles calculations. Two atomic models for the boundary have been considered, one of which contains structural units that are consistent with those observed for this orientation using electron microscopy. Doping both the grain boundary models with antimony reveals a strong driving force for segregation. Analysis of the electronic densities of states, bond populations and Mulliken charges shows that antimony creates a localized impurity state in the grain boundary and acts as a donor dopant. The resulting charge accumulation at the grain boundary together with the presence of local bonds that are metallic in character, will influence the mechanism for charge transport across the interface and this is discussed in relation to varistor applications.

The effect of pressure on optical phonon frequencies of MgB₂ has been calculated using the frozen-phonon approach based on a pseudopotential method. Grüneisen parameters of the harmonic mode frequencies are reported for the high-frequency zone-centre E_2g and B_1g and the zone-boundary E_2u and B_2u modes at A. Anharmonic effects of phonon frequencies and the implications of the calculated phonon frequency shifts for the pressure dependence of the superconducting transition temperature of MgB₂ are discussed. Also reported are Raman and optical reflectance spectra of MgB₂ measured at high pressures. The experimental observations in combination with calculated results indicate that the broad spectral features that we observed in the Raman spectra at frequencies between 500 and 900 cm^-1 cannot be attributed to first-order scattering by zone-centre modes, but originate in part from a chemical species other than MgB₂ at the sample surface and in part from a maximum in the MgB₂ phonon density of states. Low-temperature Raman spectra taken at ambient pressure showed increased scattering intensity in the region below 300 cm^-1.

Computer simulations of the β-phase of PbF₂ using a polarizable ion interaction potential are described. Studies of KF- and YF₃-doped PbF₂, as well as the pure material are included. The simulations reproduce the macroscopic observables associated with the transition to superionic behaviour well, including the heat capacity, lattice constant and conductivity. An explanation is provided of the familiar observation of the similarity of the conductivities of the superionic solid just below and of the melt just above the melting transition. Comparisons are made with diffraction and diffuse scattering studies, which confirm that the nature of the fluoride ion disorder above the transition temperature in the simulations is very similar to that deduced from experiments. This involves a cooperative excitation of the fluoride sublattice, which results in the creation of a large number of vacancies and interstitials. Detailed studies of the positional correlations between these defects reveal a high degree of order associated with specific clustering effects. These positional correlations appear to be stronger than would be anticipated from recent mean-field descriptions of the interactions between charged defects in superionic materials. The nature of the correlations is compared with that associated with the interstitial clusters found in moderately YF₃-doped PbF₂ at low temperatures.

We derive the random-phase approximation for spin excitations in general multi-band Hubbard models, starting from a collinear ferromagnetic Hartree-Fock ground state. The results are compared with those from a recently introduced variational many-body approach to spin waves in itinerant ferromagnets. As we exemplify for Hubbard models with one and two bands, the two approaches lead to qualitatively different results. The discrepancies can be traced back to the fact that the Hartree-Fock theory fails to describe properly the local moments which naturally arise in a correlated-electron theory.

The crystal structures of all layered ternary carbides called '312' phases including Ti₃AlC₂, Ti₃SiC₂ and Ti₃GeC₂ have been fully optimized by means of ab initio total-energy calculations. The equilibrium lattice parameters, the atomic positions in the unit cell and interatomic distances have been determined. The differences between the calculated and the measured lattice constants are generally less than 1%. It is also shown that c/a of the hexagonal lattices decreases from Ti₃AlC₂ to Ti₃GeC₂. The calculated bulk moduli are 190 GPa for Ti₃AlC₂, 202 GPa for Ti₃SiC₂ and 198 GPa for Ti₃GeC₂, respectively, which are comparable to that of TiC. The electronic structures reveal that the Ti(1, 2) and C atoms form a strong Ti(2)–C–Ti(1)–C–Ti(2) covalent bond chain, while the bonding between Ti(2) and M (M = Al, Si, Ge) is relatively weak. The strong Ti(2)–C–Ti(1)–C–Ti(2) covalent bond chain corresponds to the high strength and modulus, while the metallic bond corresponds to the metallic conductivity of these ternaries.

We illustrate the renormalized perturbation expansion method by applying it to a single-impurity Anderson model. Previously, we have shown that this approach gives the exact leading-order results for the specific heat, spin and charge susceptibilities and leading-order temperature dependence of the resistivity for this model in the Fermi-liquid regime, when carried out to second order in the renormalized interaction Ũ. Here we consider the effects of higher-order quasiparticle scattering and calculate the third-order contributions to the H³-term in the impurity magnetization for the symmetric model in a weak magnetic field H. The result is asymptotically exact in the weak-coupling regime, and is very close to the exact Bethe ansatz result in the Kondo regime. We also calculate the quasiparticle density of states in a magnetic field, which is of interest in relation to recent experimental work on quantum dots.

Ferroelectric-superconductor heterostructures consisting of GdBa₂Cu₃O_7-x and YBa₂Cu₃O_7-δ channels and Pb(Zr_xTi_1-x)O₃ (PZT) gate insulators were studied theoretically. We have shown that the remnant polarization P_r of the PZT gate induces a change in the carrier concentration n_h of the superconductor, supposing direct action of the Coulomb field on the carriers. The dependences of the superconducting transition temperature T_c on n_h were calculated in two cases: in the two-band model and in the phenomenological model with a parabolic dependence of T_c on n_h. The ferroelectric field effects are maximum in the superconducting film sample at a doping level where the transition temperature T_c as a function of n_h has the largest slope dT_c/dn_h. In agreement with the experiment, the shifts of T_c in the ferroelectric field |ΔT_c(±P_r)| decrease when the film thickness d increases. The form of the calculated T_c(V_g) dependences on the gate voltage V_g can be related to the ferroelectric hysteresis loop of the PZT gate insulator.

Magnetoconductance (MC) measurements have been performed on a 2140 Å thick tungsten carbide film at temperatures very close to the superconducting transition temperature T_c of the film. The data are dominated by superconducting fluctuations. A novel three-dimensional phenomenological model is proposed to explain the MC data, yielding good fits. The Larkin beta factor, β_Larkin, appeared as a fitting parameter. An expression proposed by Larkin for β_Larkin failed badly for temperatures extremely close to T_c. But at intermediate and high temperatures compared to T_c, Larkin's expression gave very good agreement in fits to the MC data. At temperatures very close to T_c, a crossover from three dimensions to two dimensions was observed in the behaviour of the MC of the film.

The phase diagram of the quasi-one-dimensional model which is most relevant to organic ferromagnets of a certain kind is considered. In this model, strong electron-phonon interaction is considered adiabatically and the coupling between local spins and π-electrons is treated within a mean-field theory. A full phase diagram is given. The results show that there are two new kinds of phase which were not revealed in previous treatments. Our results may be helpful for the synthesis of organic ferromagnets.

The shift of the electron spin-resonance (ESR) line caused by a dynamic nuclear spin polarization is measured at low temperatures (5-11 K) and X-band frequency for phosphorus-doped silicon in the concentration range (2.7-7.3)×10¹⁸ cm^-3 covering the metal-insulator transition. The samples are also characterized by the temperature dependence of their microwave electrical conductivity. The g-factor, ESR linewidth and saturation behaviour are analysed as regards their dependence on the temperature and phosphorus concentration. The variation of the integral Overhauser shift of the ESR line with the temperature and phosphorus concentration is derived and discussed.

The effect of pressure on the magnetic and electronic properties of synthetic FeS and Fe₇S₈ has been investigated by using ⁵⁷Fe Mössbauer and electrical resistance measurements on polycrystalline samples pressurized in miniature gem anvil cells up to a pressure of ∼12 GPa in the temperature range 300–5 K. FeS in the low-pressure phases (P ≲ 7 GPa) has thermally activated charge carriers and a high-spin electronic configuration along the room temperature isotherm, whereas the high-pressure monoclinic phase (P ≳ 7 GPa) adopts a magnetically quenched low-spin state and a non-metallic behaviour associated with the filled valence band. The non-metallic behaviour observed in all pressure phases is explained in terms of electron correlation between Fe:3d electrons. In contrast, Fe₇S₈ is magnetic-metallic below ∼5 GPa and diamagnetic-metallic above this pressure. The metallic behaviour is ascribed to hole conduction in the S:3p band, as inferred from the temperature dependence of the Mössbauer data. The collapse of band magnetism at ∼5 GPa in Fe₇S₈ may be due to pressure-induced band broadening, leading to a breakdown of the Stoner criterion.

Core-hole (x-ray) photoemission (XPS) provides a powerful indirect probe of the low-energy charge excitations of a many-electron system. We have previously argued that XPS can be used to study the way in which a (pseudo)gap opens for charge excitations across, for example, a metal-superconductor transition, independently of any change in the spin excitation spectrum, and so provide information about spin-charge separation. Here we consider how the loss of low-energy excitations modifies XPS spectra in the context of several simple models, considering particularly the case of gap opening for both s- and d-wave superconductors, and find that XPS, like the nuclear magnetic resonance technique, is in principle sensitive to nodes in the superconducting gap function.

A theoretical investigation is made of the plasma-wave instability mechanism in a two-dimensional (2D) electron fluid in a field-effect transistor (FET) in the presence of a perpendicular magnetic field. The influence of electron collisions with impurities and/or phonons is also taken into account. The 2D electron fluid in the FET channel is treated within the framework of hydrodynamics. The treatment is valid for a nondegenerate electron fluid in which the mean free path for interelectronic collisions is much smaller than the device length and the mean free path due to impurities and/or phonons. It is shown that a relatively low direct current should be unstable because of magnetoplasma-wave amplification due to the reflection of the wave from the device boundaries. The role of an applied magnetic field is additive: the greater the magnetic field, the larger the wave increment. In that sense an applied magnetic field may be used to compensate (or overcome) the subtractive role played by collisions on plasma-wave generation. Such a ballistic FET is promising for the generation of tunable electromagnetic radiation in the terahertz frequency range.