Table of contents

Density-based ab initio molecular dynamics has been used to investigate the stability and ground-state geometries of heteronuclear clusters of and . Our investigations of these clusters indicate that the s - p bonded electrons favour a tetrahedral coordination, which plays a significant role in stabilizing the geometries of these clusters. We also report a remarkable ground-state structure for the cluster, namely a face-centred cube with the Al atoms at the face centres forming an octahedron and Li atoms at the corners of the cube. The stability analysis based on the energetics shows that these clusters do not conform to the magic shell numbers observed for homonuclear alkali atom clusters.

An interaction between two heavy electrons mediated by two light electrons is investigated within the asymmetric Hubbard model on a square cluster with sites. The pair correlation function describing the probabilities of all relative positions of the heavy electrons is calculated by an approximative method. An effective attraction is found to exist in a certain range of model parameters.

We propose a configuration interaction mechanism that leads to hole pairs with zero repulsion energy which are exact eigenstates of the two-band Hubbard Hamiltonian. The two-hole pairs have symmetry and arise from degenerate states at the Fermi level; we show that they must exist independently of the band filling. To discuss the possible relevance of these states to the problem of pairing in high- superconductors we solve five- and nine-site model clusters with four holes. The quasiparticles become dressed by the interaction with the background holes and get paired with a set of valence band parameters well established for high- cuprates. We predict a number of important experimental facts such as binding energies of the correct order of magnitude, the symmetry of the order parameter and the singlet - triplet energy separation of the Cooper pairs.

We study the planar antiferromagnetic Heisenberg model on a decorated hexagonal lattice, involving both classical spins (occupying the vertices) and quantum spins (occupying the middle of the links). This study is motivated by the description of a recently synthesized molecular magnetic compound. First, we trace out the spin- degrees of freedom to obtain a fully classical model with an effective ferromagnetic interaction. Then, using high-temperature expansions and Monte Carlo simulations, we analyse its thermal and magnetic properties. We show that it provides a good quantitative description of the magnetic susceptibility of the molecular magnet in its paramagnetic phase.

We study here the effect of local lattice distortion on the electronic structure of non-isochoric alloys with large size difference between the constituents using the augmented space recursion. In particular we study such effects in CuPd and CuBe alloys.

We present an all-electron fully charge-self-consistent Korringa - Kohn - Rostoker coherent potential approximation (KKR-CPA) study of the electronic structures of disordered bcc alloys over the entire composition range. Specific computations are reported for x = 0.0, 0.25, 0.50, 0.75, and 1.0. Extensive comparisons with the predictions of the Nb-based rigid-band model (RBM) and other theoretical results, as well as with the relevant experimental results insofar as they are available are made. The particular issues that we focus on concern the evolution of the Fermi surface (FS), and the changes in the density of states and the superconducting transition temperature of Nb with increasing Mo content. The N- and H-centred FS sheets of Nb are found to shrink essentially rigidly, but the -centred sheets evolve in a highly non-rigid-band manner. The x = 0.25 Mo alloy displays an especially large disorder-induced smearing of the -centred FS sheets. Direct experimental information concerning the FS is available only for the N-centred sheet via positron annihilation and in this regard our results are in accord with the measurements. Concerning superconductivity, we have computed the Hopfield parameters and for the Nb and Mo sites, and used the results to obtain for via the McMillan formula. We find that this simple scheme describes the observed composition dependence of in reasonably well.

The plane-wave pseudopotential approach to the density-functional theory (DFT) in the local-density approximation (LDA) is used for an ab initio calculation of pressure-dependent structural, lattice-dynamical, and dielectric properties of cubic silicon carbide (3C SiC). Whereas the influence of hydrostatic pressure on the structural and the underlying bonding properties is treated within the DFT-LDA, the linear-response theory is applied to describe the pressure dependence of the zone-centre phonon frequencies, the dielectric constant, and the Born effective charge of 3C SiC. Furthermore, the results for 3C SiC are compared with the corresponding ones for silicon and diamond.

We study the lasing action due to nonlinear interactions of photons with boson elementary excitation, such as phonons and excitons, and point out the distinct features from the conventional laser model described by the two-level model. External feedback by means of cavity mirrors is unnecessary for the lasing action as well as for the increasing absorption optical bistability. It is shown that the Landau theory of the second-order phase transition is applicable to the threshold behaviour of the present mirrorless laser model.

In zero field, shows thermally activated behaviour for all values of x. For charge ordering occurs at 250 K, with long-range antiferromagnetic ordering at lower temperatures. For a range of compositions a first-order magnetic-field-induced insulator - metal transition produces changes in resistivity of up to 12 orders of magnitude at low temperatures. These conducting states are metastable, resulting in a large hysteresis in resistivity with changes in both magnetic field and temperature. There is a marked relationship between the resistivity and the magnetic state of the material. Below the charge-ordering temperature, metamagnetic transitions occur which transform the magnetic correlations from either paramagnetic or antiferromagnetic to ferromagnetic. The range of compositions for which these metamagnetic transitions occur, the fields required to induce the ferromagnetic state, and the irreversible changes in the nature of the magnetic ordering all correlate with the field-induced changes in resistivity.

Numerical studies of the dimensionless conductance g in 3D metal - insulator systems are reported. A site quantum percolation model is defined. It consists of two semi-infinite ideal metal electrodes and a disordered sample of size located between them. The disorder of the sample is controlled by the metal fraction p of conducting particles randomly occupying the sites of the cubic lattice with probability p. A tight-binding one-electron Hamiltonian with diagonal disorder and a probability density of site energies of the form is considered. Magnetic field is also introduced into the model. The conductance g is calculated using the Landauer - Büttiker formula and the Green's function technique. It is found that above the classical percolation threshold - that is, for - a second critical point exists denoted as . In the region , , where is the localization length, the system is localized, while in the range where the conductance tends to indicate metallic-type behaviour. By fitting the estimated data on versus ln g to the approximate relation for the scaling function valid in the vicinity of the critical point, the critical conductance is estimated to be and the correlation length critical exponent is estimated to be . Using a finite-size scaling technique and are also found. Both estimates of are expressed in units of and are in good agreement with one another. It is found that in the region where the system indicates positive magnetoconductance typical for a disorder-induced localized states phase, while in the region the magnetoconductance is negative as expected for an extended states phase.

Polyaniline films prepared via the camphorsulphonic acid (CSA)m-cresol solution processing route have been synthesized with doping levels in the range of 10 - 90%. The electrical conductivity of these films has been measured as a function of temperature between 10 and 300 K. At a doping level of 30% the onset of metallic transport is observed, and at 60% the films are found to exhibit metallic transport down to 135 K, and have a maximum room-temperature conductivity of . The results are modelled in terms of a heterogeneous model of fluctuation induced tunnelling (FIT) and metallic transport.

The high-frequency response of electrons in double quantum wells (DQWs) under an in-plane magnetic field is considered. The absorption, the Voigt effect and the transverse dipole moment due to electron transitions between tunnel-coupled levels are calculated for excitation by an electric field parallel to the 2D plane; the depolarization field, which is perpendicular to the 2D plane, is also taken into account. Strong modification of the intersubband absorption spectrum (the appearance of two absorption peaks, which demonstrate different collisionless broadening and shift) is found under increasing magnetic field. The spectral dependencies of the Voigt effect and induced dipole moment are calculated. Such dependencies are different in essence for small magnetic fields, for which both tunnel-coupled states are occupied; for intermediate magnetic fields, for which the Fermi level intersects the anticrossing gap; and for large fields, for which the electrons are localized in two valleys of the lowest level. Numerical estimates of these effects are presented for typical DQW structures.

We have measured the magnetoresistance of a variety of structures to search for effects associated with composite fermions (CF) near the Landau filling factor . We find evidence for effects due to randomization of semiclassical ballistic CF trajectories. These produce magnetoresistance features similar to those observed near zero magnetic field. However, we were not able to reproduce the recent CF magnetic focusing experiment despite using devices of very similar quality to those used in the original experiment. We also searched, without success, for phenomena due to phase coherence of CF. The relative ease with which the various magnetoresistance effects are seen in CF is discussed, in part with the aid of semiclassical simulations. It is discovered that inhomogeneities of carrier density cause the magnetoresistance anomalies to be smeared out, largely as a result of spatial variations in the effective magnetic field experienced by the CF. We find also that experiments which are based on randomization of trajectories are more resilient to this spatial variation.

Low-frequency shot noise and dc current profiles for a double-barrier resonant-tunnelling structure (DBRTS) under a strong magnetic field applied perpendicular to the interfaces have been studied. Structures with a 3D and 2D emitter have both been considered. The calculations, carried out with the Keldysh Green's function technique, show strong dependencies of both the current and noise profiles on the bias voltage and magnetic field. The noise spectrum appears sensitive to charge accumulation due to barrier capacitances, and both noise and dc current are extremely sensitive to the Landau level broadening in the emitter electrode and can be used as a powerful tool to investigate the latter. As an example, two specific shapes of the level broadening have been considered - a semi-elliptic profile resulting from the self-consistent Born approximation, and a Gaussian one resulting from the lowest-order cumulant expansion.

The temperature-dependent thermoelectric power S of insulating and metallic Bi-2212 and Tl-2212 samples are scaled to universal master curves. For insulating samples, S passes through a peak at a characteristic temperature , which decreases with increasing carrier concentration. For metallic samples a scaling parameter (= dS/dT at high temperatures) decreases with increasing carrier density. It is argued that is related to the energy needed for activation conduction whereas the change in may be due to increase in with carrier density, where n is the concentration and is the effective mass of the carriers.

We study the dynamics of a 2D array of Josephson junctions biased with both dc and ac currents. Within certain ranges of the dc current intensity a locking between the natural oscillation frequency of the array and that of the ac forcing term occurs, giving rise to periodic solutions. As expected, a set of Shapiro steps appears in the curve. We show that there is no one-to-one correspondence between the value of on the Shapiro step and the dynamical state of the array. In particular for a frustration equal to 0.5, besides the well-known ground state, g.s., of the array (the checkerboard-like vortex configuration), there exist other dynamical states accessible to the system. These latter are characterized by the same average voltage of the g.s. but different average energies and vortex configurations, with one or more domain walls. These `new' states are stable against small thermal fluctuations and phase perturbations. A better insight into the physical conditions needed to generate them has been obtained by studying the dynamical behaviour of a ladder as a function of its size and of its orientation with respect to the external bias current The relevance of our observations to the experimental studies of the array dynamics performed on a microscopical scale is briefly discussed.

Measurements of the superconducting transition temperature of with K (sample 1) and with K (sample 2) have been performed under a pressure up to 10 GPa by the inductive method. With increasing pressure, of sample 1 initially increases, then has a maximum and finally decreases down to 6 K at 9.6 GPa. An irregularity in the dependence of versus P is observed at about 8 GPa. For sample 2, demonstrates a qualitatively similar behaviour with an additional dip in the low-pressure range. The suppression of is explained within the framework of the Bilbro - McMillan model.

The dynamic properties of thin films described by the Ising model in a transverse field (TIM) have been studied under the random-phase approximation. The frequencies of soft modes and surface modes have been obtained. For films with reduced surface interaction (compared to the bulk), the soft mode corresponds to a surface-like mode in the ferroelectric phase but to a bulk-like mode in the paraelectric phase. Conversely, for films with an enhanced surface interaction, the soft mode is a bulk-like mode in the ferroelectric phase and a surface-like mode in the paraelectric phase. The number of surface-like modes in the ferroelectric phase can be greater than one; the number increases as the temperature approaches the Curie temperature, and does not depend on the in-plane wavevector for a given temperature in the ferroelectric phase. However, there is only one surface-like mode in the paraelectric phase, and its character becomes bulk-like at large wavevector. The surface modes can be clearly seen from the frequency dependence of the dynamic susceptibility; the surface mode pole increases in strength with decreasing film thickness. The frequency dependences of optical reflectivity coefficients have also been obtained. The reflection peaks due to the surface modes lie below the bulk reststrahl band in the ferroelectric phase of films with reduced surface ferroelectricity, and also in the paraelectric phase of films with enhanced surface ferroelectricity; otherwise, they lie within the reststrahl band.

The thermal expansion of was measured under pressures up to 20 kbar. The large positive magnetovolume effect, caused by the onset of the Mn magnetism, is found to be shifted towards lower temperatures with pressure, and vanishes around 15 kbar. Above this pressure only the Gd sublattice shows long-range magnetic order. Between 6 and 15 kbar the Gd and Mn sublattices order separately. The pressure-induced splitting of the ordering temperatures is ascribed to the Mn magnetism instability, which is observed for certain compounds.

As a generalization of the Mattis - Gallinar effect (which predicts that the mass of an exciton depends upon its internal kinetic energy), I derive a formula for the mass tensor of the exciton that includes the effect of `exciton hopping' or Heller - Marcus mechanism, which is particularly important for the mobility of Frenkel-like excitons. If is the ijth component of the inverse mass tensor , and if the mass tensors of the electron and hole are proportional, with , then

where is an internal excitonic kinetic energy associated with the crystal lattice vector R, is the reduced mass tensor of the electron and hole divided by the total Wannier mass tensor, and is a matrix element of the exciton-hopping energy operator H. If the exciton becomes Frenkel like or localized in the sense that the expectation value , and that , then the inverse mass tensor in the Frenkel limit becomes

Thus, the (otherwise divergent) mass tensor of the Frenkel exciton remains finite as a consequence of the Heller - Marcus mechanism. On the other hand, for Wannier excitons one has , and

which means that in the Wannier limit. Finally, some comments are made about the various (experimental) predictions implicit in the above derived formula for the exciton's translational mass.