Table of contents

The quantum oscillations of the conductivity components of two-dimensional electron systems with finite width are evaluated explicitly as functions of the electron Fermi energy for a set of magnetic fields. The theoretical magnetoconductivity reproduces well the main features of the data on Si inversion layers at 140 and 110 nm obtained by Skocpol et al. (1984).

A model pair-correlation function for a dense electron gas is used to determine the local field correction function. In the static mean field approximation the result is analytic and depends on the value of the pair-correlation function at zero inter-particle separation.

RPA predictions of an antiferromagnetic Wigner glass in 2D and 3D systems at low temperature are presented. A discussion of existing and forthcoming experimental evidence is given.

Recently Bhatt (1985) has predicted that for a non-interacting disordered insulator the low-frequency dielectric response should diverge at low temperatures (but at temperatures larger than the Coulomb gap) as T^-14/. Low-temperature data are presented for an uncompensated Si:As sample (n approximately 0.87 n_c) which does not appear to support this prediction even though the DC and 10 Hz data exhibit Mott variable-range hopping conduction. An alternative analysis is presented which suggests the temperature dependence of epsilon '( omega ,T) is very similar to sigma ( omega ,T) for the sub-linear frequency-dependent phonon-assisted hopping process.

A simple fractal time model is presented for relaxation in condensed matter and theoretical investigation shows that the 'anomalous' relaxation in condensed matter is the result of the breakdown of the adiabatic approximation and one needs three different time scales to describe an intermittent relaxation process instead of a continuous relaxation process. The present model can not only give the stretched exponential relaxation exp(-(t/ tau )^beta ) naturally, but also explain the observed time scaling behaviour of beta .

The Si, Al distribution in tetrahedral sheets of micas has been analysed by the use of Monte Carlo simulation and by the calculation of electrostatic energies. A new method for the calculation of electrostatic energies for short-range-ordered distributions has been developed. The results of the analysis demonstrate that the Si, Al distribution is mainly controlled by the electrostatic requirements of homogeneous dispersion of Al and local balance of inter-layer cations. Furthermore, electrostatic interactions between contiguous layers also constitute a significant factor controlling the tetrahedral cation distribution. Electrostatic energies of long-range-ordered models based in the para or in the meta disposition of Al are very similar, indicating that there is no preference for a particular long-range ordered distribution. This result justifies the distribution model found by NMR analysis, which is long-range-disordered, with the meta and para dispositions of Al equally favoured.

The authors present and describe a new embedded-cluster approach for calculating both the electronic and the spatial structure of point defects in ionic crystals with self-consistent incorporation of the polarisation effects into the eigenvalue spectrum and the total energy of a crystal. For the first time both the electronic structure and the ionic displacements within a large cluster containing a defect are obtained in the framework of the same calculating scheme. It permits one to describe correctly back-coupling between redistribution of the electron density in a defective region and polarisation of the rest of the crystal outside the cluster, which can play a vital role for the study of small polaron effects. Making use of a 45-atom cluster with 175 electrons and the semi-empirical INDO method, the authors have simulated the impurity-induced trapping of a hole in the (Li)⁰ centre in an MgO crystal. The calculations do not use a priori assumptions and do confirm that one-centre localisation of a hole in the ground state is energetically favourable. They show that polarisation energies can differ considerably for the ground and charge-transfer excited states of the defect. It is also demonstrated that the generally accepted model of the O^- hole polaron is oversimplified: a considerable charge redistribution between Li⁺ and another O^- along the (100) direction takes place.

A Green function procedure for calculating the inner displacement about an impurity in a crystal lattice has been developed. The application to a substitutional impurity at the metal ion position in the fluorite lattice shows that both for the rigid ion model and for the shell model, the inner displacement is identical in form to that of the perfect lattice. However, the changes in the equilibrium positions of the neighbours of the impurity need to be taken into account when evaluating atomic displacements of the strained crystal.

The mean-field renormalisation group method is used to study the bond-diluted q-states Potts model in a transverse field. The critical surface in the transverse field-temperature-concentration space is obtained for different dimensionalities, and some critical exponents are estimated.

The response of the incommensurate structure with a free boundary on the varying equilibrium wave-vector is studied within the Frenkel-Kontorowa model, the model with a piecewise parabolic potential and the random pinning model. The penetration depth of the equilibrium configuration into the metastable region is calculated. It is shown to remain finite for the piecewise parabolic model and the random model. On the other hand the depth diverges on approaching the unpinned configuration in a Frenkel-Kontorowa model. The relation to the interfaces and the thermal hysteresis in incommensurate structures is also discussed.

The authors present and analyse the luminescence spectra of free excitons at high density in CuI observed in picosecond time-resolved experiment. They show that, in insulators (such as CuI, CuCl, CuBr, . . .), the LO-phonon-plasmon resonance can take place during the excitonic regime of the electron-hole system. As a result, the free exciton indirect luminescence is strongly influenced by the LO-phonon-plasmon interaction (i.e. by free carriers) as demonstrated by the lineshape theory which the authors develop. The experiments are interpreted in the framework of this model.

On the basis of the diagrammatic method, a new interpolation between long- and short-range correlations in an electron liquid is presented. In the interpolation scheme, the spin-parallel and spin-antiparallel correlations are studied separately. The authors evaluate numerically the local-field factor from short-range Coulomb repulsion by solving the integral equation for the particle-particle ladder interaction. The irreducible particle-hole interaction is constructed from an approximation interpolation between the RPA dynamically screened Coulomb interaction and the ladder interaction. The local-field factor from the exchange interaction is evaluated from the exchange polarisation function of lowest order in this irreducible particle-hole interaction. An interrelation between the two local-field factors is discussed.

For pt.I see ibid., vol.19, p.4247. A numerical study is made of the spin-parallel and spin-antiparallel correlation functions in an electron liquid, based on a new interpolation scheme presented in the preceding paper. A detailed examination of the correlation energy evaluated from these two correlation functions is given.

Luminescence transitions associated with manganese have been studied in the GaAlAs layers and GaAs-GaAlAs superlattices. In GaAlAs, manganese shows a behaviour characteristic of a centre that is partly deep and partly hydrogenic. In a superlattice, the ionisation energy of manganese increases as a function of the well width: it is 110 meV in GaAs, 132 meV in a 67 AA well and 192 meV in a 13 AA well. The change in ionisation energy can be explained by taking into account both the 'deep' and the hydrogenic character of manganese. Changes in ionisation energies are compared with theoretical calculations of the heavy hole confinement energy.

The author presents a numerical method for calculating the integrated density of states and the localisation length in quasi-one-dimensional tight-binding disordered systems. The results for the one-dimensional Anderson model with off-diagonal disorder confirm that the singularities for the density of states and the localisation length are in the form predicted by Dyson. In two dimensions the singularity for the density of states near E=0 approaches the form rho (E) varies as E^{- phi} for weak off-diagonal disorder. The author obtained approximately ¹/₃ for the exponent phi consistent with current fractal viewpoints. Some results for strong off-diagonal disorder in two dimensions where the singularity is of a different nature are also presented.

The authors report the first direct measurement of the electrical anisotropy of ZrS_3-xSe_x compounds. The microwave cavity perturbation technique is used to measure the conductivity and the dielectric constant of these n-type semiconductors along two crystal axes (b and a), for samples covering the entire composition range. The conductivity is dominated by a single activation regime in the 300-500K range and is interpreted in terms of the presence of two donor impurity levels and a compensation varying with composition. The electrical anisotropy between the two directions is found to be relatively small and a 3D electrical behaviour is believed to be associated to these compounds. The composition dependence of the dielectric constant is found to be related to the superposed electronic and lattice contributions and a jump near the x=2 composition may be associated with a possible 1D to 2D structural transition. A ratio of epsilon ₁/// epsilon _{1 perpendicular to} approximately=2 is measured and is attributed to the normal anisotropy associated with non-cubic crystals.

The author derives a matrical equation giving the electron distribution functions in the different sub-bands encountered in one- and two-dimensional quantum wells. He takes account properly of inelastic scattering and inter-sub-band transitions. He deduces an analytical result for the conductivity limited by different electron-photon mechanisms, and show that for certain special cases a relaxation time may be defined.

The authors consider the effect of molecular impurities on the kinetic characteristics of electrons in non-polar liquids. A straightforward similarity law is proposed in the framework of the Lekner-Cohen theory (1967) that makes it possible to estimate the effect of the impurities on the drift velocities as well as on the characteristic and mean energies of electrons in liquids with additions, provided that the foregoing characteristics in pure molecular gases are known.

The linear dynamics of double-sublattice antiferromagnets is considered near the temperature of the phase transition where the value of sublattice spin is not constant. The Landau-Lifshitz equations are substituted by non-dissipative Onsager-type equations which take into account the dispersion of the kinetic coefficients and also S₁² not=const. The structural stability of the equations chosen is provided. The natural frequencies of the magnetic subsystem are calculated on this basis, the thermodynamic powers and the values of the sublattice magnetisation being calculated on the basis of the Landau potential of the fourth order. The phase diagram of such a magnetic material, containing a tricritical point in the (H,T) plane, is described in detail. The magnetic subsystem has three natural frequencies. It is proved that in strong fields the frequency of the vibrations is soft which is connected with non-constant spin value. In weak fields the frequency corresponds to the anti-ferromagnetic resonance.

The phase transition in the langbeinite Cd₂(NH₄)₂(SO₄)₃ has been studied via the EPR of Mn²⁺. The phase transition temperature has been determined to be T_c=94.5+or-0.5K. The spin-Hamiltonian parameters have been computed using a rigorous least-squares fitting procedure, numerically diagonalising the spin Hamiltonian and simultaneously fitting a large number of EPR line positions obtained for several orientations of the external magnetic field on a digital computer. It is suggested that the phase transition below T_c is due to the freezing of (SO₄)^2- rotations.

Measurements of the chlorine nuclear spin-lattice relaxation time are reported for the antifluorite K₂OsCl₆ in the temperature range 17 to 300K. This substance undergoes a cubic-to-tetragonal structural phase transition at a temperature T_c of about 40K. Except at low temperatures, where impurity effects become important, the temperature dependence of the relaxation rate obeys an equation of the form T₁^-1=CT²/(T-T_c). This result is consistent with a Raman two-phonon relaxation mechanism for an undamped soft mode described by a dispersion curve of the form omega (q)= omega ₀+ alpha _q². As T_c is approached from above the recovery of the nuclear magnetisation becomes non-exponential, and can be represented as a double exponential characterised by two time constants T₁^L and T₁^S. This result is accounted for by assuming that the fluctuations responsible for the relaxation have the symmetry of the rotary lattice mode and that these fluctuations occur on two very different scales in spatially localised regions in the specimen. Below T_c the relaxation time T_1Z and T_1XY associated with the two resonance lines in the tetragonal phase are different and T_1Z>T_1XY. This observation is explained as a consequence of the two-dimensional nature of the correlations in this compounds.

High-purity zinc selenide single crystals have been doped with indium in the concentration range from 0.03 to 30 p.p.m. by means of the vapour-phase transport technique. The concentration of indium has been precisely determined by thermal neutron activation analysis. The photoluminescence (PL) spectra measured at 4.2K show the I₂ line, donor-acceptor pair emission lines and two broad emission bands around 1.98 and 2.20 eV. The emission intensities are found to be strongly affected by the native defect concentrations. The temperature dependence of the PL spectrum suggests that the 1.98 eV emission band is a self-activated emission related to an associated defect involving In_Zn and a zinc vacancy.

The embedding method invented by Inglesfield (1981) is a method for solving the Schrodinger equation for a small but interesting part of the larger system. It is based on minimising the energy by varying the wavefunction within a closed surface surrounding the region of interest. The correct non-local energy-dependent boundary conditions on this surface then appear as a surface potential term in the functional to be varied. The authors show that in the usual LCAO Green function method there exists a way to accomplish this same embedding using a matrix operator, with structure similar to the boundary condition kernel of Inglesfield's method.