Interacting electrons in disordered wires: Anderson localization and low-T transport

We study the conductivity sigma(T) of interacting electrons in a low-dimensional disordered system at low temperature T. For weak interactions, the weak-localization regime crosses over with lowering T into a dephasing-induced "power-law hopping." As T is further decreased, the Anderson localization in Fock space crucially affects sigma(T), inducing a transition at T = T(c), so that sigma(T < T(c)) = 0. The critical behavior of sigma(T) above T(c) is ln sigma(T) proportional to -(T - T(c))(-1/2). The mechanism of transport in the critical regime is many-particle transitions between distant states in Fock space.     

Interacting electrons in a two-dimensional disordered environment: effect of a zeeman magnetic field

The effect of a Zeeman magnetic field coupled to the spin of the electrons on the conducting properties of the disordered Hubbard model is studied. Using the determinant quantum Monte Carlo method, the temperature- and magnetic-field-dependent conductivity is calculated, as well as the degree of spin polarization. We find that the Zeeman magnetic field suppresses the metallic behavior present for certain values of interaction and disorder strength and is able to induce a metal-insulator transition at a critical field strength. It is argued that the qualitative features of magnetoconductance in this microscopic model containing both repulsive interactions and disorder are in agreement with experimental findings in two-dimensional electron and hole gases in semiconductor structures.     

Interacting electrons in quantum dots

The ground states of N-electron parabolic quantum dots in the presence of a perpendicular magnetic field are investigated. Rigorous lower bounds to the ground-state energies are obtained. It is shown that our lower bounds agree well with the results of exact diagonalization. Analytic results for the lower bounds to the ground-state energies of the quantum dots in a strong magnetic field (known as electron molecule) agree very well with numerically calculated lower bounds.     

The scaling theory of electrons in disordered solids: Additional numerical results

We present extensive numerical results applying the finite size scaling method to the theory of electrons in disordered systems. A method is developed for studying the localisation length in 1-dimensional systems of finite cross section. By studying these results as a function of cross-section and using scaling ideas, we derive the critical properties of 2-D and 3-D systems. We calculate transport properties as a function of temperature which can then be compared with experiment.     

Quantum interference of electrons in disordered metals

Investigation of the galvanomagnetic properties of disordered metals in weak magnetic fields [r(H)?l, wherer(H) is the electron trajectory radius andl, the electron free path], proved to be one of the effective experimental methods of studying disordered metals. The phase difference between the interfering electron waves is affected by the presence of magnetic flux in the sample. One of the observable effects is the oscillatory magnetoresistanceK(H) of multiconnected samples predicted by Altshuleret al (1981). The period ofK(H) oscillations for the hollow cylinders, networks or chains with orifices cross-sections areasS isΔH=φ ₀/2S [whereφ ₀=hc/e]. The amplitude and the phase of the oscillations depend on the spin orbit interaction, the intensity of superconductive fluctuation etc. It should be noted that in small “mesoscopic” single loops the oscillations with the periodΔH?φ ₀/S were also observed recently (see also Altshuleret al 1987 included in this issue).     

Theories of electrons in one-dimensional disordered systems

A critical survey of the literature on the theory of electronic states in, and electron transmission through, models of one-dimensional disordered solids and liquids is given in the first part. Reference to work on three-dimensional systems is included, especially where exact results have been obtained. The relationship between this subject and the problem of elastic vibrations in disordered solids is pointed out. A complete exposition of the authors' work on one-dimensional conductivity is then presented. It provides a rigorous solution of the problem of average resistance, and of the variance (fluctuations) of resistance, for important classes of disorder which are carefully and precisely defined. Conclusions regarding the role of disorder with respect to the transmission properties are presented and discussed. It is also pointed out that, with appropriate modifications, the results apply generally to wave propagation in inhomogeneous media.     

The inverse scattering problem for singular oscillating potentials

In this paper we show how to apply the Gel'fand-Levitan equations with singular oscillating potentials. We give the general procedure for solving these equations and we illustrate the method by some examples.     

Interacting electrons on a two-dimensional surface: planar vs. spherical geometries

The center-of-mass excitations are identified in the spectrum of electrons on a two-dimensional surface in the lowest Landau level. The correspondence between the quantum numbers labeling electron states on a sphere and on a plane is drawn. The excitation spectrum on a sphere with increasing radius is shown to converge to that on a plane. In particular, in the presence of a lateral confinement (i.e. for the case of quantum dots), identical series of magic states appear in both cases. Also, a class of interaction potentials which lead to the fractional quantum Hall effect in an extended system are identified.     

The inverse Bremsstrahlung absorption in the presence of Maxwellian and non-Maxwellian electrons

Inverse Bremsstrahlung absorption(IBA) of an intense laser field in plasma containing Maxwellian and nonMaxwellian(with Kappa and q-nonextensive distribution functions) electrons is studied analytically. Our results show that IBA decreases with an increase in temperature at high intensities and a decrease in plasma density for all kinds of distribution functions. Another striking result is that IBA is independent of the laser intensity at low intensity but is dependent on it when the intensity is going to rise. Also, it could be find that the behavior of the absorption as the function of laser intensity for the Kappa distribution with κ = 10 at low intensity is close to that for the Maxwellian distribution, but at high intensity it is close to that in the presence of q-nonextensive electrons with q = 0.9. These results provide insights into the inverse Bremsstrahlung absorption in the laser–plasma interactions.     

Magnetoconductivity of disordered two dimensional tight binding electrons in CPA

The magnetotransport properties of a tight binding model of electrons on a two dimensional square lattice with diagonal disorder and in a perpendicular magnetic field is investigated. The disorder is treated in the coherent potential approximation (CPA) and a quasiclassical solution of the Harper equation is used to calculate the one particle Green's function. Analytical expressions for the CPA vertex corrections to the magnetoconductivity are derived. Numerical results for the density of states and the diagonal magnetoconductivity are discussed. The vertex correction vanishes if the Harper band width is neglected.