One-electron green function of a high density disordered system

A new, self-consistent decoupling scheme is proposed for the electronic Green function in a dense, weak scatterers random field.     

Electron spectral density in a disordered system of hard sphere scatterers

The spectral density of an electron propagating in a disordered system of hard sphere scatterers is studied by use of a self-consistent approximation for the self-energy. The spectral density at fixed wavenumber is found to be a single-peaked function of energy. The approximation yields a sharp wavenumber-dependent band edge. For large wavenumbers the spectral density is well approximated by a Lorentzian, but for small wavenumbers it is dominated by a characteristic square root singularity at the band edge.     

Electronic localization in disordered systems

A brief review is given of the current understanding of the electronic structure, transport properties and the nature of the electronic states in disordered systems. A simple explanation for the observed exponential behaviour in the density of states (Urbach tails) based on short-range Gaussian fluctuations is presented. The theory of Anderson localization in a disordered system is reviewed. Basic concepts, and the physics underlying the effects of weak localization, are discussed. The scaling as well as the self-consistent theory of localization are briefly reviewed. It is then argued that the problem of localization in a random potential within the so-called ladder approximation is formally equivalent to the problem of finding a bound state in a shallow potential well. Therefore all states are exponentially localized in d=1 and d=2. The fractal nature of the states is also discussed. Scaling properties in highly anisotropic systems are also discussed. A brief presentation of the recently observed metal-to-insulator transition in dequals;2 is given and, finally, a few remarks about interaction effects in disordered systems are presented.     

Electronic bandstructure of disordered superlattices

The disordering of semiconductor superlattices is analysed in the spatial Fourier domain. It is demonstrated that disordering is equivalent to suppressing the higher-order Fourier coefficients of the alloy profile. Two superlattice bandstructure algorithms are developed in the Fourier domain which allow the electronic envelope function and energy to be determined. The first employs the effective mass approximation. The second is a 14-bandk·pwhich includes nonparabolicity, anisotropy and noncentrosymmetry which are particularly relevant in the determination of nonlinear optical coefficients.     

Correlations in a non-equilibrium disordered system

Correlations in a one-dimensional model are studied as it evolves between different disordered equilibrium states. The disorder is generated by an external agency (e.g. a heat reservoir) which induces stochastic behaviour. Even though the time scales for the evolution of the system and the intrinsic motion of the constituent particles are distinctly different there is a complicated interplay between the two processes as observed in static and dynamic structure factors.     

Electronic transport in substitutionally disordered systems

We derive a theory of electronic transport in substitutionally disordered systems by extending the Molecular Coherent Potential Approximation (MCPA) of Tsukada to the calculation of transport quantities. At the same time it is an extension of the CPA transport theory existing so far. Our transport theory allows for the investigation of impurity clustering, of correlations and of fine-structure on transport quantities.Work performed within the research program of the Sonderfor-schungsbereich 125 Aachen-Jülich-Köln     

Direct comparison between potential landscape and local density of states in a disordered two-dimensional electron system

The local density of states (LDOS) of the adsorbate-induced two-dimensional electron system (2DES) on n-InAs(110) is studied by scanning tunneling spectroscopy. In contrast to a similar 3DES, the 2DES LDOS exhibits 20 times stronger corrugations and rather irregular structures. Both results are interpreted as consequences of weak localization. Fourier transforms of the LDOS reveal that the k values of the unperturbed 2DES still dominate the 2DES, but additional lower k values contribute. To clarify the origin of the LDOS patterns, we measure the potential landscape of the 2DES area. We use it to calculate the expected LDOS and find reasonable agreement between calculation and experiment.     

ε-expansion for the density of states of a disordered system near an Anderson transition

The density of states for the Schrödinger equation with a Gaussian random potential is calculated in a space of dimension d=4?ε in the entire energy range, including the vicinity of an Anderson transition.     

Landau levels in disordered alloys

The electronic structure of a substitutionally disordered alloy in a uniform magnetic field has been studied on a simple model of scattering potentials (zero range potentials). The coherent potential and single-site aproximation have been employed. It turned out that in wide energy region the Dingle temperature, characterizing the decay of the amplitude of de Haas — van Alphen oscillations, is determined by the part of self-energy which does not depend on magnetic field. The field dependent part is important only for a few Landau levels at the bottom of the band. The results can be applied to simple metals and semi-metals.     

Charge transfer between percolation levels in a system with an artificial,strongly disordered potential

We observe a hysteresis in the magnetoresistance of mesoscopic samples with a disordered antidot lattice. When the Fermi level lies in between two Landau levels, the Faraday electric field induces a change in the charge of two closed, intercalated electron trajectories in the artificial strongly disordered potential. The total transferred charge is approximately equal to 40e. Depending on whether this transfer is towards the inner or outer closed trajectory (which is determined by the direction of the magnetic field sweep) the potential barrier for trajectories that traverse the sample will increase or decrease.     

Electronic structure of disordered BCC alloys

This paper describes and analyses a self-consistent cluster coherent potential approximation calculation of the electron density of states of a random, binary alloy on abcc lattice.     

First-order transition in a three-dimensional disordered system

We present the first detailed numerical study in three dimensions of a first-order phase transition that remains first order in the presence of quenched disorder (specifically, the ferromagnetic-paramagnetic transition of the site-diluted four states Potts model). A tricritical point, which lies surprisingly near the pure-system limit and is studied by means of finite-size scaling, separates the first-order and second-order parts of the critical line. This investigation has been made possible by a new definition of the disorder average that avoids the diverging-variance probability distributions that plague the standard approach. Entropy, rather than free energy, is the basic object in this approach that exploits a recently introduced microcanonical Monte Carlo method.     

Electronic heat capacity in disordered graphene systems

We analyzed the electronic heat capacity of graphene systems in the presence of disorder. We consider the case of strong scatterers, working in the unitary limit. The temperature dependence of the electronic heat capacity is analyzed. Close to the clean limit we obtained the quadratic temperature dependence, corrected with a temperature and disorder dependent factor which slightly enhance the heat capacity. At very low temperatures, and in the presence of disorder, we obtained a linear temperature dependence of the electronic heat capacity. We also analyzed the temperature dependence of the electronic heat capacity in the case of extrinsic graphene.     

Long range density correlations in disordered solids

Although the structure of a glass closely resembles that of a dense liquid over short length scales, its solidity implies that the two-particle distribution function is long range. In this paper the explicit form of this long range behaviour is derived in terms of the elastic constants of the glass and the relationship is shown between density fluctuations and the microscopic form of the displacement vector u(r). With minor modifications these results are valid also for a crystal. Several ramifications of these results are explored.     

Electronic structure of disordered Pd3Fe

The electronic structure of disordered Pd₃Fe is studied within an almost self-consistent KKR-CPA procedures. Our starting point are the self-consistent potentials for the ordered ferromagnetic Pd₃Fe obtained by the LMTO method. We perform the ferromagnetic calculation and examine the influence of disorder on the electronic structure of this alloy through the analysis of the Bloch spectral functions and densities of states and compare our results with experiment. We also propose a mechanism for the formation of magnetic moments in ferromagnetic alloys.     

Quantum Brownian motion in a one-dimensional disordered system

We study the diffusion of a quantum Brownian particle in a one-dimensional periodic potential with substitutional disorder. The particle is coupled to a dissipative environment, which induces a frictional force proportional to the velocity. The dynamics for arbitrary temperature is studied by using Feynman's influence-functional theory. We calculate the mobility to lowest order in the disorder and strength of the periodic potential. It is shown that for weak dissipation the linear mobility, which vanishes atT=0 due to localization effects, may exhibit a maximum and a subsequent minimum with increasing temperature. The relation to the diffusion of heavy particles in metals or doped semiconductors is briefly discussed.