Local Green Function Research Articles

Nonperturbative calculation of the chemisorption binding energy

An exact and general expression for the binding energy of chemisorbed atoms on tight-binding solid surfaces is derived. In addition to the strength of coupling between the adatom and the surface, the expression involves only the free local Green functions of the atomic array responsible for chemisorption and that of the adatom. As an example, results are presented for "chemisorption" at a single site of a Bethe lattice.

Use of the recursion method in the study of disordered systems

Applied to the determination of the density of states of disordered systems, the recursion method permits the local Green's function to be written as a continued fraction. We examine the effect that truncating this fraction has upon the local Green's function and present a means of reducing this effect. Further, a self-consistent approach for obtaining the local Green's function is developed. This approach is shown to be suitable for the study of disordered systems.

Magnetic moments for different local atomic configurations in Fe-Cr alloys

Studies local magnetic moments in binary alloys as a function of alloy concentration. A two-sublattice model accounts also for the antiferromagnetic solutions found in the Cr-rich region. The effect of local atomic configuration is considered and the shift in atomic energy levels due to charge transfer is taken into account. The continued fractions technique is employed for calculations of the Local Green functions. The Coulomb repulsion term is treated in the alloy analogy approximation and the intra-atomic exchange term is treated by the Hartree-Fock approximation. Calculations are performed for parameters corresponding to Fe-Cr alloys. The magnetic moments of Cr and Fe agree with experimental data: ferromagnetic (up to 70 at.% Cr) and antiferromagnetic (above 83 at.% Cr) phases were found. The ferromagnetic moment of Fe decreases linearly against the number of Cr atoms in the vicinity; the rate, however, is concentration dependent. The magnetic moment of Fe in pure chromium is 1.5 mu B and Fe is antiferromagnetically coupled to Cr atoms.

Properties of an Anderson impurity in the local spin fluctuation limit

Abstract We discuss a selfconsistent second-order self-energy approximation for the d-electron propagator within the Anderson model at any temperature. The frequency dependent impurity spin susceptibility is also obtained using the calculated local Green's function and displayed as function of temperature.

Localisation in random systems

Presents new methods of characterising localised states. In one method, the wavefunction amplitudes are plotted as spatial maps in both two-dimensional and three-dimensional random systems. These amplitudes are obtained from local Green functions expressed in the continued fraction form and the Haydock-Heine-Kelly scheme (HHK) is used in numerical evaluations. Another method examines the convergence of the local Green function as a function of the truncation parameter n, where n is the number of steps down the continued fraction. The behaviour of the coefficients in the HHK continued fraction can be used in a Mobius transformation analysis to give information about localisation. The model systems studied are the random binary alloys and the Anderson Hamiltonian. Extended states are shown to be very likely present even in the two-dimensional Anderson model at small enough W.

Wavefunction localization in a binary alloy

The nature (localized or extended) of the eigenstates of a large disordered system is studied by evaluating the imaginary part of the local Green's function at the specific eigenvalues over various atomic sites. The latter is obtained from the recursion method of Haydock-Heine-Kelly. An explicit calculation on an 841-atom cluster of random binary alloy in a square lattice ensures us that this approach is able to provide the relevant answers in even larger systems. In addition to confirming the usual conjectures about localization in a random binary alloy, several interesting points show up in the result of the model calculation. For example, the localized states in the minority band are correlated to certain clustering of the minority atoms. Their specific eigenvalues, which are not easily identified from the peaks in the d.o.s., are accurately found through the |ζ| 2 vs. energy plots at the specific sites.

A Local Green's Function Method for the Numerical Solution of Heat Conduction and Fluid Flow Problems

A new coarse-mesh computational method for the numerical solution of heat conduction and fluid flow problems is formally developed and applied to sample problems. The method is based upon formal use of Green's functions, which are defined locally over subdomains of the original system under consideration. The formal development of the local Green's function method for the solution of heat conduction problems is presented and discussed. Numerical solutions of sample problems for one-dimensional heat conduction with constant thermal conductivity, one-dimensional heat conduction with temperature-dependent thermal conductivity, and two-dimensional heat conduction with constant thermal conductivity are given, and these results are compared with results obtained using the finite difference and finite element methods. The formal development of the local Green's function method for the solution of fluid flow problems is then also presented and discussed; the numerical solution of a sample problem for simple one-dimensional incompressible fluid flow with viscous heating is also given.

Study of the electronic local density of states using the cluster-Bethe-lattice method: Application to amorphous III-V semiconductors

The cluster-Bethe-lattice method is extended to study the Weaire-Thorpe $s{p}^{3}$ Hamiltonian. We derive a transformation which makes it possible to calculate the local density of states of a system described with a four-orbital Hamiltonian by using the local Green's function of a one-orbital Hamiltonian. We study the effects on the density of states of the presence of like-atom bonds in amorphous III-V semiconductors. We analyze two models: (a) like-atom bond in tetrahedral configuration, and (b) like-atom bond in triangular pyramidal configuration. Our results are in agreement with the experimental data.