Self-consistent Green Function Research Articles

Ground state excitations in HoCo 2

Spin excitations in a single crystal of the Laves phase compound HoCo 2 have been studied using inelastic neutron scattering. At 4 K three modes are observable: an in-phase spin precision acoustic mode and two out-of-phase optic modes involving the rare earth spins. A self-consistent Green's function RPA theory has been used to analyze the data and obtain exchange and crystal field parameters.

Simpler expression for evaluating the density matrix in the self-consistent Green's-function method

In a recent publication describing a self-consistent Green's function for use in studying defects in solids, one of the major steps was evaluating the density matrix ${\ensuremath{\rho}}_{\mathrm{mn}}$ which describes the valence charge density in a basis of localized orbitals. We have since discovered an algebraic identity which considerably simplifies that evaluation, and we here present the simplified form for ${\ensuremath{\rho}}_{\mathrm{mn}}$.

Self-consistent Green's-function method I. Approximate approach to normalizing the crystal wave function

Using the Green' s function method, the effect of the error in the calculated normalization for the band wave function on the results of self-consistent calculations is investigated. The sensitivity of self-consistently calculated conduction-band parameters to the approximate estimation of the normalized integral is shown to be slight. The investigati on is carried out for metallic lithium in the approximation of a frozen atomic core. The exchange potential is chosen according to Kon and Shen.

Self-Consistent Green's-Function Calculation of the Ideal Si Vacancy

We have developed a method for solving the Green's-function equations describing an isolated localized defect in an otherwise perfect crystal. It yields a charge density in sufficinet detail to allow recalculation of the potential and iteration to self-consistency. The method is applied to the ideal (unrelaxed) vacancy in silicon, in the ionic-pseudopotential, local-exchange-correlation approximation.

Theoretical Studies of Disorder Scattering in Compound Semiconductor Alloys

Disorder scattering in semiconductor alloys is studied by employing Green's function method. As a first approximation, Yonezawa's self-consistent Green's function is applied to the problem. The scattering potential of the alloying atoms is determined empirically by comparing experimental and theoretical band edge shifts. Calculation with In 1- x Ga x As case demonstrates that the present calculation gives much lower mobility than Brooks' in a good agreement with the experiments.

Green function theory of chemisorption on sp-hybrid crystals

A self-consistent Green function calculation of the adatom charge transfer (Δ q) and the chemisorption energy (Δ E) is performed for hydrogen and the halogens on Si and Ge substrates, which are modeled by sp-hybrid orbital chains. The effect of Shockley surface states on the hydrogen chemisorption process is studied in some detail. From the chemisorption point of view, the behaviour of Si resembles that of Ge, the (111) surfaces having a smaller value of |Δ E| than the (100) ones for all the adsorbates considered. In the case of the halogens, the strong reactivity of fluorine is confirmed by the large values obtained for Δ q and |Δ F|.

Self-consistent electron Green function of a high-density disordered system

A self-consistent decoupling scheme is devised for studying the one-electron Green function of a high-density disordered system. The corrections to the optical potential and the white-noise, one-dimensional model are calculated in detail and comparison are made with conventional perturbation techniques.

Chemisorption theory in the Hartree-Fock approximation

To overcome the limitation of conventional quantum chemistry computer programs using the Hartree-Fock approximation which can only handle small clusters of atoms, Dyson's equation is used to embed an adsorbate/absorbent cluster in the surface of the semi-infinite adsorbent. The embedding problem is formulated correctly, but to have a practical scheme, an approximate version is needed. This version uses a tight-binding electron Green function in the adsorbent beyond the cluster, but the correct self-consistent Green function in the adsorbate/adsorbent cluster. Calculations have been made for hydrogen on the (100) surfaces of two simple, and two face-centred cubic s band solids.

Theory of Tunneling into Impurity Band

The theory of tunneling into an impurity band across a junction is developed by using the self-consistent Green's function in a ramdom array of impurity potential. If a short range potential is assumed for the impurity potential, the tunneling current density is expressed in terms of the proper self-energy Σ and the first and second derivatives of the current with respect to applied voltage are obtained. The results are examined numerically and it is shown that d 2 J /d V 2 - V curve should have a structure around the energy gap between the impurity band and the main band. In the impurity band, the d J /d V - V curve reflects the influence of Im Σ , while in the main band region it reflects the parabolic behaviour of the density of states because of the smaller contribution of Im Σ .

Two-Loop Approximations to Propagators in theσModel

A simple and systematic procedure is established for directly generating perturbation theory for the $\ensuremath{\sigma}$ model order by order in the number of loops rather than in powers of the bare coupling constant. This self-consistent Green's-function method is demonstrated by deriving the already known tree and one-loop approximations, and then is applied to the much more complex problem of the two-loop approximations to the propagators. The explicit form is displayed for these, and it is demonstrated that in the limit of no symmetry breaking and zero pion bare mass, the renormalized pion mass remains at zero as is required by the Goldstone theorem. These are the essential first steps toward calculating a unitary pion-pion scattering amplitude with this model to the two-loop order.

Self-Consistent Green's-Function Approach to the Electron-Gas Problem

The electron-gas problem is investigated by means of a self-consistent Green's-function formalism with the aim of developing practical approximation schemes for metallic densities. The work is based on the Dyson equation for the single-particle propagator $G[U]$ as a functional of an external potential $U$. The self-energy functional $\ensuremath{\Sigma}[U]$, appearing in the Dyson equation, is evaluated by perturbation theory in terms of the exact $G[U]$, thereby leading to a self-consistent problem. A hierarchy of approximations is generated by summing successively larger sets of graphs for $\ensuremath{\Sigma}[U]$. The Dyson equation is expanded in a functional Taylor series in $U$ and yields a nonlinear integral equation for the $U=0$ propagator as well as linear integral equations for the $U=0$ higher-order Green's functions, with kernels dependent on $\frac{\ensuremath{\delta}\ensuremath{\Sigma}}{\ensuremath{\delta}U}$. In applications of the theory, the emphasis is on calculating the longitudinal dielectric function $\ensuremath{\epsilon}$ in terms of the contracted four-point Green's function. The linear integral equation for the latter is solved after making a low-momentum dominance approximation to the kernel. The result is a general, but approximate, closed-form expression for $\ensuremath{\epsilon}$ which can be used for different choices of $\ensuremath{\Sigma}$. The following five approximations for $\ensuremath{\epsilon}$, based on different approximations for $\ensuremath{\Sigma}$, are presented: the Hartree-Fock, random-phase, generalized random-phase, second-stage random-phase, and low-high-density approximations. The last approximation is designed to work well at the two extremes of the density spectrum and, hopefully, also at metallic densities. The long-wavelength plasmon dispersion relations obtained from two different versions of the generalized random-phase approximation for $\ensuremath{\epsilon}$ agree closely with the results of Kanazawa et al. and of Singwi et al.

New self-consistent green function treatment of the Kondo problem

Abstract A new self-consistent treatment of the so-called s-d exchange model is presented. The treatment is based on the Roth prescription for linearizing many body equations of motion.

Perturbation instabilities of the Kondo problem

Recent calculations of the low temperature properties of dilute magnetic alloys differ with respect to their predictions concerning the existence of an instability of the normal ground state when the impurity is anti-ferromagnetically or ferromagnetically coupled to the conduction electrons. In the process of developing a self-consistent Green function formulation based upon the singlet and triplet two particle Green functions, we have obtained results which suggest the resolution of this difference.