Green Function Matching Research Articles

Nonlocal surface plasmons by Poisson Green's function matching

The Poisson Green's function for all space is derived for the case in which an interface divides space into two separate semi-infinite media, using the Green's function matching method. Each of the separate semi-infinite constituent parts has its own dynamic, nonlocal polarizability, which is taken to be unaffected by the presence of the interface and is represented by the corresponding bulk response property. While this eliminates Friedel oscillatory phenomenology near the interface with p ∼ 2pF , it is nevertheless quite reasonable and useful for a broad range of lower (nonvanishing) wavenumbers, p < pF. The resulting full-space Poisson Green's function is dynamic, nonlocal and spatially inhomogeneous, and its frequency pole yields the surface plasmon dispersion relation, replete with dynamic and nonlocal features. It also accommodates an ambient magnetic field.

Green’s function matching method for one- and zero-dimensional heterostructures

A method for the calculation of the Green's function of one-dimensional (wirelike) and zero-dimensional (boxlike) heterostructures is developed. The method is based on the formalism of surface Green's function matching (SGFM) for discrete media. The matching formulas are derived for structures consisting of an infinite ``external'' medium with an embedded array of wires (boxes), periodic in two (three) dimensions, for an arbitrary shape of the matching surface. Efficient algorithms to calculate the domain Green's functions are also proposed. Unlike the supercell methods widely used to compute the electronic structure of one- and zero-dimensional systems that scale with the supercell size, the developed approach scales with the interface size, which makes it extremely efficient to study systems such as disordered alloys, clusters of defects, and nanoscale materials. We employ it to calculate the localized and extended electronic states of a periodic array of $\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{As}$ (001) nanowires using an $s{p}^{3}{s}^{*}$ tight-binding Hamiltonian with spin-orbit coupling.

SGFM and the new FISIM states

The Surface Green's Function Matching (SGFM) method is useful to distinguish the bulk effects from the surface ones since it calculates the two Green's functions separately in a neat and direct way. We have used this feature of the method to establish the correct interpretation of the Frontier Induced Semi-Infinite Medium (FISIM) states. We discuss the valence band electronic structure of the (001) oriented II–VI wide band gap zinc-blende semiconductor compounds. We have found three characteristic surface resonances besides the known bulk bands. Two of these resonances correspond to the anion-terminated surface and the third one to the cation terminated one. Further, we have shown that three non-dispersive (001)-surface-induced bulk states are also characteristic of these systems. These are neither surface nor Bloch states. These are states localized in planes perpendicular to the surface with non-vanishing spectral weight inside the bulk. They are not Bloch states since they are the consequence of the surface-boundary condition and their characteristics depend on the direction of the surface, they are therefore, surface-induced bulk states. In this talk, I briefly review our description of these systems. I also quote that similar states are present in other systems as calcopirites and at interfaces and superlattices, as well. These states are, actually, a general wave property and appear as the consequence of the boundary condition set by the presence of any frontier. For that reason, we have decided to call them Frontier Induced Semi-infinite Medium (FISIM) states.

A general-purpose approach for calculating transport in contact–molecule–contact systems: TARABORD implementation and application to a polythiophene-based nanodevice

We present a general-purpose approach for calculating quantum transport properties of contact–molecule–contact systems, based on nonequilibrium surface Green's function matching. The method is quite general and may be applied to systems described at different levels of accuracy, e.g., tight binding and ab initio. The computer program TARABORD that implements the general formalism is applied to various nanoscale systems. Our results for infinite carbon chain and porphyrin tapes are shown to be in good agreement with previous studies. We further apply the method to a polythiophene-based nanodevice and explain the main features of transport characteristics in terms of the molecular energy levels and coupling to gold nanocontacts.

The adiabatic molecule–metal surface interaction: Theoretical approaches

Ab initio methods for calculating the adiabatic electronic properties of a single isolated molecule interacting with a metal surface are reviewed. First the fundamental approaches of Anderson, Grimley, and Newns for chemisorption, as well as of Zaremba and Kohn, for physisorption, are outlined. Then the density-functional theory and its approximations are considered. The different models for the adsorbate system are described. They comprise those in which the system has a finite volume---i.e., the cluster, the slab, and the supercell models---and those which take into account the semi-infinite nature of the substrate---i.e., the embedding approach based either on the Dyson equation or on Green's-function matching. Those definitions are also introduced that we deem important for the understanding of the physical properties of systems to be presented in this article. The lack of full screening in a localized region around the adsorbate, and hence the existence of long-range Friedel's oscillations induced by the adsorbate in the metal, are discussed. The way in which the lack of full screening influences the calculated adsorption energies is estimated by the grand-canonical functional. Recent ab initio results on physisorption of a noble-gas atom on metals deal mainly with the limits of validity of the simpler effective-medium theory and with the anticorrugating effect of He. Atomic chemisorption is considered in order to deal with the concept of bonding at a metal. Dissociative chemisorption calculations mainly treat the ${\mathrm{H}}_{2}$ metal system. Here both the adiabatic electronic properties and the sticking probabilities recently obtained using the ab initio potential-energy surfaces are analyzed. Carbon monoxide chemisorption, lateral interactions between adsorbates, adatom diffusion, and chemisorption on stepped surfaces are presented as prototypes of the large variety of ab initio results currently available. Finally, the conclusions are devoted to the respective merits of the different theoretical approaches and to some future directions.

Simultaneous surface Green's-function matching for discrete systems with N interfaces

The surface Green's-function matching (SGFM) method for discrete systems is extended to the case of arbitrary multilayer structures, so that matching is simultaneously effected at an arbitrary number N of interfaces. In this way all the SGFM formulas are obtained in a compact 2 N × 2 N supermatrix form, ready for practical calculations. As an illustration, the vibrational properties of multilayer one-dimensional systems are considered.

Embedding approach to the isolated adsorbate.

An embedding method is proposed, based upon Green-function matching, for calculating the electronic properties of an isolated adsorbate. The self-consistent single-particle Schr\odinger equation is solved in a localized region containing the adsorbate and that part of the substrate mainly perturbed by it. The extended substrate is taken into account exactly by an effective embedding potential. The advantages of the method for the adsorption problem are discussed and tested by a calculation of the electronic properties of isolated Si and N adatoms on Al, modeled as jellium. In the former case excellent agreement is found with the results previously computed by other methods, in the latter, not previously investigated by a first-principles approach, the ioniclike character of the bond is seen in the calculated charge densities and densities of states. Finally the problem of the lack of screening due to the presence of an adatom on a simple metal surface is estimated by the generalized phase-shift theory. This effect turns out to be an important contribution to the atom-surface interaction energies, and it is corrected to first order by the use of the grand-canonical energy functional. \textcopyright{} 1996 The American Physical Society.

Quantum size effect in the photoemission intensity emitted from thin metal films

Photoemission spectra are calculated for thin films of Ag on Au(111) using the method of Green's function matching. For very low photon energies ( ω ≲ 10 eV) the peak intensities of the thin film states oscillate with the film thickness. These oscillations are caused by the relaxation of the k ⊥ -conservation of the optical excitation in photoemission.

The resonance image states at the (111) surface of fcc metals

On surfaces of many metals the vacuum level is situated above an energy gap and therefore resonance image states can exist outside the energy gap. The (111) surface of a model fcc crystal, with the vacuum level above the upper edge of the energy gap L 1 was considered here, allowing study of the influence of the crystal band structure on the energy spectrum and broadening of the resonance image states. Calculations, based on the Green function matching, were performed for different values of the matrix element of the crystal potential V 111. It was found that for decreasing V 111 (which increase the energy distance between the vacuum level and the upper edge of the energy gap) the absolute value of the binding energy of the resonance image state decreased. A comparison of this conclusion with experimental results was presented and discussed.

Image induced surface resonance of clean (001) and (111) surface of aluminium

The effect of an image potential on the local surface density of states is investigated in the framework of a nearly free electron model by employing the matching Green function method. The influence of the image plane position on the shift and broadening of image induced surface resonance is discussed. Finally, results are compared to experimental data and other theoretical calculations.

Comment on "Theory of Incomplete Crystals and Crystalline Interfaces" by F. Garcia-Moliner and V. R. Velasco

The relation between the discrete Surface Green's Function Matching approach of Garcia-Moliner and Velasco (Physica Scripta 34, 257 (1986)) and atom-removal or ideal construction approaches is clarified. Both approaches are shown to give identical results for an "ideal" surface in the tight-binding approximation. Here "ideal" is defined by the condition that the Hamiltonian matrix elements in the crystal fragment keep their bulk values.

Embedding calculations for deep impurity states in semiconductors

Abstract A method of calculating deep impurity states in semiconductors is presented within the context of a multiple-scattering formulation. An embedding matrix for the host crystal is set up using matching Green function techniques at the impurity cluster surface in the host crystal. The method allows for a cluster of variable geometry to be embedded. Results for the non-self-consistent case are obtained for a number of impurities, including gold, manganese, oxygen and nitrogen, at unrelaxed positions in a silicon host crystal.

Electronic response to surface atomic displacements on Mo (001)

The electronic contribution to the energy of surface phonons is decomposed into a wavevector-dependent term which depends only on the response function in the surface region, plus a wavevector-independent term giving the energy change due to a uniform surface displacement. The wavevector-dependent term is evaluated for the unreconstructed Mo (001) surface, using the matching Green function method to calculate the electronic response function, and the rigid muffin-tin approximation to determine the electron-phonon matrix elements. It is found that the large density of the surface states at the Fermi energy, and the states bonding the surface atoms to the bulk, favour lateral displacements, through the wavevector of the corresponding surface phonon anomaly disagrees with the experimentally observed reconstruction. Periodic vertical displacements of the surface atoms are energetically unfavourable.

The local density of states and the local environment in alloys

The local density of states of a concentrated alloy can be calculated by an extension of the matching Green function method. This involves the inversion of a matrix with the form of tight binding between bonds. The method is applied to calculating the bandstructure and local density states of a square-well model of ordered LiMg. At low energies near the bottom of the band the local density of states is fairly uniform throughout the crystal, but at higher energies it approaches the bulk value for each atom. The relationship between this approach, which stresses the local environment, and nearly-free-electron perturbation theory is explained. Finally the implications of the work for soft X ray results and charge transfer are considered.

Surface states and photoemission from Mo (001)

With the matching Green function method and a simple surface potential, two sp-d hybridisation-gap surface states were found at Gamma on Mo (001), one very close to the Fermi energy and one at -3.3 eV. Another resonance appeared just under EF on moving away from Gamma . The results are in agreement with directional photoemission experiments. The origin of the Gamma surface states is studied.

The electronic structure of surfaces with the matching green function method: I. General formalism

The matching Green function method can be used to construct the Green function for a metal with a surface from Green functions for the bulk metal G M and vacuum G 0. The matching procedure is discussed for various forms of boundary joining the metal and vacuum, using Bloch Green functions with fixed wavevector parallel to the surface. The density of states in the surface atomic cell can be found easily, and a formula is derived for the change in total density of states caused by a surface in terms of surface values of G M and G 0. This is applied to the Ni(001) surface, and the behaviour at band edges is examined.

The electronic structure of surfaces with the matching green function method: II. fcc and bcc transition metal surfaces

Using the matching Green function method, the densities of states at (001) surfaces of Ni (fcc) and Mo (bcc) are calculated. Fixing the wavevector parallel to the surface, the surface density of states at Ni(001) is similar to the bulk, with band edge singularities rounded off and reflected in big surface resonances. Changes are much greater in the case of Mo(001), and the surface density of states has a central peak in the minimum of the bulk density of states. This peak arises from the 4d level in the surface atoms interacting weakly with the substrate and with neighbouring surface atoms. Our results are compared with angular resolved photoemission theory and experiment — in the case of Ni all the experimental peaks correspond to bulk k-conserving transitions, though some surface resonances in the Mo surface density of states show up in photoemission.

The density of states at surfaces and the phase-shift rule

When a surface is made, 1/4 of an electronic state is removed at band edges for each value of the wavevector parallel to the surface. This is shown by using a mode-counting argument, and also by the matching Green function method in which the change in density of states is given in terms of surface values of the bulk and vacuum Green functions. The removal of 1/4 of a state at the bottom of the band, with the requirement of charge neutrality, leads to the surface phase-shift rule.

Calculation of Green functions in crystals with the matching Green function method

The Green function for a crystal can be found by matching the KKR Green function onto an atomic Green function over the surface of an atomic cell. The band structure can be found by this method. The atomic sphere approximation which uses an energy-independent KKR Green function can be applied to this method.

The binding energy of Li3

The Wigner–Seitz method provides a good effective potential, including correlation effects, for alkali molecules as well as metals. Here it is used with the matching Green function method to calculate the binding energy of linear Li3. This turns out to be −0.068 a.u. per molecule, relative to free atoms, at an equilibrium internuclear separation of 5.1 a.u., compared with −0.051 a.u. for the binding energy of Li2 obtained in a similar calculation.