Intra-atomic Coulomb Repulsion Research Articles

Role of Electron Correlation in Charge Transfer to Atoms Leaving Metal Surfaces

The fraction of atoms which appear in a charge state different from the dominant adiabatic (usually neutral) one after scattering or sputtering from a metal surface is calculated. We use a time-dependent Anderson Hamiltonian with an intraatomic Coulomb repulsion term. An approximate solution is found by using only a small subset of electronic states. The intraatomic correlation is taken into account by not allowing double occupation of the atomic orbital. The dependence of the non-adiabatic fraction upon the atom velocity v is similar to the one found by using a non-interacting Hamiltonian, and is proportional to exp (–c/v). Some experimental results are discussed, but true quantitative comparison is at present not possible.

The intra-atomic coulomb repulsion and the distribution of charge states of atoms leaving metal surfaces

The final charge state of an atom leaving a metal surface is calculated, assuming an N-fold degenerate atomic orbital which is in resonance with the conduction band of the metal. The theory is based on an Anderson Hamiltonian approach, and an expansion into states with a small number of e-h pairs is used. The intra-atomic Coulomb repulsion is taken into account by not allowing double occupation of the atomic orbital, i.e. it is taken as infinite. For exponentially decreasing interaction matrix elements and if the atom moves sufficiently slowly the probability that the non-adiabatic charge state will result has the form exp (− c/ν), where ν is the velocity of the adatom motion away from the surface. When the atom valence level ϵ a is above the Fermi level the constant c is found to be larger than in the non-interacting (or N = 1) case, and when ϵ a lies below ϵ F it is found to be smaller. The relevance of the effect for the charge distribution observed in atom scattering and sputtering is discussed.

Model calculations for the anomalous M4,5VV Auger spectrum for dilute palladium in silver.

A model Hamiltonian is introduced for an impurity in a filled band host, and where the intra-atomic electron interaction U on the impurity site is included. The Auger spectrum ending in two holes in the valence band (VV) is solved exactly for the impurity. For a certain range of values of U there is besides the normal Cini-Sawatzky quasiatomic peak a new, discrete two-hole state at much lower binding energy. For a one-dimensional system the two-hole problem is treated exactly and the solution is used to explain the nature of the new two-hole bound state. Also, a self-consistent mean-field type of treatment is applied to elucidate the origin of the two bound states. Extensions of the model to include the intra-atomic Coulomb interaction on the host atoms show also that interatomic quasiatomic Auger processes contribute to the decay of the initial impurity core hole. In connection with this, a detailed comparison between the Cini and Sawatzky expressions for the spectral distribution function is performed. The solution for the model Hamiltonian is used to explain the strong anomaly of the Pd ${M}_{4}$,5VV Auger spectrum for dilute palladium alloys with silver. By a schematization of the palladium local density of states, a direct comparison between the calculated and the experimental spectrum is made and a good agreement is found. By variations of the local density of states and the intra-atomic Coulomb repulsion, the conditions for the appearance of the anomalous peak are investigated.

On the electrical conductivity of intermediate valence compounds

Abstract A decoupling scheme is presented for the evaluation of generalized susceptibilities of a periodic array of rare earth ions. This decoupling is exact in the limit of infinite intra-atomic Coulomb repulsion U of the 4f electrons and to order V 4 of their hybridization energy with conduction electrons. As an example the current-current correlation function and the resulting electrical conductivity are evaluated.

Chemisorption on contaminated metals

A Green-function calculation is performed to study how the presence of an impurity in a metal affects its chemisorption properties as the impurity nears the surface. The Anderson-Newns model is adopted to take account of the intra-atomic Coulomb repulsion ( U) on the adatom. Comparisons of the results obained for U = 0 and U ≠ 0, within the restricted Hartree-Fock approximation, pointedly show the importance of including the U contribution. Findings are presented for atomic hydrogen adsorbed on a Ni(Cu)-contaminated Cu(Ni) substrate. The effects of the impurity on the energy levels of the localized adatom states, chemisorption energies and charge transfer are described in detail.

Chemisorption on contaminated metals

Abstract A Green-function calculation is performed to study how the presence of an impurity in a metal affects its chemisorption properties as the impurity nears the surface. The Anderson-Newns model is adopted to take account of the intra-atomic Coulomb repulsion ( U ) on the adatom. Comparisons of the results obained for U = 0 and U ≠ 0, within the restricted Hartree-Fock approximation, pointedly show the importance of including the U contribution. Findings are presented for atomic hydrogen adsorbed on a Ni(Cu)-contaminated Cu(Ni) substrate. The effects of the impurity on the energy levels of the localized adatom states, chemisorption energies and charge transfer are described in detail.

A new pairing possibility in heavy fermion superconductors

Abstract Hybridization coupled bands of lozalized and itinerant states can produce pairing by double hybridization. The mechanism is illustrated for a periodic Anderson model. The effective Hamiltonian generated in a second order Schrieffer-Wolff transformation contains an exchange interaction which reduces the intra-atomic Coulomb repulsion and favours pairing.

Itinerant magnetism in metallic glasses

Abstract It is argued that when a ferromagnetic transition metal T (e.g. Fe) is mixed with a metalloid M to form a metallic glass (having a narrow band of conduction electrons) the competing effects of the 3- d intra-atomic Coulomb repulsion and of the interaction between conduction and d -electrons make the magnetic moment of T -atoms to vanish when the concentration x of T -atoms is smaller than a critical concentration x c . Experimental data for the magnetic moment of iron atoms in Fe x B 1- x is analyzed along this line and a satisfactory fit is obtained. Inclusion of structural as well as compositional disorder effects could result in a better agreement between theory and experiment.

Charge Density Wave-Soliton Model for Se and Te

A new microscopic theory is proposed for the electronic and lattice structures of crystal and defects of Se and Te. Consideration of the valence bond picture shows that electron correlation in valence P electrons produces a charge density wave (CDW) of vector nature, the vector CDW (VCDW), which has the period of three and keeps every atom neutral. Defects including valence alternation pairs and recombinations of helical chains may be generated as' low energy solitonic excitations of the VCDW. Amorphous Se and Te may be regarded as an assembly of solitonic excitations in the VCDW. A formulation of the VCDW and its soli tonic excitations is given in the HF approximation. Valence P electrons are described by an INDO type Hamiltonian with the nearest neighbour transfer and exchange interactions, intraatomic Coulomb repulsion and exchange and interatomic Coulomb repulsion. The remaining closed shell part of each atom is represented as a core with a repulsive potential. The lattice geometry is determined by the balance of the cohesive force of P electrons and the repulsion of cores. The effective intraatomic Coulomb interaction in a neutral atom has the form of a negative on-site interaction which stabilizes the VCDW. An equation is obtained which determines self-consistently the electronic and lattice structures of the VCDW and its solitonic defects. The VCDW and its defects always accompany not only an electron density modulation but also a bond order modulation so that they have lattice structures distorted from a standard cubic lattice. The trigonal lattice of the crystalline Se and Te can be explained as due to the presence of the VCDW.

An Application of CPA to Binding Energy of Many Adatoms on Metallic Surface

In this paper we consider a system of many adatoms adsorbed on a metallic surface. The surface electronic states, the binding energy and the change in work function due to charge transfer are calculated on the basis of CPA as functions of coverage. The partial density of states at different atomic sites are numerically computed for different values of coverage, intra-atomic Coulomb repulsion parameter and atomic level of the adatom.

Critical study of the functional-integral method applied to the itinerant magnetism

We have studied the Anderson model using the functional-integral technique within the static approximation and at the saddle points, with the hope of clarifying a few of the primary difficulties which have hindered the understanding of itinerant magnetism using this technique. The intra-atomic Coulomb repulsion term Un\ensuremath{\uparrow}n\ensuremath{\downarrow} has been resolved into four different classes of quadratic forms of the electron number operator, representing a generalization of transformations previously proposed in the literature. In particular, we analyze in which conditions the use of such identities yield Anderson's Hartree-Fock result. We conclude that the application of the functional-integral method to the study of the Anderson and Hubbard models does not suffer from any arbitrariness, or ambiguity, as has been claimed in the literature.

On Superconductivity in Narrow‐Band Alloys

AbstractTwo different approaches to disordered superconductors are examined to derive a random contact model on the basis of nonlocal electron‐phonon coupling. The formalism, aimed at transition metal alloys in the weak‐coupling regime, takes into account both, the finite‐range pairing interaction, and the intraatomic Coulomb repulsion of the tightly bound electrons. The superconducting transition temperature of AcB1−c alloys is calculated for the nonmagnetic and magnetic cases.

Comparative study of reconstructed silicon and diamond (111) surfaces modelled by small clusters

Reconstruction on (111) Si and diamond surfaces is investigated by employing the MINDO/3 quantum chemistry procedure to optimise the geometries of clusters representing these surfaces. Localised molecular orbitals are constructed to interpret the reconstruction mechanisms in terms of bond changes. The clusters consist of eight Si or C atoms together with bond saturating hydrogens. Since two of the eight Si/C atoms represent first layer atoms, the cluster can spontaneously discriminate between these two atoms and therefore both 1 × 1 and 2 × 1 reconstruction can be modelled. It is found that the Si cluster indeed experiences an asymmetrical distortion in which one atom is raised with respect to the surface while the other is lowered. These displacements are accompanied by asymmetric dehybridisation of surface bonds and a transfer of charge between the two surface atoms as expected for such a Jahn-Teller distortion. Intra-atomic Coulomb repulsion in the raised, negatively charged atom is shown to be an important factor in opposing the reconstruction. In contrast to the Si cluster, the diamond cluster hardly shows any buckling, but considerable relaxation occurs. The structure does not differ substantially from a 1 × 1 reconstructed configuration. The reluctance of the diamond surface to undergo a Jahn-Teller distortion is ascribed to partial graphitisation of this surface.

Diatomic-molecule model for a mixed-valence system

A model for a homopolar diatomic molecule is presented. It contains the following: (a) one $s$-like and one $f$-like orbital per atom, (b) an interatomic transfer term between the $s$ states, (c) an interatomic hybridization term between $s$ and $f$ states, (d) a very strong intra-atomic Coulomb repulsion between two $f$ electrons, and (e) an intra-atomic Coulomb repulsion between $s$ and $f$ electrons. The ground-state energy for the two-electron system is analyzed in detail for a variety of cases. The phenomenon of mixed valence is examined. It is found that the Coulomb interaction between $s$ and $f$ electrons tends to suppress the average occupation of $f$ states between values of one-third and one; depending on the other parameters, the occupation tends to take either values between zero and one-third or one, the full occupation.

Valence transition in SmS: A theoretical calculation

The valence transition of Sm in samarium monochalcogenides is computed in a two band model. Abrupt or continuous transitions are obtained varying the ratio G/V, where G is the intra-atomic Coulomb repulsion between 4f and conduction electrons and V is the hybridization between them.

Ground state of Hubbard model on 2 × 2 × 2 lattice

The energy and the total spin of the ground state of Hubbard model on 2 × 2 × 2 lattice are calculated for various values of the intra-atomic Coulomb repulsion I. The total spin S of the ground state assumes the smallest value when the electron number N is 2, 3 or 6, irrespective of the value of I. For N = 5, S is 3 2 and is independent of I, too. For N = 4 or 7, S assumes the smallest value when I is not very large, and the ground state becomes completely ferromagnetic when I exceed 39 or 200 times the inter atomic transfer energy, respectively.

Surface electronic properties ofd-band perovskites: Study of theπbands

The surface electronic properties of $d$-band perovskites such as SrTi${\mathrm{O}}_{3}$ are investigated in some detail using a Green's-function method and a linear-combination-of-atomic-orbitals model developed in our previous work. We consider the nine energy bands ($\ensuremath{\pi}$ bands) associated with the ${t}_{2g}$ $d$ orbitals of the cation and the corresponding $p$ orbitals of the oxygen ions. Exact expressions for the local density of states (LDS) of cations and anions at and near a (001) surface are derived and evaluated for a variety of surface conditions. It is found that the LDS of a surface cation is substantially enhanced in the energy range of the filled valence bands when surface states occur in the forbidden band gap. This increase in density results from surface enhancement of the covalent mixing of $d$ orbitals into valence-band wave functions. The surface-enhanced covalency leads to a substantial increase in the number of electrons occupying surface cation $d$ orbitals if intra-atomic Coulomb repulsion is neglected. An approximate Hartree-Fock treatment is employed to investigate the effect of Coulomb repulsion among excess electrons in surface orbitals. Approximately self-consistent solutions for the LDS are obtained. These solutions show that band-gap surface states are forced to lie substantially nearer to the conduction-band edge than predicted by the non-self-consistent theory. Two competing effects arise when the electron occupation is altered on the surface cations. First, there is an increase in the interatomic Coulomb repulsion among the excess $d$-orbital electrons. Second, there is a corresponding decrease in the interatomic Coulomb repulsion (Madelung potentials) because of the reduction in the ionic charges. The intra-atomic Coulomb repulsion dominates for the case of an ideal surface and surface bands are repelled from the midgap region. It is suggested that a surface oxygen vacancy concentration of a few percent can alter the balance between interatomic and intra-atomic Coulomb repulsion resulting in the appearance of band-gap surface bands. These results are employed to suggest a possible explanation of the results of several recent photoemission experiments on the surface states of SrTi${\mathrm{O}}_{3}$ and Ti${\mathrm{O}}_{2}$.

Superconducting and normal state properties of dilute alloys of LaSn 3 containing Ce impurities

The dependence of the superconducting transition temperature T c on Ce impurity concentration and the specific heat jump at T c as a function of T c are reported for the system ( La Ce)Sn 3. The experimental results are analyzed using a theory due to Kaiser concerning the effect on superconductivity of nonmagnetic localized resonant impurity states This analysis yields values for the intraatomic Coulomb repulsion parameter U eff and the Ce local density of states at the Fermi level N ℓ (E F). The results of low temperature normal state heat capacity and magnetic susceptibility measurements which give independent estimates of N ℓ (E F) are also reported. A large pressure dependence of the T c of ( La Ce)Sn 3 alloys was observed for pressures up to 20 kbar. This behavior is similar to that previously observed in several other superconducting matrix-Ce impurity systems in which the Ce solute 4f electron shell undergoes a continuous-pressure induced demagnetization.

Transport properties determinations of the one-dimensional, half-filled band Holstein-Frölich modified Hubbard model

The magnetic susceptibility, electrical conductivity, and specific heat of the Holstein-Fröhlich modified Hubbard model are obtained with the restriction that the chemical potential μ be identically equal to one-half the intra-atomic electronic Coulomb repulsion U. Contributions to the conductivity for all driving frequencies ω are obtained. The specific heat calculation yields electron-phonon interaction corrections, but the susceptibility results are the same as those for the insulator limit Hubbard model.

Selfconsistent model calculations of electronic states at narrow-band-metal surfaces

For a nondegenerate narrow energy band spanned by a semiinfinite chain of three-dimensional atoms, the electronic potential and the electron density of states are calculated selfconsistently in the vicinity of the chain end. The electron-electron interaction is treated in the Hartree-Fock approximation, using the Green function method. The results for the potential and the density of states are discussed in terms of the parameters which determine the bulk electronic structure, such as the Fermi energy E F and the intra- and interatomic Coulomb repulsion k 0 and K 1. Futhermore, the self consistent method is extended to an impurity atom at the chain end. The existence of bonding and antibonding surface states is found to depend on both the bulk and impurity parameters, such as the intraatomic Coulomb repulsion U α and the nearest neighbour hopping element T.