Impurity model

Most of the present implementations of the CPA on the ab-initio level, both for bulk and surface cases, assume a lattice occupied by atoms with equal radii of Wigner-Seitz (or muffin-tin) spheres. The effect of charge transfer which can seriously influence the alloy energetics is often neglected. Several methods were proposed to account for charge transfer effects in bulk alloys, e.g., the so-called correlated CPA , or the screened-impurity model . The application of these methods to alloy surfaces seems to be rather complicated. 

The calculation of the core levels of LajCuO discussed above was performed within the cluster approximation wherein the dependence of the spectral shape on the oxygen band-width is missed out. In order to include the effect of the oxygen 2p derived band on the spectral shape, the core-level photoemission calculation has to be performed within the impurity model which includes the O 2p band-width (instead of a single O 2p level). For reasonable values of the hybridization strength, t, the range of values of A is such that the Cu appears close to the bottom of the... 

We discussed above the analysis of core-level spectra from cuprates which contain only a single hole in the d-band per Cu ion. This makes an irrelevant parameter within an impurity model. However, analysis can also be carried out for systems where [7dd plays a significant role. This is illustrated by the analysis of the core-level spectrum of LaCoOj carried out within the impurity model (Chainani et al, 1992). This oxide is modelled by the (CoOg) cluster with the transition-metal ion being formally in the 3 + oxidation state and in an octahedral crystal field. One has to therefore take into account interactions between various configurations such as d >, d Z, > >. ... 

In the case of a single site junction with two (spin-up and spin-down) states and Coulomb interaction between these states (Anderson impurity model), the linear conductance properties have been successfully studied by means of the EOM approach in the cases related to Coulomb blockade [203, 204] and the Kondo effect [205]. Later the same method was applied to some two-site models [206-209], Multi-level systems were started to be considered only recently [210,211], Besides, there are some difficulties in building the lesser GF in the nonequilibrium case (at finite bias voltages) by means of the EOM method [212-214],... 

In the limit of a single-level quantum dot (which is, however, a two-level system because of spin degeneration) we get the Anderson impurity model (AIM)... 

We consider the following model Hamiltonian (which can be called the multilevel Anderson impurity model, the Hubbard model, or the quantum cluster model)... 

This model is quite universal, describing a variety of correlated electron systems coupled to the leads the Anderson impurity model, the multilevel quantum dot with diagonal noninteracting Hamiltonian quantum dots, when the off-diagonal matrix elements of eap describe hopping between individual dots, and, finally, the ID and 2D quantum point contacts. 

The Anderson impurity model is used to describe the Coulomb interaction on a single site ... 

The Anderson Z+l impurity model16,17 was used to obtain a measure of the core-hole electron attraction U (Equation 1). The Z+l impurity model chosen here assumes that the impurity states (5d orbitals on atom with core-hole) are largely decoupled from the other host states, in contrast to the Clogston-Wolf model, which assumes that the impurity-host hybridization matrix element is unchanged from the host-host21. The former is used for two reasons it is sufficiently valid since we are interested only in the relative changes in AU with respect to bulk Pt, and it is more convenient. 

FIG. 3.33. (a) Comparison of the FDTO model (solid lines) with the experimental (symbols) of Crone et al. [59] for a Ca/MEH-PPV/Ca electron only device, (b) Comparison of the FDTO model (dashed line) and FDTO with background impurity model (solid curve) with the experimental data for A1/MEH-OPV5/ITO (curve 1) and for A1/MEH-OPV5/PEDOT/ITO (curve 2). The thickness of both samples is 110 nm. 

P. Schmitteckert, F. Evers, Exact Ground State Density-Functional Theory for Impurity Models Coupled to External Reservoirs and Transport Calculations, Phys. Rev. Lett. 100 (2008) 08640. 

Kogler U., Winter J., ERO-TEXTOR 3D-Monte-Carlo Code for Local Impurity Modeling in the Scrape-Off-Layer of TEXTOR, Report Jill-3361, Jiilich, 1997... 

XANES is one of powerful tools for the study of chemical states of lanthanoid compounds. Most of the conclusions drawn from the XANES for the lanthanoid compounds have been concerned with the chemical states or characteristics of the electronic structures. In particular, valences of lanthanoids have been studied using such spectra (2). They were obtained by assigning some of the peaks in the spectra to different valences. By using the Anderson impurity model, the valences were derived from intensities of shake-up peaks (3). 

Bianconi ct al. adopted the Anderson impurity model and assumed prominent change of the electronic structure which resulted in the shake-up (3). This restructuring of the bands was attributed to a large 4/ - core hole interaction. Soldatov et al. took the same shake-up model and successfully got theoretical XANES with the peaks A-D, by convoluting multiplescattering XANES spectra obtained for the two electron configurations for the final states due to the shake-up (6). 

Equations (5.7) and (5.8) are derived in Refs.([90, 91, 92]), except for the last terms which are explained below. As can be seen, the Madelung part of the energy and potential is calculated using the effective medium [n], while the intrasite part is solved for the atom kind density, and this leads to a non-vanishing net charge for the alloy component systems. This is corrected for by using the Screened Impurity Model (SIM) [93, 81, 94, 95] and leads to the last terms in the above equations. 

Fig. 16.48 This residual density of states was pointed out theoretically to appear in the unitarity limit scattering by non-magnetic impurities in p- or d-wave superconductors in a heavy fermion study.49 From this result it became possible to explain the BCS-like temperature dependence of the penetration depth, A,50 which supported strongly the. 9-wave pairing model in high-7 , superconductors at an early stage, in terms of the d-wave + impurity model.51 53...

In this sense, atomic multiplet theory provides complementary information about the valence state. One can take the view that this information should be used, and then blended in some way with the conceptual framework of the Anderson single-impurity model, so that the matrix elements coupling the / electrons to the conduction band can continue to play the decisive role in determining the extent of / electron localisation. 

The intensity of the weaker structure is observed to depend on the partner element in the intermetallic. The manifestation of intermediate valence in the 3d — 4/ XAS and other core and outer spectra of Ce intermetallics has been interpreted in the framework of the Anderson impurity model [628]. 

On the other hand, although spectra of Ce and Yb have been thus interpreted, no impurity model calculations of core- and outer-level spectra of Sm, Eu and Tm appear to have been reported so far. Indeed, the Anderson Hamiltonian is reputedly unsuitable for the interpretation of such systems. In the interesting cases of YbP [630] and YbA 3 [631], impurity model calculations have been performed by considering Yb as the hole-analogue of Ce. 

The results this section are very relevant to the discussion in chapter 11 of the Anderson impurity model and the quasiatomic orbital collapse model. It is significant, in particular, that the transition occurs for rather small clusters, smaller than might perhaps be expected for the impurity model to be applicable. The quasiatomic model provides a straightforward explanation for the varying degrees of oxidation observed in [695] the chemical activity of the lanthanide atoms is greater when the orbitals are in an expanded or outer-well state than when they are in a contracted or inner-well one. On the other hand, an important issue which needs to be determined is over what range of cluster sizes an effective conduction band actually appears, since its presence provides the hybridisation forces which play a crucial role in the impurity model. 

The screening-impurity model implies a strong-electron coupling. The strong polarization of the sp electronic density of the chalcogen by Li" ions induces a negative charge defect behind the transition-metal site and reinforces the local positive potential around it. This favors a localization of the transferred electron to this site. The more polarizable the anion, e.g., the Li-ZrSej system, the more important is the effect. 

As the next step in understanding the factors influencing crystal shape, and the effect of solvents and impurities, models... 

We conclude that more work is need. In particular it would be useful to repeat the TB-LMTO-CPA calculations using also other methods for description of charge transfer effects, e.g., the so-called correlated CPA, or the screened-impurity model. One may also ask if a full treatment of relativistic effects is necessary. The answer is positive , at least for some alloys (Ni-Pt) that contain heavy elements. 

This seems counterintuitive in the first place but is easily explained. A ten-atom unit cell with nine correct but one false atom may serve as a computational impurity model for a 10% doping scenario. To get to only 1% of doping, a hundred-atom unit cell with ninety-nine correct atoms and one false atom is needed. 

Whilst there have been several theoretical investigations of the effect of hybridisation on the crystal-field excitations within the ground multiplet (Maekawa et al. 1985, Lopes and Coqblin 1986), there have been relatively few in which the spin-orbit level is explicitly included. Cox et al. (1986) have shown, in the context of the Anderson impurity model, that when is comparable to the spin-orbit splitting, the inelastic peak is broadened and shifted to lower energies. Given that the cross-section is weak, at about half the intensity of the praseodymium spin-orbit cross-section, they concluded that the transition was unlikely to be seen except in heavy-fermion compounds with low values of This appears to be confirmed by the failure to observe such a transition in CePdj in recent measurements on HET (Osborn, unpublished). On the other hand, the... 

The first equation shows that the center of the quasiparticle bands lies at an energy above the original conduction band Fermi level. This should be compared with the position Tg = aT of the Kondo resonance in the impurity model. The second equation simply results from the charge constraint QflN = g, which is now enforced only on the average in contrast to the impurity model. The occupation f(0) is obtained by setting equal to the actual value of 1 IN. The quasiparticle bands are the result of a hybridization with an effective strength K Here r iT) is the average fraction of sites without f occupation,... 

The computational technique used to treat the generalized Anderson impurity model in the slave boson representation will be described in some detail. For an extensive discussion see Coleman (1984). In Appendix A we represented the CEF states of stable 4f" shells (i.e., with integer occupation n) by pseudofermions. In the present case of unstable shells with possible 4f and 4f configurations we need an additional slave boson field for the 4f° state. The interesting physical quantities, static as well as dynamic, can be calculated in terms of the fully renormalized fermion and slave boson Matsubara Green s functions... 

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