Showing papers on "Coherent potential approximation published in 1995"

Introduction to Wave Scattering, Localization, and Mesoscopic Phenomena

Abstract: Quantum and Classical Waves.- Wave Scattering and the Coherent Potential Approximation.- Coherent Waves and Effective Media.- Diffusive Waves.- The Coherent Backscattering Effect.- Renormalized Diffusion.- The Scaling Theory of Localization.- Localized States and the Approach to Localization.- Localization Phenomena in Electronic Systems.- Mesoscopic Phenomena.

Ground-state properties of ordered, partially ordered, and random Cu-Au and Ni-Pt alloys

Abstract: We have studied the ground-state properties of ordered, partially ordered, and random Cu-Au and Ni-Pt alloys at the stoichiometric 1/4, 1/2, and 3/4 compositions in the framework of the multisublattice single-site (SS) coherent potential approximation (CPA). Charge-transfer effects in the random and the partially ordered alloys are included in the screened impurity model. The prefactor in the Madelung energy is determined by the requirement that the total energy obtained in direct SS CPA calculations should equal the total energy given by the Connolly-Williams expansion based on Green's function calculations for the ordered alloys that do not rely on the single-site approximation. We find that the prefactor to a large degree is independent of a lattice constant, concentration, and a long-range-order parameter and may be considered constant for a given alloy system. The calculated heats of formation for the ordered alloys are in good agreement with experimental data. For all the alloys the calculated ordering energy and the equilibrium lattices parameters are found to be almost exact quadratic functions of the long-range-order parameter.

Dispersion of elastic waves in random particulate composites

Abstract: Elastic wave propagation in a discrete random medium is studied to predict dynamic effective properties of composite materials containing spherical inclusions. A self‐consistent method is proposed which is analogous to the well‐known coherent potential approximation in alloy physics. Three conditions are derived that should be satisfied by two effective elastic moduli and effective density. The derived self‐consistency conditions have the physical meaning that the scattering of a coherent wave by the constituents in the effective medium vanishes, on the average. The frequency‐dependent effective wave speed and coherent attenuation can be obtained by solving the self‐consistency conditions numerically. At the lowest resonance frequency, the phase speed increases rapidly and the attenuation reaches the maximum in the composites having a large density mismatch. The lowest resonance is caused mainly by the density mismatch between matrix and particles and higher resonances by the stiffness mismatch. The dispersion and attenuation of longitudinal and shear waves are affected by the lowest resonance much more than by higher ones. The lowest resonance frequency of particles in the effective medium is found to be higher than that of a single particle embedded in the matrix material of composites due to the stiffening effect. The results obtained from the present theory are shown to be in good agreement with previous experimental observations of Kinra et al. [Int. J. Solid Struct. 16, 301–312 (1980)]. Part of the calculated results are compared with those computed by the Waterman and Truell theory. The present theory is in better agreement with the experiments for the examples dealt with.

Wave Scattering and the Effective Medium

Abstract: This chapter provides an overview of wave scattering and the effective medium. In the classical scalar wave case, the single scatterer is taken to be a sphere of radius R with dielectric constant. When there are infinitely many scatterers, the T -matrix and the exact Green's function are impossible to obtain accurately. However, it is determined that in the wave vector representation, the averaged Green's function is given by a particular function. For the three-dimensional (3D) coherent potential approximation (CPA), the evaluation of the Green's function is perhaps the most time-consuming part of the numerical calculation. A useful and efficient approach to the calculation of the 3D Green's function is to compile a numerical table of the density of states for the ordered lattice and store it in computer memory. The diagonal Green's function can then be obtained from an equation, which involves only one integration.

Impurity Effects of Heavy Fermion Semiconductors

Abstract: The effects of doped impurities of heavy fermion semiconductors are studied on the basis of the periodic Anderson model with randomly distributed Kondo holes. The slave boson mean-field theory is applied to treat the strong Coulomb interaction on f -orbitals, while the effect of disorder is analyzed by the coherent potential approximation (CPA). It is shown that the low-temperature behaviors of specific heat and resistivity are strongly affected by a small amount of impurities due to the formation of an impurity band in the hybridization gap. The results are compared with the experimental observation in the doped heavy fermion semiconductor (Ce 1- x La x ) 3 Bi 4 Pt 3 .

An augmented-space recursion in the k-space representation

Abstract: We present here a technique for the calculation of configurationally averaged quantities in the reciprocal k-space representation, such as the spectral function and complex band structures. We apply the technique to AgPd alloys in conjunction with the tight-binding linearized muffin-tin orbital basis. We also indicate why the same technique is ideal for application to the more accurate screened KKR and allows us to go beyond the single-site coherent potential approximation and include multi-site effects such as short-ranged ordering and local lattice distortions due to size mismatch of the constituent atoms.

Random matrix theory for CPA: generalization of Wegner's n-orbital model

Abstract: We introduce a generalization of Wegner's (1979) n-orbital model for the description of randomly disordered systems by replacing his ensemble of Gaussian random matrices by an ensemble of randomly rotated matrices. We calculate the one- and two-particle Green functions and the conductivity exactly in the limit n to infinity . Our solution solves the coherent potential approximation equation of the (n=1) Anderson model for arbitrarily distributed disorder. We show how the Lloyd model is included in our model.

Build-up and decoherence of optical transients in disordered semiconductors

Abstract: For a model two-band semiconductor with static disorder, suddenly illuminated by intense light, the averaged non-equilibrium Green function can be obtained within the coherent potential approximation. Explicit solutions found previously are analyzed on numerical examples of the transient photoexcited distribution. The results are used to test the semigroup property of the propagators and the analogous factorization of the particle correlation function known as the generalized Kadanoff-Baym ansatz. Both properties hold much better if quasiparticle states are used instead of the bare particles. The quasiparticle modification of the ansatz is motivated formally and verified on numerical data

CPA theory with correlative effects: application to the νs(PF3) stretch of PF3/Pt(111)

Abstract: We present an approach based on the coherent potential approximation (CPA) with allowance for small to moderate correlations among sites and apply it to a vibrational Hamiltonian for less than full coverage. The CPA averaged Hamiltonian is employed to interpret the IRAS spectra of the νs(PF3) stretch of PF3/Pt(111). Island formation is modeled by introducing a correlation between occupied and unoccupied sites (admolecules and “holes”), which results in an additional effective potential term in the averaged Hamiltonian. The correlative effect is thought to originate from the band formation of the PF3 orbitals at intermediate coverages; which perturbs the vibrational frequency of oscillators in near proximity. The model suggests a different interpretation of the split band structure of the νs(PF3) lineshape at intermediate coverages than has been previously purported. The parameters invoked in the model are either readily determined from, or consistent with those inferred from, the experimental system.

Multiple-scattering approach to the s-f model in ferromagnetic semiconductors above the curie temperature

Abstract: For the s-f model in ferromagnetic semiconductors, it is necessary to treat simultaneously multiple scattering on the same site and scattering due to f spin correlation between different sites. In this paper, one-site multiple scattering is taken into account using a t-matrix formalism, and the exchange scattering via f spin correlation between different sites is treated using a two-spin correlation function and an appropriate decoupling scheme. The results show good agreement with those of the coherent potential approximation in the high-temperature limit. The calculated energy of the bottom of the band is reasonable, even at the Curie temperature (${\mathit{T}}_{\mathit{C}}$), for a wide range of IS/W, where W is the bandwidth of the conduction band and IS is the exchange interaction energy.

Antiferromagnetic instability of heavy-fermion alloys with conduction band impurities

Abstract: The antiferromagnetic instability of heavy-fermion alloys with conduction band impurities is examined in the single-site coherent-potential approximation with the strong correlation treated by the slave-boson technique of Kotliar and Ruckenstein. The variation of the paramagnetic-antiferromagnetic phase boundary with the impurity concentration is studied in the case of isoelectronic doping. Our results show that the isoelectronic doping favours the formation of antiferromagnetism if the impurities increase the cell volume, thus suppressing the c-f mixing, which is in agreement with experimental observations in Ce(Cu1-xAgx)6 and Ce(Cu1-xAux)6. The obtained phase diagram can also be used to explain the effect of nonisoelectronic substitutions of Al for Cu in CeCu6.

The coherent potential approximation in the description of spin wave resonance

Abstract: The coherent potential approximation method is applied to spin wave resonance in thin ferromagnetic films. The approach takes into account a natural disorder connected with different states of spin components. The resonance spectra with a finite line-width are calculated for the b.c.c. (100) film and S = 1/2. The results obtained show that the half-widths of the surface as well as the volume peaks depend on the surface anisotropy parameter.

Strong vertex corrections from weak disorder in 2D d-wave superconductors

Abstract: We show that weak static random potentials have pronounced effects on the quasiparticle states of a 2Dd-wave superconductor close to a node We prove that the vertex correction coming from the simplest crossed diagram is important even for a nonmagnetic potential The leading frequency and momentum dependent logarithmic singularities in the self-energy are calculated exactly to second order in perturbation theory The self-energy corrections lead to a modified low energy density of states which depends strongly on the type of random potential and which can be measured in experiments There is an exceptional case for a potential with extremely local scatterers and opposite nodes separated by (π, π) where an exact cancelation takes place eliminating the leading frequency dependent singularity in the simplest crossed diagram A comparison of the perturbative results with a self-consistent CPA (coherent potential approximation) for the nonmagnetic disorder reveals qualitative differences in the self-energy at the smallest energies which are due to the neglectance of vertex corrections in CPA

Ultrafast Dynamics and Quantum Transport of Electrons in Strongly Disordered Semiconductors

Abstract: The new experiments on the response of electrons in semiconductors to femtosecond optical pulses call for developing adequate theoretical tools. A promising approach has been found in using the non-equilibrium Green functions approximately factorized on the basis of the so-called generalized Kadanoff—Baym ansatz. The present work investigates the validity of such approach on an example of a semiconductor with an alloy scattering, where the coherent potential approximation allows to construct the non-equilibrium Green functions directly, so that an explicit comparison with the ansatz decoupling is possible. The ansatz for the electron distribution is in this case justified as far as the quasiparticle picture for the individual electrons is appropriate.

Electronic structure and optical properties of si/ge superlattices

Abstract: A new approach that combines various calculational methods is presented for studying the effect of the Si-Ge interface onto the electronic and optical properties of SinGem superlattices (SLs). In particular, our approach employs: i) the tight-binding (TB) method to calculate the band structure of the SinGem SLs which exhibit an abrupt or diffused Si-Ge interface, ii) the coherent potential approximation (CPA) method, in order to describe the interdiffusion across the Si-Ge interface and, finally, iii) the Kubo-Greenwood in order to obtain the optical-absorption coefficient of the SL. This approach is applied on a strained symmetrized Si5Ge5 SL and our results confirm recent theoretical and experimental ones that support the finding that interdiffusion across the interface of the SL degrades the strength of the optical transitions. According to our findings, this degradation is mainly attributed to the widening of the energy gap of the SL that follows the interdiffusion. The present method is more efficient than others based on calculating transition matrix elements explicitly, because it incorporates the effects of randomness on both the density of states and the optical-transition matrix elements through a single step in the framework of the CPA and the Kubo-Greenwood formula.

The effects of the interfacial structures on magnetoresistance in metallic superlattices

Abstract: The effects of interfacial structures on the electronic transport properties in layered structures are investigated within the framework of the coherent potential approximation. In this paper, the two types of interfacial structures between a magnetic slab and a non-magnetic slab are assumed to exist in the superlattice. The first one, named the flat interface, is that the average distribution number of magnetic ions is nearly constant through the interfacial layers. The second, named the diffused interface, is that the average distribution number of magnetic ions decreases gradually in interfacial layers from the magnetic slab to the non-magnetic slab. It is shown within the framework of the mean field approximation that for the resistance the flat interface always shows larger absolute values than the diffused interface and that for the magnetoresistance ratio the value of it depends on the relative position of electron energy levels of magnetic and non-magnetic ions. Making a comparison between the experimental and calculational results, we can say that the spinflop scattering of conduction electrons due to the isolated localized spins is expected to play a major role in the case of the diffused interface where the superlattice shows the large magnetoresistance ratio.

Coherent potential approximation approach to electronic structure of DNA.

Abstract: The electronic structure of DNA is theoretically investigated by use of the coherent potential approximation. Even when the sequence of the four kinds of bases is nonperiodic, guanine block forms the persistent highest valence band edge, and adenine block forms the persistent lowest conduction band edge state. According to the calculated joint density-of-states energy profiles, the site first attacked by the lowest excitation is adenine block. After this excitation, electrons are generated at adenine sites, and holes are generated at guanine sites. The resulting electronic structures of the valence band and conduction band suggest that the base complementarity in DNA produces the complementarity in the density-of-states divergences of the excited electrons and holes. This complementarity lowers the excitation instability in the DNA chains.

Weighted two particle Green's functions in the CPA

Abstract: We extend the two particle theory of disordered systems within the coherent potential approximation CPA to obtain weighted contributions to averaged two particle resolvents which arise from separate alloy components. Starting from first principles in a model of diagonal disorder and the single site approximation for a binary substitutional alloy $A_cB_{1-c}$ we extend the approach of a fundamental paper by Velick{\'y} to evaluate various weighted forms of a general class of two particle Green's functions. Applications in a wide range of linear response theory are discussed in detail as well as the behavior of the weighted functions in a strong disorder limit. To exemplify our analytic calculations the optical absorption in a disordered model- alloy is studied numerically.

Band Structure Theory

Abstract: Semiconductor electronics provides an excellent demonstration of the close connection between modern engineering and quantum physics. It was an understanding of the electronic structure of semiconductors in the 1940s that led to the invention of the first transistor (Bardeen and Brattain, 1948; Brattain and Bardeen, 1948; Shockley and Pearson, 1948)—the backbone of modern computers. Since then, quantum mechanics has been an integral part of the progress of modern electronics technology. As devices become smaller, reaching submicron dimensions where electrons and holes traverse the active region of devices without experiencing a collision (the ballistic transport regime), quantum effects become even more important. Band structure studies deal with the energy levels and wave functions of electrons in materials and their relations to material properties. This chapter will begin by introducing the basic concepts of energy bands (Section 5.1). We will then describe two of the simplest band structure methods used for crystalline semiconductors—the tight-binding method (Section 5.2) and the plane-wave method (Section 5.3). The important band structure results for pure semiconductors are summarized in Section 5.4. The difficulties associated with the aperiodic potentials in an alloy and their effects on band gaps are discussed in Section 5.5. The remaining sections are devoted to the treatment of disordered alloys using the Green function methods, including the coherent potential approximation (CPA) (Soven, 1967; Velicky et al., 1968; Kirpatrick et al., 1970) and the perturbation method (PT). Both CPA and PT will be formulated for semiconductor alloys in this chapter and will be used to treat effects on band-edge states. These formalisms will be applied to detailed calculations of band structures of semiconductor alloys in Chapter 7.

Yibrational coupling in disordered systems: Solid Hz and Di

Abstract: High-resolution Raman measurements were performed of the intramolecular vibrational transition in mixed crystals of (o-H2) x (p-H2)1-x and (o-D2) x (p-D2)1-x The spectra obtained clearly show the effect of coupling between the vibrational states of the two constituent molecules. Calculations of the line shapes by the coherent potential approximation and by diagonalization of the dynamical matrix of a 5324 molecule supercell are compared with the experimental results.

Vibrational properties of thin films of ultraheavily doped semiconductors

Abstract: The pseudospin model for the G 1−x P x semiconductor alloy is considered in the coherent potential approximation. The phonon density of states in ultraheavily doped semiconductor thin films is investigated as a function of impurity concentration and the position of a monatomic layer inside the film. The obtained results show the dependence of the local density of states on the surface conditions