Single-site Coherent Potential Approximation Research Articles

Ab initio approaches to high-entropy alloys: a comparison of CPA, SQS, and supercell methods

We present a comparative study of different modeling approaches to the electronic properties of the \(\text {Hf}_{0.05}\text {Nb}_{0.05}\text {Ta}_{0.8}\text {Ti}_{0.05}\text {Zr}_{0.05}\) high-entropy alloy. Common to our modeling is the methodology to compute the one-particle Green’s function in the framework of density functional theory. We demonstrate that the special quasi-random structures modeling and the supercell, i.e., the locally self-consistent multiple-scattering methods, provide very similar results for the ground state properties such as the spectral function (density of states) and the equilibrium lattice parameter. To reconcile the multiple-scattering single-site coherent potential approximation with the real space supercell methods, we included the effect of screening of the net charges of the alloy components. Based on the analysis of the total energy and spectral functions computed within the density functional theory, we found no signature for the long-range or local magnetic moments formation in the \(\text {Hf}_{0.05}\text {Nb}_{0.05}\text {Ta}_{0.8}\text {Ti}_{0.05}\text {Zr}_{0.05}\) high-entropy alloy; instead, we find possible superconductivity below \(\sim 9\)K.

Auxiliary coherent medium theory for lattice vibrations in random binary alloys with mass and force-constant disorders

The inevitable and random impurities or defects can significantly influence the lattice-vibrational properties of materials and devices. Thus, the capability of effectively treating disorder effects is indispensable for theoretical simulations. In this paper, we report an auxiliary coherent medium theory, in the framework of multiple scattering theory, to simulate disordered vibrational systems containing both mass and force-constant disorders. In this method, the physical Green's function is related to an auxiliary Green's function by introducing a separable force-constant model to describe disordered systems. As an important result, the force-constant disorder can be transformed to a diagonal-like disorder in the auxiliary Hamiltonian while maintaining the important force-constant sum rule. In combination with the single-site and cluster coherent potential approximation, the configurational average over the auxiliary Green's function can be performed to obtain the configuration-averaged physical properties. To demonstrate the effectiveness of this method, we apply it to a one-dimensional harmonic chain with atomic disorders and find our calculations agree very well with the exact results for a wide range of mass and force constants. Moreover, we show that the phonon transport property of disordered devices can be derived based on the auxiliary Green's function formalism in combination with vertex corrections. The auxiliary coherent medium theory features easy implementation and feasible incorporation with diagrammatic technique in many-body perturbation and various cluster approximations, providing an important approach to analyze disorder effects on the vibrational properties. Moreover, it is also straightforward to apply the present formalism to treat the general atomic disorder in electronic systems.

Real-space cluster dynamical mean-field approach to the Falicov-Kimball model: An alloy-analogy approach

It is long known that the best single-site coherent potential approximation (CPA) falls short of describing Anderson localization (AL). Here, we study a binary alloy disorder (or equivalently, a spinless Falicov-Kimball (FK)) model and construct a dominantly analytic cluster extension that treats intra-cluster ($1/d$, $d$=spatial dimension) correlations exactly. We find that, in general, the irreducible two-particle vertex exhibits clear non-analyticities before the band-splitting transition of the Hubbard type occurs, signaling onset of an unusual type of localization at strong coupling. Using time-dependent response to a sudden local quench as a diagnostic, we find that the long-time wave function overlap changes from a power-law to an anomalous form at strong coupling, lending additional support to this idea. Our results also imply such novel "strong" localization in the equivalent FK model, the simplest interacting fermion system.

First-principles study of electronic properties of B and C doped CuNNi3

We have performed ab initio electronic structure calculations for and () alloys using the Green's-function-based Korringa–Kohn–Rostoker method, formulated within atomic sphere approximation. The disorder in sub-lattice is treated within single-site coherent potential approximation. The spin-polarized calculations predict CuNNi3 and its alloys and to be non-magnetic for the entire doping range. For ordered phase, the density of states (DOS) at Fermi energy is mainly composed of Ni 3d states with small contributions from N 2p and Cu 3d states as well. Additionally, we observe a high DOS peak at which arises from Ni and Cu 3d states. For both and alloys, the DOS at Fermi energy decreases monotonically with concentration. This is in sharp contrast to what is expected for a hole doped system with high DOS peak below Fermi energy. The decrease in DOS at Fermi energy is more prominent in alloys. Hence the doping is found to be more deteriorating to superconductivity than . Moreover, the doping induced effects are not entirely rigid-band like, rather a moderate redistribution of electronic states is observed.

Compositional trends in Ni-Mn-Ga Heusler alloys: first-principles approach

In this work we present a systematic investigation of magnetic and structural properties of a broad range of Ni-Mn-Ga alloys by means of the density functional theory. Calculations are carried out for the cubic austenitic phase. The effect of chemical disorder is simulated by using the single-site coherent-potential approximation and the spin-polarized generalized gradient approximation. Equilibrium lattice parameters, bulk moduli, total magnetic moments, and formation energies of a wide range of Heusler alloys have been mapped on compositional ternary diagrams that give a bigger picture of the variety of physical properties of this family of alloys.

Disordered photonic crystals: a cluster coherent potential approach using photonic Wannier functions

We present a cluster coherent potential approach for disordered photonic crystals (PhCs) that is based on maximally localized Wannier functions. In particular, the Wannier basis facilitates an efficient representation of the photonic band structure of a defect-free PhC and the Green’s function thereof, which we discuss first. Moreover, the Wannier basis allows for adapting elaborate approaches developed for the analysis of disorder in electronic and phononic systems to PhCs. Our detailed studies reveal that neither the virtual crystal approximation nor the single-site coherent potential approximation (CPA) provides a reliable description of the effects of disorder in PhCs. Rather, we demonstrate that a cluster based CPA yields qualitatively and quantitatively useful results even for strong disorder. In all these approaches, we include multiple bands, enforce the proper translational properties of the effective medium, and incorporate interaction beyond nearest neighbor coupling. We also discuss the efficient evaluation of the corresponding system of equations. Our results establish a firm basis for various extensions, such as to the theory of Anderson localization or random lasing in disordered PhCs.

Coherent potential approximation as a voltage probe

Coherent potential approximation (CPA) has widely been used for studying the residual resistivity of bulk alloys and electrical conductivity in systems with structural disorder. Here, we revisit the single-site CPA within the Landauer-B\"uttiker approach applied to the electronic transport in layered structures and show that this method can be interpreted in terms of the B\"uttiker voltage-probe model that has been developed for treating phase-breaking scattering in mesoscopic systems. We demonstrate that the on-site vertex function, which appears within the single-site CPA formalism, plays the role of the local chemical potential within the voltage-probe approach. This interpretation allows the determination of the chemical potential profile across a disordered conductor, which is useful for analyzing results of transport calculations within the CPA. We illustrate this method by providing several examples. In particular, for layered systems with translational periodicity in the plane of the layers, we introduce the local resistivity and calculate the interface resistance between disordered layers.

The effects of magnetic and nonmagnetic impurities on electronic properties of semiconductor multilayers

We present a theoretical study of electronic states for a semiconductor multilayer consisting of a binary alloy, by using the single-site coherent potential approximation (CPA) and the tight-binding model. In this study the self-energy depends on the layer number. This dependence was neglected in previous studies. Our results for both nonmagnetic semiconductor (NMS) and diluted magnetic semiconductor (DMS) multilayers are presented. We found that, with increasing the nonmagnetic (chemical) impurity concentration, some of the van-Hove singularities in local density of states (LDOS) disappeared. In addition, the applicability of CPA in appearance of a gap in LDOS has been investigated. In the presence of magnetic impurity, the bands are broadened due to the impurity spin fluctuation, and in the high impurity concentration, the van-Hove singularities in the LDOS may completely disappear and the curves become smooth.

Optical absorption spectrum in disordered semiconductor multilayers

The effects of chemical disorder on the electronic and optical properties of semiconductor alloy multilayers are studied based on the tight-binding theory and single-site coherent potential approximation. Due to the quantum confinement of the system, the electronic spectrum breaks into a set of subbands and the electronic density of states and hence the optical absorption spectrum become layer-dependent. We find that, the values of absorption depend on the alloy concentration, the strength of disorder, and the layer number. The absorption spectrum in all layers is broadened because of the influence of disorder and in the case of strong disorder regime, two optical absorption bands appear. In the process of absorption, most of the photon energy is absorbed by the interior layers of the system. The results may be useful for the development of optoelectronic nanodevices.

Chemical and magnetic impurity effects on electronic properties of semiconductor quantum wires

We present a theoretical study of electronic states in magnetic and nonmagnetic semiconductor quantum wires. The effects of chemical and magnetic disorder at paramagnetic temperatures are investigated in single-site coherent potential approximation. It is shown that the nonmagnetic impurity shifts the band of carriers and suppresses the van Hove singularities of the local density of states (LDOS) depending on the value of impurity concentration. The magnetic impurity, however, broadens the band which depends on the strength of exchange coupling, and in the high impurity concentration, the van Hove singularities in the LDOS can completely disappear and the curves become smooth.

Single-particle spectrum for a model of fermions interacting with two-level local excitations on a lattice: A dynamical CPA approach

The problem of motion of a single electron interacting with a periodic lattice of two-level systems is investigated within a spinless fermion model. The Green's function is calculated in a single-site dynamical coherent potential approximation which is equivalent to DMFT. The picture of one-electron density of states is obtained for various values of the tunnel splitting and coupling between the electron and two-level system. The occurrence of a band splitting with increase of the coupling is demonstrated.

Self-consistent theory of scattering at disordered interfaces in layered nanostructures

A self-consistent theory of electron scattering at the real disordered interfaces in the layered nanostructures is developed. This theory generalizes, particularly, the well known quantum mechanics results for the electron transmission through and reflection from the perfect potential steps/wells/barriers on the case of the intermixed (alloylike) interfaces. The closed analytical expressions for the probabilities of the specular and diffuse electron transmission and reflection at a single disordered interface are obtained in the self-consistent single-site coherent potential approximation (CPA) and the effective mass approximation for the electronic spectra of different layers. The exact (in the adopted approximations) quantum mechanical transmission amplitude for the electron traveling through two disordered interfaces of a trilayer is also obtained. These results allow studying the interfacial scattering at any angle of an electron incidence at an interface, any materials making up a multilayer (any potential profile and effective masses) and any concentrations of atoms mixed at an interface (particularly, at a nonzero average defect scattering strength). It is shown that the diffuse scattering (caused by the imaginary part of the coherent potential) vanishes at the grazing (with a very small perpendicular to an interface component of velocity) electron incidence at an interface leading to practically specular reflection from an interface (channeling affect). The specular scattering also dominates at close to normal to an interface electron incidence and small interfacial scattering potential fluctuations (from its average value). The diffuse scattering diminishes the specular transmission but may increase or decrease the specular reflection at a disordered interface and permits scattering to the areas (of the parallel to an interface electron momentum component) inaccessible for specular scattering at the perfect interfaces. The obtained specular transmission probability over a potential well of a metallic trilayer exhibits additional (to the conventional resonance states) oscillations caused by the real (average) part of the coherent interfacial potential. The interface roughness associated with the long-range layers' thicknesses fluctuations is accounted for through the semiclassical approximation for the obtained specular transmission probability through a metallic trilayer. For the case of an insulating spacer the obtained tunneling magnetoresistance (TMR) ratio may be expressed (for thick spacer) in the Slonczewski-type form but with the electron polarization and interface factors defined by the electron transmission probabilities (for different spin channels) through a spacer with disordered interfaces. The obtained results are believed to be important for the giant magnetoresistance (GMR) and TMR effects in the real nanostructures with disordered interfaces.

Cluster coherent potential approximation for the electronic structure of disorderedalloys

We extend the single-site coherent potential approximation (CPA) to include the effects ofnon-local disorder correlations (alloy short-range order) on the electronic structure ofrandom alloy systems. This is achieved by mapping the original Anderson disorder problemto that of a self-consistently embedded cluster. This cluster problem is then solvedusing the equations of motion technique. The CPA is recovered for cluster sizeNc = 1. Various new features, compared to those observed in CPA, and related to repeatedscattering on pairs of sites, reflecting the effect of short-range order are clearlyvisible in the density of states. It is explicitly shown that the cluster-CPA methodalways yields a positive-definite density of states. Anderson localization effectshave been investigated within this approach. In general, we find that Andersonlocalization sets in before band splitting occurs, and that increasing partial orderdrives a continuous transition from an Anderson insulator to an incoherent metal.

Ab initiocalculation of the elastic properties ofAl1−xLix(x⩽0.20)random alloys

Ab initio total energy calculations, based on the exact muffin-tin orbital (EMTO) theory, are used to determine the elastic properties of ${\mathrm{Al}}_{1\ensuremath{-}x}{\mathrm{Li}}_{x}$ random alloys $(x\ensuremath{\leqslant}0.20)$ in the face-centered-cubic crystallographic phase. The compositional disorder is treated within the framework of the single-site coherent potential approximation (CPA). The effect of the local lattice relaxation on the elastic constants is estimated using a supercell technique. We study the effect of the single-site approximation by comparing the theoretical ground-state properties calculated using different corrections to the Madelung energy. We find that the calculated equilibrium volumes and alloy formation energies strongly depend on the approximations employed in the Poisson equation, in accordance with former observations. At the same time, the experimental trends of the elastic moduli of disordered $\mathrm{Al}\penalty1000-\hskip0pt\mathrm{Li}$ alloys are well reproduced by the EMTO-CPA method. Using these theoretical results we show that the nonlinear effect of Li addition on the elastic constants originates from the detailed band structure of Al near the Fermi level.

Effects of impurities on the magnetic property in copper oxides

We study effects of the nonmagnetic impurities on the magnetic property in the CuO 2 plane of copper oxides. We calculate the spin susceptibility in the normal state, for the CuO 2 plane with nonmagnetic impurities substituted for Cu atoms, on the basis of the d–p model. We take account of the impurity scattering and the Coulomb interaction at each Cu site within the single-site coherent potential approximation and the fluctuation-exchange approximation, respectively. Our result implies that the nonmagnetic impurities suppress the antiferromagnetic spin fluctuations which mediate the superconductivity in high-temperature superconductors.

Phonons in random alloys: The itinerant coherent-potential approximation

We present the itinerant coherent-potential approximation (ICPA), an analytic, translationally invariant, and tractable form of augmented-space-based multiple-scattering ${\mathrm{theory}}^{18}$ in a single-site approximation for harmonic phonons in realistic random binary alloys with mass and force-constant disorder. We provide expressions for quantities needed for comparison with experimental structure factors such as partial and average spectral functions and derive the sum rules associated with them. Numerical results are presented for ${\mathrm{Ni}}_{55}{\mathrm{Pd}}_{45}$ and ${\mathrm{Ni}}_{50}{\mathrm{Pt}}_{50}$ alloys which serve as test cases, the former for weak force-constant disorder and the latter for strong. We present results on dispersion curves and disorder-induced widths. Direct comparisons with the single-site coherent potential approximation (CPA) and experiment are made which provide insight into the physics of force-constant changes in random alloys. The CPA accounts well for the weak force-constant disorder case but fails for strong force-constant disorder where the ICPA succeeds.

Band structure of highly mismatched semiconductor alloys: Coherent potential approximation

The many-impurity Anderson model is applied to compound semiconductor alloys in which metallic anion atoms are partially substituted by highly electronegative atoms at low concentrations. The interaction between the localized states derived from the electronegative atoms and the Bloch states of the semiconductor matrix is treated in a single-site coherent-potential approximation. The solution for the Green's function provides dispersion relations and broadenings for the conduction-band states. The calculations validate the dispersion relations previously obtained from the two-level band anticrossing model. The restructured dispersion relations and optical absorption coefficient are calculated and compared with experimental results of ${\mathrm{GaAs}}_{1\ensuremath{-}x}{\mathrm{N}}_{x}$ alloys.

Spin-polarized tunneling in ferromagnetic double barrier junctions

Spin-polarized tunneling in FMS/M/FMS double tunnel junctions where FMSs are ferromagnetic semiconductor layers and M is a metal spacer is studied theoretically within the single-site coherent potential approximation (CPA). The exchange interaction between a conduction electron and localized moment of the magnetic ion is treated in the framework of the s-f model. The spin polarization in the FMS layers is observed to oscillates as a function of the number of atomic planes in the spacer layer. Amplitude of these oscillations decreases with increasing the exchange interaction in FMS layers.

Spin-polarized tunneling through a thin-film

The effect of spin-disorder scattering on perpendicular transport in a magnetic monolayer is considered within the single-site Coherent Potential Approximation (CPA). The exchange interaction between a conduction electron and localized moment of the magnetic ion is treated with the use of the s–f model. Electron-spin polarization is evaluated in the tunnel current which comes from the different densities of spin-up, spin-down conduction electrons at the Fermi level in a ferromagnetic semiconductor (EuS). Calculated results are compared with some tunneling experiments.

Self-consistent cluster CPA methods and the nested CPA theory

The coherent potential approximation (CPA), is a useful tool to treat systems with disorder. Cluster theories have been proposed to go beyond the translation invariant single-site CPA approximation and include some short-range correlations. In this framework one can also treat simultaneously diagonal disorder (in the site-diagonal elements of the Hamiltonian) and non-diagonal disorder (in the bond energies). It proves difficult to obtain reasonable results, free of non-analyticities, for lattices of dimension higher than one ( D>1). We show electronic structure results obtained for a Hubbard model, treated in mean-field approximation, on a square lattice and a simple cubic lattice, with the simultaneous inclusion of diagonal and non-diagonal disorder. We compare the results obtained using three different methods to treat the problem: a self-consistent 2-site cluster CPA method, the Blackman–Esterling–Berk single-site like extension of the CPA and a nested CPA approach.