Preface Acknowledgements Notation Part I. Overview and Background Topics: 1. Introduction 2. Overview 3. Theoretical background 4. Periodic solids and electron bands 5. Uniform electron gas and simple metals Part II. Density Functional Theory: 6. Density functional theory: foundations 7. The Kohn-Sham ansatz 8. Functionals for exchange and correlation 9. Solving the Kohn-Sham equations Part III. Important Preliminaries on Atoms: 10. Electronic structure of atoms 11. Pseudopotentials Part IV. Determination of Electronic Structure, The Three Basic Methods: 12. Plane waves and grids: basics 13. Plane waves and grids: full calculations 14. Localized orbitals: tight binding 15. Localized orbitals: full calculations 16. Augmented functions: APW, KKR, MTO 17. Augmented functions: linear methods Part V. Predicting Properties of Matter from Electronic Structure - Recent Developments: 18. Quantum molecular dynamics (QMD) 19. Response functions: photons, magnons ... 20. Excitation spectra and optical properties 21. Wannier functions 22. Polarization, localization and Berry's phases 23. Locality and linear scaling O (N) methods 24. Where to find more Appendixes References Index.

Electronic Structure: Basic Theory and Practical Methods

We review the methods which have been developed over the past several years to determine the behavior of solids whose properties vary randomly at the microscopic level, with principal attention to systems having composition variation on a well-defined structure (random "alloys"). We begin with a survey of the various elementary excitations and put the dynamics of electrons, phonons, magnons, and excitons into one common descriptive Hamiltonian; we then review the use of double-time thermodynamic Green's functions to determine the experimental properties of systems. Next we discuss these aspects of the problem which derive from the statistical specification of the microscopic parameters; we examine what information can and cannot be obtained from averaged Green's functions. The central portion of the review concerns methods for calculating the averaged Green's function to successively better approximation, including various self-consistent methods, and higher-order cluster effects. The last part of the review presents a comparison of theory with the experimental results of a variety of properties---optical, electronic, magnetic, and neutron scattering. An epilogue calls attention to the similarity between these problems and those of other fields where random material heterogeneity has played an essential role.

The theory and properties of randomly disordered crystals and related physical systems

Electrons in disordered systems and the theory of localization

The body of research on (III,Mn)V diluted magnetic semiconductors initiated during the 1990's has concentrated on three major fronts: i) the microscopic origins and fundamental physics of the ferromagnetism that occurs in these systems, ii) the materials science of growth and defects and iii) the development of spintronic devices with new functionalities. This article reviews the current status of the field, concentrating on the first two, more mature research directions. From the fundamental point of view, (Ga,Mn)As and several other (III,Mn)V DMSs are now regarded as textbook examples of a rare class of robust ferromagnets with dilute magnetic moments coupled by delocalized charge carriers. Both local moments and itinerant holes are provided by Mn, which makes the systems particularly favorable for realizing this unusual ordered state. Advances in growth and post-growth treatment techniques have played a central role in the field, often pushing the limits of dilute Mn moment densities and the uniformity and purity of materials far beyond those allowed by equilibrium thermodynamics. In (III,Mn)V compounds, material quality and magnetic properties are intimately connected. In the review we focus on the theoretical understanding of the origins of ferromagnetism and basic structural, magnetic, magneto-transport, and magneto-optical characteristics of simple (III,Mn)V epilayers, with the main emphasis on (Ga,Mn)As. The conclusions we arrive at are based on an extensive literature covering results of complementary ab initio and effective Hamiltonian computational techniques, and on comparisons between theory and experiment.

/pdf/theory-of-ferromagnetic-iii-mn-v-semiconductors-24pzayfeji.pdf

Theory of ferromagnetic (III, Mn) V semiconductors

This review summarizes recent first-principles investigations of the electronic structure and magnetism of dilute magnetic semiconductors (DMSs), which are interesting for applications in spintronics. Details of the electronic structure of transition-metal-doped III-V and II-VI semiconductors are described, especially how the electronic structure couples to the magnetic properties of an impurity. In addition, the underlying mechanism of the ferromagnetism in DMSs is investigated from the electronic structure point of view in order to establish a unified picture that explains the chemical trend of the magnetism in DMSs. Recent efforts to fabricate high-TC DMSs require accurate materials design and reliable TC predictions for the DMSs. In this connection, a hybrid method (ab initio calculations of effective exchange interactions coupled to Monte Carlo simulations for the thermal properties) is discussed as a practical method for calculating the Curie temperature of DMSs. The calculated ordering temperatures for various DMS systems are discussed, and the usefulness of the method is demonstrated. Moreover, in order to include all the complexity in the fabrication process of DMSs into advanced materials design, spinodal decomposition in DMSs is simulated and we try to assess the effect of inhomogeneity in them. Finally, recent works on first-principles theory of transport properties of DMSs are reviewed. The discussion is mainly based on electronic structure theory within the local-density approximation to density-functional theory.

First-principles theory of dilute magnetic semiconductors

A single-band model Hamiltonian is used to describe the electronic structure of a three-dimensional disordered binary alloy. Several common theories based on the single-site approximation in a multiple-scattering description are compared with exact results for this Hamiltonian. The coherent-potential theory of Soven and others is shown to be the best of these. Within the appropriate limits, it exhibits dilute-alloy, virtual-crystal, and well separated impurity-band behavior. Hubbard and Onodera's and Toyozawa's simple model density of states is employed in numerical calculations for a wide variety of concentrations and scattering-potential strengths. Explicit results are exhibited for the total density of states, the partial density contributed by each component, and such $k$-dependent properties as the Bloch-wave spectral density and the distribution function. These illustrate the general conclusions as well as the limitations of the quasiparticle description.

Single-Site Approximations in the Electronic Theory of Simple Binary Alloys

The coherent-potential approximation (CPA) for single-particle properties of electrons in a disordered alloy ${A}_{x}{B}_{1\ensuremath{-}x}$ (Soven and others) is extended to complex admittances. The one-electron Kubo formula is used. The CPA is viewed as a single-site decoupling of the averaged multiple-scattering expansion. It properly gives the exact formulas in the limits of weak scattering (Edwards) and of dilute alloys (Langer). For any $x$ and any random-potential strength, CPA satisfies a number of physical conditions, including energy and particle-number conservation. The CPA equations are exactly soluble for a single-band model with short-ranged random scatterers. The vertex corrections are related to the response of local densities to a given disturbance. For the electrical conductivity $\ensuremath{\sigma}$, they vanish. Variation of $\ensuremath{\sigma}$ with the randompotential strength is studied numerically. A low-mobility region appears well before the band splits. In the split-band limit, CPA yields a reasonable finite $\ensuremath{\sigma}$ in the host band, but it fails in the impurity band.

Theory of Electronic Transport in Disordered Binary Alloys: Coherent-Potential Approximation

The coherent-potential approximation (CPA) is extended to study general band shapes and systems having orbital degeneracy. This permits its application to realistic systems, in particular the $\mathrm{Ni}\mathrm{Cu}$ alloys. The effects of alloying on a highly asymmetric model density of states characteristic of some of the features of the density of states in fcc transition metals are considered in detail. A model Hamiltonian for paramagnetic $\mathrm{Ni}\mathrm{Cu}$ is constructed using a basis of orthogonalized plane waves and tight-binding $d$ functions. Orbital degeneracy and hybridization are treated as in paramagnetic Ni. Effects of alloying are assumed to be restricted to the diagonal elemensts of the $d\ensuremath{-}d$ block. The model is applicable to the Ni-rich alloys, as is the approximation used to obtain simple solutions of the full CPA equations. The results are consistent with recent photoemission data on $\mathrm{Ni}\mathrm{Cu}$, and with the "minimum polarity" hypothesis used by Lang and Ehrenreich. They are incompatible with the rigid-band model because the scattering potential of the random alloy is strong compared to the peak widths. Rather than a rigid shift of the density of states, the calculated concentration dependence shows that the main peaks remain stationary while changing magnitude and shape. Decomposition of the total density of states into Ni and Cu contributions confirms that, for the expected position of the Fermi level, the $d$ holes are located primarily on Ni sites.

Paramagnetic Ni Cu Alloys: Electronic Density of States in the Coherent-Potential Approximation

The effects of alloy disorder on the electronic structure of ${\mathrm{Hg}}_{1\ensuremath{-}x}{\mathrm{Cd}}_{x}\mathrm{Te}$ are examined with the use of the coherent-potential approximation. An empirical tight-binding scheme, including spin-orbit effects, is employed. The choice of parameters is given special emphasis. A new HgTe band structure is obtained. Alloying effects are illustrated by quasiparticle spectral densities, total and projected densities of states, and self-energy corrections to the virtual-crystal energy bands. Strong cation $s$ scattering results in significant damping far from the band edges and accounts for the split-band behavior seen in photoemission experiments. The unusual bowing effects of the fundamental band gap and that associated with the ${E}_{1}$ transition are well explained. The weak scattering regime is shown to apply near the band edges. The electron mobility due to alloy scattering is large and does not appear to limit the observed magnitude.

Electronic structure of Hg 1-x Cd x Te

A computational scheme is described which simplifies many Green's-function calculations of energy-dependent quantities such as the density of states through a novel use of analytic properties Calculations are performed at complex energies well above the real axis where the quantities of interest are slowly varying Physical results are then obtained by analytically continuing Green's-function matrix elements back to real energies using an efficient numerical procedure based on Taylor-series expansions The approach is simple, versatile, and particularly well suited for evaluating the complicated Brillouin-zone integrals which often appear in Green's-function calculations In recent coherent-potential-approximation (CPA) calculations for ${\mathrm{Hg}}_{1\ensuremath{-}x}{\mathrm{Cd}}_{x}\mathrm{Te}$, the use of this technique cut the required computer time by about a factor of 3

B. Velický

Papers

Single-Site Approximations in the Electronic Theory of Simple Binary Alloys

Theory of Electronic Transport in Disordered Binary Alloys: Coherent-Potential Approximation

Paramagnetic Ni Cu Alloys: Electronic Density of States in the Coherent-Potential Approximation

Electronic structure of Hg 1-x Cd x Te

Simplification of Green's-function calculations through analytic continuation