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

Plasmonics is a research area merging the fields of optics and nanoelectronics by confining light with relatively large free-space wavelength to the nanometer scale - thereby enabling a family of novel devices. Current plasmonic devices at telecommunication and optical frequencies face significant challenges due to losses encountered in the constituent plasmonic materials. These large losses seriously limit the practicality of these metals for many novel applications. This paper provides an overview of alternative plasmonic materials along with motivation for each material choice and important aspects of fabrication. A comparative study of various materials including metals, metal alloys and heavily doped semiconductors is presented. The performance of each material is evaluated based on quality factors defined for each class of plasmonic devices. Most importantly, this paper outlines an approach for realizing optimal plasmonic material properties for specific frequencies and applications, thereby providing a reference for those searching for better plasmonic materials.

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Searching for better plasmonic materials

Searching for Better Plasmonic Materials

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

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

A simple interpolation scheme for paramagnetic fcc transition and noble metals has been developed and extended to the ferromagnetic state of Ni. It is based on the representation of $d$ and conduction bands by linear combinations of atomic orbitals and orthogonalized plane waves, respectively, and includes hybridization effects through the use of k-dependent matrix elements. The energy bands of augmented-plane-wave calculations from first principles for Cu and paramagnetic Ni are fitted with an rms deviation of about 0.12 eV. The density of states of paramagnetic Ni is calculated and shown to be significantly influenced by hybridization. A self-consistent calculation of the ferromagnetic band structure of Ni is carried out by the incorporation of correlation effects through the use of an intra-atomic Coulomb interaction patterned along the lines suggested by Gutzwiller, Hubbard, and Kanamori. Experimental information relating to the magnetization, ferromagnetic Kerr effect, Fermi surfaces, neutron magnetic form factor, electronic specific heat, and high-field susceptibility is used to determine the parameters characteristic of the ferromagnetic state and to check the predictions of the resulting band structure. The k-dependent splitting of the bands averages 0.37 eV in the vicinity of the Fermi level. The wave functions resulting from these calculations are shown to be sufficiently realistic to permit the calculation of the total charge density in Cu and the magnetic form factor of Ni. The use of approximate spin-polarized wave functions appropriate to the solid demonstrates the importance of both unpaired and paired electrons to the magnetic form factor. The net conduction-electron polarization is found to be small and positive. The effective $s\ensuremath{-}d$ exchange energy changes sign between the central and outer parts of the Brillouin zone. The inclusion of spin-orbit effects is discussed, and the reduction of the density of states at the Fermi level due to this interaction is calculated. The effect is too small to explain the presence of ferromagnetism in Ni and its absence in Pd and Pt.

Interpolation Scheme for Band Structure of Noble and Transition Metals: Ferromagnetism and Neutron Diffraction in Ni

Earlier work dealing with the optical properties of Cu and Ag is extended along two directions. The optical properties of Au are discussed and interpreted in terms of intra- and interband processes as well as plasma effects as elementary excitations of the system. In addition, the previous tentative interpretation of the low-energy optical structure in terms of interband transitions near $L$ and $X$ in the Brillouin zone is examined carefully by means of absolute calculations of the imaginary part of the frequency-dependent dielectric constant, using as input data the results of band calculations as well as Fermi surface experiments. The agreement of the results for all three noble metals with experiment strongly supports the previous interpretation. It is shown that in metals, sharp optical structure may arise from transitions between relatively flat, filled bands, such as the upper $d$ band, and empty states just above the Fermi surface. This structure complements that arising from transitions at critical points and accounts for the region in the noble metals where direct interband transitions first set in. Finally, the present calculations are used as a basis for comment on recent data of Spicer and Berglund and the relative importance of direct and indirect transitions in photoemission processes.

H. Ehrenreich

Papers

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

Interpolation Scheme for Band Structure of Noble and Transition Metals: Ferromagnetism and Neutron Diffraction in Ni

Optical Properties of Noble Metals. II.