The exact density functional for the ground-state energy is strictly self-interaction-free (i.e., orbitals demonstrably do not self-interact), but many approximations to it, including the local-spin-density (LSD) approximation for exchange and correlation, are not. We present two related methods for the self-interaction correction (SIC) of any density functional for the energy; correction of the self-consistent one-electron potenial follows naturally from the variational principle. Both methods are sanctioned by the Hohenberg-Kohn theorem. Although the first method introduces an orbital-dependent single-particle potential, the second involves a local potential as in the Kohn-Sham scheme. We apply the first method to LSD and show that it properly conserves the number content of the exchange-correlation hole, while substantially improving the description of its shape. We apply this method to a number of physical problems, where the uncorrected LSD approach produces systematic errors. We find systematic improvements, qualitative as well as quantitative, from this simple correction. Benefits of SIC in atomic calculations include (i) improved values for the total energy and for the separate exchange and correlation pieces of it, (ii) accurate binding energies of negative ions, which are wrongly unstable in LSD, (iii) more accurate electron densities, (iv) orbital eigenvalues that closely approximate physical removal energies, including relaxation, and (v) correct longrange behavior of the potential and density. It appears that SIC can also remedy the LSD underestimate of the band gaps in insulators (as shown by numerical calculations for the rare-gas solids and CuCl), and the LSD overestimate of the cohesive energies of transition metals. The LSD spin splitting in atomic Ni and $s\ensuremath{-}d$ interconfigurational energies of transition elements are almost unchanged by SIC. We also discuss the admissibility of fractional occupation numbers, and present a parametrization of the electron-gas correlation energy at any density, based on the recent results of Ceperley and Alder.

Self-interaction correction to density-functional approximations for many-electron systems

Topological insulators are materials with a bulk excitation gap generated by the spin-orbit interaction that are different from conventional insulators. This distinction is characterized by ${Z}_{2}$ topological invariants, which characterize the ground state. In two dimensions, there is a single ${Z}_{2}$ invariant that distinguishes the ordinary insulator from the quantum spin-Hall phase. In three dimensions, there are four ${Z}_{2}$ invariants that distinguish the ordinary insulator from ``weak'' and ``strong'' topological insulators. These phases are characterized by the presence of gapless surface (or edge) states. In the two-dimensional quantum spin-Hall phase and the three-dimensional strong topological insulator, these states are robust and are insensitive to weak disorder and interactions. In this paper, we show that the presence of inversion symmetry greatly simplifies the problem of evaluating the ${Z}_{2}$ invariants. We show that the invariants can be determined from the knowledge of the parity of the occupied Bloch wave functions at the time-reversal invariant points in the Brillouin zone. Using this approach, we predict a number of specific materials that are strong topological insulators, including the semiconducting alloy ${\mathrm{Bi}}_{1\ensuremath{-}x}{\mathrm{Sb}}_{x}$ as well as $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Sn}$ and HgTe under uniaxial strain. This paper also includes an expanded discussion of our formulation of the topological insulators in both two and three dimensions, as well as implications for experiments.

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Topological insulators with inversion symmetry

Thermoelectric generators, which directly convert heat into electricity, have long been relegated to use in space-based or other niche applications, but are now being actively considered for a variety of practical waste heat recovery systems—such as the conversion of car exhaust heat into electricity. Although these devices can be very reliable and compact, the thermoelectric materials themselves are relatively inefficient: to facilitate widespread application, it will be desirable to identify or develop materials that have an intensive thermoelectric materials figure of merit, zT, above 1.5 (ref. 1). Many different concepts have been used in the search for new materials with high thermoelectric efficiency, such as the use of nanostructuring to reduce phonon thermal conductivity, which has led to the investigation of a variety of complex material systems. In this vein, it is well known, that a high valley degeneracy (typically ≤6 for known thermoelectrics) in the electronic bands is conducive to high zT, and this in turn has stimulated attempts to engineer such degeneracy by adopting low-dimensional nanostructures. Here we demonstrate that it is possible to direct the convergence of many valleys in a bulk material by tuning the doping and composition. By this route, we achieve a convergence of at least 12 valleys in doped PbTe_(1) − _(x)Se_(x) alloys, leading to an extraordinary zT value of 1.8 at about 850 kelvin. Band engineering to converge the valence (or conduction) bands to achieve high valley degeneracy should be a general strategy in the search for and improvement of bulk thermoelectric materials, because it simultaneously leads to a high Seebeck coefficient and high electrical conductivity.

Convergence of electronic bands for high performance bulk thermoelectrics

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

This review provides numerical and graphical information about many (but by no means all) of the physical and electronic properties of GaAs that are useful to those engaged in experimental research and development on this material. The emphasis is on properties of GaAs itself, and the host of effects associated with the presence of specific impurities and defects is excluded from coverage. The geometry of the sphalerite lattice and of the first Brillouin zone of reciprocal space are used to pave the way for material concerning elastic moduli, speeds of sound, and phonon dispersion curves. A section on thermal properties includes material on the phase diagram and liquidus curve, thermal expansion coefficient as a function of temperature, specific heat and equivalent Debye temperature behavior, and thermal conduction. The discussion of optical properties focusses on dispersion of the dielectric constant from low frequencies [κ0(300)=12.85] through the reststrahlen range to the intrinsic edge, and on the ass...

Semiconducting and other major properties of gallium arsenide

We have developed an improved exchange approximation for use in self-consistent atomic structure calculations and related problems. By adding an inhomogeneity correction to the Kohn-Sham-Gaspar exchange potential, we are able to obtain total energies for atoms that are consistently closer to the Hartree-Fock values than are those given by other recently proposed exchange potentials.

Improved Statistical Exchange Approximation for Inhomogeneous Many-Electron Systems

X-ray magnetic circular dichroism measurements reveal that Cu atoms in Co/Cu multilayers exhibit an induced magnetic spin moment in the d shell. The magnitude and sign of the moments and their variation with Cu thickness are in excellent agreement with moments calculated from a local spin density functional theory. The results indicate that the Cu d electrons play a large role in mediating the exchange coupling between successive Co layers.

Induced spin polarization in Cu spacer layers in Co/Cu multilayers

The theoretical foundation of the self‐consistent statistical exchange (X α) multiple scattering method based on overlapping atomic spheres is presented. After discussing the principal assumptions and approximations, the theory is illustrated by a study of the electronic structure of the TCNQ molecule. Satisfactory results are obtained for the energy level structure and electronic charge distribution if the atomic sphere radii are chosen in accordance with the following guidelines: (a) the calculated first ionization energy should agree with experiment; and (b) the calculated virial coefficient should be equal to −2. The present work suggests that the overlapping sphere model can be used to obtain realistic electronic structures for large planar organic molecules as well as for arrays of such molecules.

Multiple scattering method based on overlapping atomic spheres with application to the TCNQ molecule

Relativistic Corrections to the Band Structure of Tetrahedrally Bonded Semiconductors

We compare the energy-band structure of the T/sub c/ = 85 K phase of Bi/sub 2/Sr/sub 2/CaCu/sub 2/O/sub 8/ with that of nonsuperconducting La/sub 2/SrCu/sub 2/O/sub 6/, which has an analogous double-perovskite structure but lacks the Bi-O intergrowths. We also compare the band structures of two alternate Bi/sub 2/Sr/sub 2/CaCu/sub 2/O/sub 8/ crystal structures to illustrate the consequences of rearranging the O atoms in the Bi-O intergrowth region. Finally, we discuss the effects of Bi-O intergrowths, modulated Bi-O layers, and changes in the number of CuO/sub 2/ layers on the band structure and on superconductivity.

Frank Herman

Papers

Improved Statistical Exchange Approximation for Inhomogeneous Many-Electron Systems

Induced spin polarization in Cu spacer layers in Co/Cu multilayers

Multiple scattering method based on overlapping atomic spheres with application to the TCNQ molecule

Relativistic Corrections to the Band Structure of Tetrahedrally Bonded Semiconductors

Electronic structure of Bi2Sr