This chapter provides an overview of quasiparticle calculations in solids, and, in particular, the GW approximation (GWA). A successful approximation for the determination of excited states of solids is based on the quasiparticle concept and the Green function method. The Coulomb repulsion between electrons leads to a depletion of negative charge around a given electron, and the ensemble of this electron and its surrounding positive screening charge forms a quasiparticle. The mathematical description of quasiparticles is based on the single-particle Green function (G), whose exact determination requires complete knowledge of the quasiparticle self-energy ∑. The self-energy ∑ is a non-Hermitian, energy-dependent, nonlocal operator that describes exchange and correlation effects beyond the Hartree approximation. A determination of the self-energy can only be approximate, and a working scheme for the quantitative calculation of excitation energies in metals, semiconductors, and insulators is the so-called dynamically screened interaction or the GWA. The chapter also discusses (1) the physics and extensions of the GWA; (2) numerical aspects of GWA calculations; (3) applications of the GWA to semiconductors, insulators and metals; and (4) the relevance of GWA calculations to optical response. Finally, the chapter presents parallel algorithms both for reciprocal and real-space/imaginary-time GWA calculations and several alternative methods to determine excited states of solids within density functional theory.

Quasiparticle calculations in solids

Density-functional calculations are used to investigate hydrogen diffusion in the solid-state proton conductor BaZrO3. Activation energies and prefactors for the rate of proton transfer and reorientation are evaluated for a defect-free region of this simple cubic perovskite-structured oxide. Both semiclassical over-barrier jumps and phonon-assisted tunneling transitions between sites are considered. It is found that the classical barriers for the elementary transfer and reorientation steps are both of the order of 0.2 eV. The quantum-mechanical zero-point motion effects are found to be sizable, to effectively reduce the barrier heights, and to make the prefactors similar for the transfer and reorientation steps. The Flynn-Stoneham model [Phys. Rev. B 1, 3966 (1970)] of phonon-assisted tunneling yields an activation energy of around 0.2 eV and a very small prefactor for proton transfer, whereas the corresponding adiabatic model gives a similar activation energy but a much larger prefactor. It is suggested that the effect of other defects such as dopants has to be included for a proper description of hydrogen diffusion in this material.

Density-functional calculations of prefactors and activation energies for H diffusion in BaZrO3

Review on structural and dynamical properties of silver chalcogenides

Hydration of oxygen-deficient metal oxides causes filling of oxygen vacancies and formation of hydroxyl groups with interstitial structural protons, rotating around the oxygen in localized motion. Thermal activation from 500 to 800 K triggers delocalization of the protons by jumping to adjacent oxygen ions, constituting proton conductivity. We report quantitative analyses of proton and lattice dynamics by neutron-scattering data, which reveal the interaction of protons with the crystal lattice and proton-phonon coupling. The motion for the proton trapped in the elastic crystal field yields Eigen frequencies and coupling constants, which satisfy Holstein's polaron model for electrons and thus constitutes first experimental evidence for a proton polaron at high temperature. Proton jump rates follow a polaron model for cerium-oxygen and hydroxyl stretching modes, which are thus vehicles for proton conductivity. This confirms that the polaron mechanism is not restricted to electrons, but a universal charge carrier transport process.

Experimental neutron scattering evidence for proton polaron in hydrated metal oxide proton conductors

The bonding nature of the superionic material AgI is studied by using a pseudopotential theory. The result is compared with that for GaAs, which is a well-known semiconductor. It is found that the real space valence electron distribution between these compounds differs qualitatively, and that the bonding in AgI is determined mainly by the iodine. It is also suggested that the local electronic excitations from the bonding to the antibonding orbitals can trigger the migration of the mobile species, initiating in this way the superionic transport.

Pseudopotential Study of Bonding in the Superionic Material AgI

The ground state energy and the wavefunction of proton in the cubic perovskite-type oxides ABO 3 are studied by using the double-well potential constructed from the one-dimensional O–H–O bond. We h...

Proton Diffusion in Perovskite-Type Oxides Based on Small Polaron Model

An ionic plasma model is presented to describe the low-energy excitation of cation superionic conductors. When taking account of an effective charge of cations, the model is supported by experiments except for β-Alumina type superionic conductors.

Ionic plasma model of low-energy excitation in cation superionic conductors

The ionic conductivity and the thermoelectric power in superionic conductors are expressed as functions of the concentration of ions and the interaction energy in the framework of the lattice gas model. Under appropriate conditions, the results obtained are in good agreement with those of experiments.

Tomozo Tomoyose

Papers

Proton Diffusion in Perovskite-Type Oxides Based on Small Polaron Model

Ionic plasma model of low-energy excitation in cation superionic conductors

Ionic Conductivity and Thermoelectric Power of Superionic Conductors in the Lattice Gas Model

Influence of quadrupolar deformability on phonon dispersion in silver and copper halides

Thermal conductivity in superionic conductors