John W. Wilkins

Quasiparticle calculations in solids

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.

X-ray absorption spectra: K-edges of 3d transition metals, L-edges of 3d and 4d metals, and M-edges of palladium

Abstract The X-ray absorption spectra of the 3d and 4d transition metals have been calculated within the single-particle approximation by a new linearized augmented plane wave method. The spectra, calculated with sharp atomic and band-structure single-particle levels, have been convoluted with a Lorentzian broadening function whose width is the sum of that of the core hole and the excited electrons. Plots are shown for (i) the K-edge fine structures up to at least 100 eV above the edge for Ca, Ti, Cr, Co, Cu, and Zn, (ii) the L2, 3 white lines for Ca, Ti, Cr, Co, and Cu, (iii) the L3 white lines for Sr, Zr, Nb, Ru, Rh, and Pd, and (iv) the M2, 3 and M4,5 spectrum of Pd. Systematic features which depend on the crystal structure and the placement of the Fermi level with conduction band are briefly discussed.

Impurities block the α to ω martensitic transformation in titanium

Impurities control phase stability and phase transformations in natural and man-made materials, from shape-memory alloys1 to steel2 to planetary cores3. Experiments and empirical databases are still central to tuning the impurity effects. What is missing is a broad theoretical underpinning. Consider, for example, the titanium martensitic transformations: diffusionless structural transformations proceeding near the speed of sound2. Pure titanium transforms from ductile α to brittle ω at 9 GPa, creating serious technological problems for β-stabilized titanium alloys. Impurities in the titanium alloys A-70 and Ti–6Al–4V (wt%) suppress the transformation up to at least 35 GPa, increasing their technological utility as lightweight materials in aerospace applications. These and other empirical discoveries in technological materials call for broad theoretical understanding. Impurities pose two theoretical challenges: the effect on the relative phase stability, and the energy barrier of the transformation. Ab initio methods4,5 calculate both changes due to impurities. We show that interstitial oxygen, nitrogen and carbon retard the transformation whereas substitutional aluminium and vanadium influence the transformation by changing the d-electron concentration6. The resulting microscopic picture explains the suppression of the transformation in commercial A-70 and Ti–6Al–4V alloys. In general, the effect of impurities on relative energies and energy barriers is central to understanding structural phase transformations.

New mechanism for the alpha to omega martensitic transformation in pure titanium.

We propose a new direct mechanism for the pressure driven alpha-->omega martensitic transformation in pure titanium. A systematic algorithm enumerates all possible pathways whose energy barriers are evaluated. A new, homogeneous pathway emerges with a barrier at least 4 times lower than other pathways. The pathway is shown to be favorable in any nucleation model.

Zero-frequency current noise for the double-tunnel-junction Coulomb blockade.

We compute the zero-frequency current noise numerically and in several limits analytically for the Coulomb-blockade problem consisting of two tunnel junctions connected in series. At low temperatures over a wide range of voltages, capacitances, and resistances it is shown that the noise measures the variance in the number of electrons in the region between the two tunnel junctions. The average current, on the other hand, is linearly related to the mean number of electrons for an asymmetric pair of junctions. Thus, the noise provides additional information about transport in these devices which is not available from measuring the current alone.

Classical potential describes martensitic phase transformations between the α, β, and ω titanium phases

A description of the martensitic transformations between the , , and phases of titanium that includes nucleation and growth requires an accurate classical potential. Optimization of the parameters of a modified embedded atom potential to a database of density-functional calculations yields an accurate and transferable potential as verified by comparison to experimental and density-functional data for phonons, surface and stacking fault energies, and energy barriers for homogeneous martensitic transformations. Molecular-dynamics simulations map out the pressure-temperature phase diagram of titanium. For this potential the martensitic phase transformation between and appears at ambient pressure and 1200 K, between and at ambient conditions, between and at 1200 K and pressures above 8 GPa, and the triple point occurs at 8 GPa and 1200 K. Molecular-dynamics explorations of the kinetics of the martensitic - transformation show a fast moving interface with a low interfacial energy of 30 meV/A 2 . The potential is applicable to the study of

Low temperature electronic specific heat of simple metals

Abstract : It is reported that in simple metals the contribution to the low temperature electronic specific heat from the electron-phonon interaction dominates those from band structure and electron-electron interactions. Only the metals Na, Al and Pb have been considered since for them the band structures and Fermi surfaces are relatively well known and the phonon dispersion curves have been measured. With this data the calculations are performed with no adjustable parameters.

Extended Si |P[311|P] defects

We perform total energy calculations based on the tight-binding Hamiltonian scheme (i) to study the structural properties and energetics of the extended {311} defects depending upon their dimensions and interstitial concentrations and (ii) to find possible mechanisms of interstitial capture by and release from the {311} defects. The generalized orbital-based linear-scaling method implemented on Cray-T3D is used for supercell calculations of large scale systems containing more than 1000 Si atoms.

Electron-hole correlations in semiconductor quantum dots with tight-binding wave functions

The electron-hole states of semiconductor quantum dots are investigated within the framework of empirical tight-binding descriptions for Si, as an example of an indirect-gap material, and InAs and CdSe as examples of typical III-V and II-VI direct-gap materials. We significantly improve the energies of the single-particle states by optimizing tight-binding parameters to give the best effective masses. As a result, the calculated excitonic gaps agree within 5% error with recent photoluminescence data for Si and CdSe but they agree less well for InAs. The electron-hole Coulomb interaction is insensitive to different ways of optimizing the tight-binding parameters. However, it is sensitive to the choice of atomic orbitals; this sensitivity decreases with increasing dot size. Quantitatively, tight-binding treatments of Coulomb interactions are reliable for dots with radii larger than 15‐20 A . Further, the effective range of the electron-hole exchange interaction is investigated in detail. In quantum dots of the direct-gap materials InAs and CdSe, the exchange interaction can be long ranged, extending over the whole dot when there is no local ~onsite! orthogonality between the electron and hole wave functions. By contrast, for Si quantum dots the extra phase factor due to the indirect gap effectively limits the range to about 15 A, independent of the dot size.

Dynamic magnetic susceptibilities of valence‐fluctuation Ce compounds

We have computed dynamic susceptibilities of valence‐fluctuating Ce compunds for temperatures between 0.01 and 40 T0, where T0 is the position of the many‐body ‘‘Kondo resonance’’ in the 4f density of states. Our calculations reproduce several results seen in neutron scattering and nuclear‐magnetic‐resonance experiments: (i) nonmonotonic behavior of the magnetic relaxation rate, (ii) non‐Lorentzian behavior of the dynamic susceptibility for low temperatures, and (iii) high‐temperature T1/2 behavior of the magnetic relaxation rate. Most of the magnetic relaxation data for valence‐fluctuating Ce compunds are consistent with the Kondo resonance picture which has been applied successfully previously to thermodynamic and high‐energy spectroscopy data.