Martin Stankovski

Band widths and gaps from the Tran-Blaha functional: Comparison with many-body perturbation theory

For a set of ten crystalline materials (oxides and semiconductors), we compute the electronic band structures using the Tran-Blaha (TB09) functional. The band widths and gaps are compared with those from the local-density approximation (LDA) functional, many-body perturbation theory (MBPT), and experiments. At the density-functional theory (DFT) level, TB09 leads to band gaps in much better agreement with experiments than LDA. However, we observe that it globally underestimates, often strongly, the valence (and conduction) band widths (more than LDA). MBPT corrections are calculated starting from both LDA and TB09 eigenenergies and wave functions. They lead to a much better agreement with experimental data for band widths. The band gaps obtained starting from TB09 are close to those from quasiparticle self-consistent GW calculations, at a much reduced cost. Finally, we explore the possibility to tune one of the semiempirical parameters of the TB09 functional in order to obtain simultaneously better band gaps and widths. We find that these requirements are conflicting.

Theoretical Approach for White-LED Phosphors: from Crystal Structures to Optical Properties

Some theoretical approaches are reviewed to analyze crystallographic and optical properties of phosphors for white light emitting diodes. Stresses are placed on 1) local electro-neutrality for the structural stability of hosts, and 2) dielectric property and coordination of anion ligands around rare-earth luminescent centre for the tuning of emission colour. First-principles calculation results are also addressed.

Vertex corrections in localized and extended systems

Within many-body perturbation theory, we apply vertex corrections to various closed-shell atoms and to jellium, using a local approximation for the vertex consistent with starting the many-body perturbation theory from a Kohn-Sham Green’s function constructed from density-functional theory in the local-density approximation. The vertex appears in two places—in the screened Coulomb interaction W and in the self-energy —and we obtain a systematic discrimination of these two effects by turning the vertex in on and off. We also make comparisons to standard GW results within the usual random-phase approximation, which omits the vertex from both. When a vertex is included for closed-shell atoms, both ground-state and excited-state properties demonstrate little improvement over standard GW. For jellium, we observe marked improvement in the quasiparticle bandwidth when the vertex is included only in W, whereas turning on the vertex in leads to an unphysical quasiparticle dispersion and work function. A simple analysis suggests why implementation of the vertex only in W is a valid way to improve quasiparticle energy calculations, while the vertex in is unphysical, and points the way to the development of improved vertices for ab initio electronic structure calculations.

GW approximations and vertex corrections on the Keldysh time-loop contour: Application for model systems at equilibrium

We study the effects of self-consistency and vertex corrections on different GW-based approximations for model systems of interacting electrons. For dealing with the most general case, we use the Keldysh time-loop contour formalism to evaluate the single-particle Greens functions. We provide the formal extension of Hedins GW equations for the Greens function in the Keldysh formalism. We show an application of our formalism to the plasmon model of a core electron within the plasmon-pole approximation. We study in detail the effects of the diagrammatic perturbation expansion of the core-electron/plasmon coupling on the spectral functions in the so-called S model. The S model provides an exact solution at equilibrium for comparison with the diagrammatic expansion of the interaction. We show that self-consistency is essential in GW-based calculations to obtain the full spectral information. The second-order exchange diagram (i.e., a vertex correction) is also crucial to obtain the good spectral description of the plasmon satellites. We corroborate these results by considering conventional equilibrium GW-based calculations for the pure jellium model. We find that with no second-order vertex correction, one cannot obtain the full set of plasmon side-band resonances. We also discuss in detail the formal expression of the Dyson equations obtained for the time-ordered Greens function at zero and finite temperature from the Keldysh formalism and from conventional equilibrium many-body perturbation theory.