Trends in self-energy operators and their corresponding exchange-correlation potentials

Godby, R. W.; Schlüter, M.; Sham, L. J.

doi:10.1103/physrevb.36.6497

Cited by 486 publications

(247 citation statements)

References 16 publications

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“…These fully ab initio GW calculations generally yield very good agreement, most often better than 10-15 %, between the experimental and the calculated band structure, apart from the case of strongly correlated systems. Again for the example of diamond, Hybertsen and Louie (1985) and Godby et al (1987) have performed ab initio GW calculations and obtained a quasiparticle gap at ⌫ of E g ϭ7.38 eV and E g ϭ7.26 eV, respectively, which compare well with the experimental value of 7.3 eV (Roberts and Walker, 1967).…”

Section: Effective Hamiltonians and Effective Interactionssupporting

confidence: 50%

“…Further, an energy-dependent correlation decreases the Hartree-Fock band gap by raising the valence-band energy and lowering the conduction-band energy. There is some empirical evidence that supports the idea that even in the first iteration (that is, using just the noninteracting Green's function G 0 ) one obtains quite accurate results for oneelectron properties such as the excitation energy Louie, 1985, 1986;Godby et al, 1986Godby et al, , 1987Godby et al, , 1988Aryasetiawan and Gunnarsson, 1998) and the quasiparticle lifetime (Campillo et al, 1999;Schö ne et al, 1999;Echenique et al, 2000;Campillo, Silkin, et al, 2000;Keyling et al, 2000;Silkin et al, 2001;Spataru et al, 2001). This is important for practical applications of the GW approach since, despite its formal simplicity, the practical solution of the self-consistent GW equations is a formidable task, which has been carried out only recently: self-consistent calculations were performed for the homogeneous electron gas (Holm and von Barth, 1998;Holm and Aryasetiawan, 2000;García-Gonzá lez and Godby, 2001), simple semiconductors, and metals (Shirley, 1996; Schö ne and Eguiluz, 1998).…”

Section: First Iteration Step: the Gw Approximationmentioning

confidence: 85%

“…IV.A.2. In any case, DFT is a good starting point for further calculations, and starting from the work of Louie (1985, 1986), and Godby et al (1986Godby et al ( , 1987Godby et al ( , 1988, today ab initio GW calculations are mostly performed using Kohn-Sham results as ingredients (to be precise, the Kohn-Sham eigenvalues and eigenfunctions are used to construct the self-energy of the GW form). These fully ab initio GW calculations generally yield very good agreement, most often better than 10-15 %, between the experimental and the calculated band structure, apart from the case of strongly correlated systems.…”

Section: Effective Hamiltonians and Effective Interactionsmentioning

confidence: 99%

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Electronic excitations: density-functional versus many-body Green’s-function approaches

2002

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Electronic excitations lie at the origin of most of the commonly measured spectra. However, the first-principles computation of excited states requires a larger effort than ground-state calculations, which can be very efficiently carried out within density-functional theory. On the other hand, two theoretical and computational tools have come to prominence for the description of electronic excitations. One of them, many-body perturbation theory, is based on a set of Green's-function equations, starting with a one-electron propagator and considering the electron-hole Green's function for the response. Key ingredients are the electron's self-energy ⌺ and the electron-hole interaction. A good approximation for ⌺ is obtained with Hedin's GW approach, using density-functional theory as a zero-order solution. First-principles GW calculations for real systems have been successfully carried out since the 1980s. Similarly, the electron-hole interaction is well described by the Bethe-Salpeter equation, via a functional derivative of ⌺. An alternative approach to calculating electronic excitations is the time-dependent density-functional theory (TDDFT), which offers the important practical advantage of a dependence on density rather than on multivariable Green's functions. This approach leads to a screening equation similar to the Bethe-Salpeter one, but with a two-point, rather than a four-point, interaction kernel. At present, the simple adiabatic local-density approximation has given promising results for finite systems, but has significant deficiencies in the description of absorption spectra in solids, leading to wrong excitation energies, the absence of bound excitonic states, and appreciable distortions of the spectral line shapes. The search for improved TDDFT potentials and kernels is hence a subject of increasing interest. It can be addressed within the framework of many-body perturbation theory: in fact, both the Green's functions and the TDDFT approaches profit from mutual insight. This review compares the theoretical and practical aspects of the two approaches and their specific numerical implementations, and presents an overview of accomplishments and work in progress. CONTENTS

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Section: Effective Hamiltonians and Effective Interactionssupporting

confidence: 50%

Section: First Iteration Step: the Gw Approximationmentioning

confidence: 85%

Section: Effective Hamiltonians and Effective Interactionsmentioning

confidence: 99%

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Electronic excitations: density-functional versus many-body Green’s-function approaches

2002

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“…Furthermore we calculated the electronic structure using three different exchange-correlation functionals, namely the GGA approximation with the parameterization of Perdew et al 18 , the GGA+U functional 37 , and the orbital dependent exchange functional B3LYP 19 . While GGA renders possible the treatment of a larger number of atoms, it is known to underestimate the band gap 38 . With B3LYP, only smaller systems can be treated, but the calculated band gap is in fair agreement with experimental values 39 .…”

Section: High Resolution Transmission Electron Microscopy (Hrtem) Andmentioning

confidence: 99%

A chemically driven insulator–metal transition in non-stoichiometric and amorphous gallium oxide

et al. 2008

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Insulator-metal transitions are well known in transition metal oxides, but inducing an insulator-metal transition in the oxide of a main group element is a major challenge. Here we report the observation of an insulator-metal transition, with a conductivity jump of seven orders of magnitude, in highly non-stoichiometric, amorphous gallium oxide of approximate composition GaO 1.2 at a temperature around 670 K. We demonstrate through experimental studies and density-functional-theory calculations that the conductivity jump takes place at a critical gallium concentration and is induced by crystallization of stoichiometric Ga 2 O 3 within the metastable oxide matrix -in chemical terms by a disproportionation. This novel mechanism -an insulator-metal transition driven by a heterogeneous solid state reactionopens up a new route to achieve metallic behaviour in oxides that are expected to exist only as classic insulators.Insulator-metal transitions belong to the most fascinating phenomena in condensed-matter physics 1,2 . Since Mott's landmark work 3,4 it has been known that in crystalline solids strong electron-electron interactions can cause an insulator-metal transition. One example is crystalline Cr-doped vanadium oxide, (V 1-x Cr x ) 2 O 3 , which shows a Mott transition from a paramagnetic Mott insulator to a strongly correlated metal upon an increase in pressure, a lowering of temperature, or a decrease in dopant level 5,6 . In non-crystalline solids structural disorder can also lead to an insulator-metal transition on account of Anderson localization 7 .As shown by Anderson 7 and Mott 8 , in any non-crystalline material the lowest states in the conduction band are localized, i.e. they are electron traps. Only for energies above the mobility edge, E c , do states become non-localized or extended. If the Fermi energy E F is below the mobility edge, states at the Fermi level are localized and the material is an electronic insulator. If, however, the number of electrons increases and the Fermi energy rises above the mobility edge, the material becomes metallic (Anderson transition). As transition metals change their valence state easily, most examples of insulator-metal transitions concern transition metal compounds 4-6,9-11 . The above considerations do not, however, exclude the possibility of inducing an insulator-metal transition in a simple binary oxide of a main group element, even without doping. Instead, large deviations from the ideal stoichiometry, i.e. high defect concentrations, provide a high concentration of electronic defects (self-doping). And if, in addition, the oxide is amorphous, there are two phenomena, strong structural disorder and strong chemical disorder, which could result in an insulator-metal transition.Here we report such a case: Highly non-stoichiometric, amorphous gallium oxide with an approximate chemical composition GaO 1.2 shows an unprecedented insulator-metal transition, with a jump in conductivity of ca. 7 orders of magnitude at temperatures as high as 670 K. We show that this in...

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“…19 Aryasetiawan and Stott 20,21 also found the exact XC potential of DFT for some smaller atoms using a presumably more accurate approach which had the additional advantage of offering insight into the so called v-representability problem of DFT. In solids, early progress toward an exact DF XC potential was made by Godby et al 22,23 who actually constructed their XC potential as a solution to the Linearized Sham-Schlüter equation (LSS). 23 The self-energy of their choice was again that of the GW approximation (GWA).…”

Section: Introductionmentioning

confidence: 99%

Correlation potential in density functional theory at the GWA level: Spherical atoms

2007

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As part of a project to obtain better optical response functions for nano materials and other systems with strong excitonic effects we here calculate the exchange-correlation (XC) potential of density-functional theory (DFT) at a level of approximation which corresponds to the dynamicallyscreened-exchange or GW approximation. In this process we have designed a new numerical method based on cubic splines which appears to be superior to other techniques previously applied to the "inverse engineering problem" of DFT, i.e., the problem of finding an XC potential from a known particle density. The potentials we obtain do not suffer from unphysical ripple and have, to within a reasonable accuracy, the correct asymptotic tails outside localized systems. The XC potential is an important ingredient in finding the particle-conserving excitation energies in atoms and molecules and our potentials perform better in this regard as compared to the LDA potential, potentials from GGA:s, and a DFT potential based on MP2 theory.

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Trends in self-energy operators and their corresponding exchange-correlation potentials

Cited by 486 publications

References 16 publications

Electronic excitations: density-functional versus many-body Green’s-function approaches

Electronic excitations: density-functional versus many-body Green’s-function approaches

A chemically driven insulator–metal transition in non-stoichiometric and amorphous gallium oxide

Correlation potential in density functional theory at the GWA level: Spherical atoms

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