<i>Ab‐initio</i> theory of semiconductor band structures: New developments and progress

Bechstedt, F.; Fuchs, F.; Kresse, Georg

doi:10.1002/pssb.200945074

Cited by 124 publications

(84 citation statements)

References 94 publications

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Section: ͑13͒mentioning

confidence: 99%

“…22,29,32,34,41,42,47,64,65 They roughly fall into two categories. The first comprises different exchange-correlation functionals in H 0 , e.g., exact exchange in the optimized effective potential ͑OEPx͒ approach, 32,66 hybrid functionals, 34,65 and LDA+ U. 25,29,47 All these variants do not increase the computational cost of the G 0 W 0 calculation ͑although some xc functionals might be more computationally expensive than others in the ground-state calculation͒ but their adequacy is not known a priori and has to be carefully investigated on a case by case basis.…”

Section: ͑13͒mentioning

confidence: 99%

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First-principles modeling of localizeddstates with theGW@LDA+Uapproach

et al. 2010

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First-principles modeling of systems with localized d states is currently a great challenge in condensedmatter physics. Density-functional theory in the standard local-density approximation ͑LDA͒ proves to be problematic. This can be partly overcome by including local Hubbard U corrections ͑LDA+ U͒ but itinerant states are still treated on the LDA level. Many-body perturbation theory in the GW approach offers both a quasiparticle perspective ͑appropriate for itinerant states͒ and an exact treatment of exchange ͑appropriate for localized states͒, and is therefore promising for these systems. LDA+ U has previously been viewed as an approximate GW scheme. We present here a derivation that is simpler and more general, starting from the static Coulomb-hole and screened exchange approximation to the GW self-energy. Following our previous work for f-electron systems ͓H. Jiang, R. I. Gomez-Abal, P. Rinke, and M. Scheffler, Phys. Rev. Lett. 102, 126403 ͑2009͔͒ we conduct a systematic investigation of the GW method based on LDA+ U͑GW @LDA+U͒, as implemented in our recently developed all-electron GW code FHI-gap ͑Green's function with augmented plane waves͒ for a series of prototypical d-electron systems: ͑1͒ ScN with empty d states, ͑2͒ ZnS with semicore d states, and ͑3͒ late transition-metal oxides ͑MnO, FeO, CoO, and NiO͒ with partially occupied d states. We show that for ZnS and ScN, the GW band gaps only weakly depend on U but for the other transition-metal oxides the dependence on U is as strong as in LDA+ U. These different trends can be understood in terms of changes in the hybridization and screening. Our work demonstrates that GW @LDA+U with "physical" values of U provides a balanced and accurate description of both localized and itinerant states.

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Section: ͑13͒mentioning

confidence: 99%

Section: ͑13͒mentioning

confidence: 99%

First-principles modeling of localizeddstates with theGW@LDA+Uapproach

et al. 2010

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“…35 Because of the delocalization error, currently, reliable bandgap prediction is dependent on the use of many-body Green function theory, such as the GW approximation. 2,36 In this paper, we focus on the issues of bandgap calculation and derivative discontinuity within DFT for a given functional. The conventional functional derivative perspective of Perdew and Levy, 37,38 and Sham and Schlüter [39][40][41] shows that the functional derivative discontinuity of the exchangecorrelation density functional plays a critical role in the correct prediction of bandgaps, or the chemical hardness.…”

Section: Introductionmentioning

confidence: 99%

Derivative discontinuity, bandgap and lowest unoccupied molecular orbital in density functional theory

Yang

Cohen

Mori‐Sánchez

2012

The Journal of Chemical Physics

177

178

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The conventional analysis of Perdew and Levy, and Sham and Schlüter shows that the functional derivative discontinuity of the exchange-correlation density functional plays a critical role in the correct prediction of bandgaps, or the chemical hardness. In a recent work by the present authors, explicit expressions for bandgap prediction with all common types of exchange-correlation functionals have been derived without invoking the concept of exchange-correlation energy functional derivative discontinuity at all. We here analyze the two approaches and establish their connection and difference. The present analysis further leads to several important results: (1) The lowest unoccupied molecular orbital (LUMO) in DFT has as much meaning in describing electron addition as the highest occupied molecular orbital (HOMO) in describing electron removal. (2) Every term in the total energy functional contributes to the energy gap because of the discontinuity of the derivative of the density (or density matrix) with respect to the number of electrons, ((∂ρ s (r , r))/∂N ) v s , at integers. (3) Consistent with the Perdew-Levy-Sham-Schlüter conclusion that the exact Kohn-Sham energy gap differs from the fundamental bandgap by a finite correction due to the functional derivative discontinuity of the exchange-correlation energy, we show that the exchange-correlation functional cannot be an explicit and differentiable functional of the electron density, either local or nonlocal. The last result is further strengthened when we consider Mott insulators. There, the exact exchange-correlation functional needs to have an explicitly discontinuous (nondifferentiable) dependence on the density or the density matrix. (4) We obtain exact conditions on the derivatives of total energy with respect to the spin-up and spin-down number of electrons.

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“…44,45 The theoretical underestimations of band gaps and other energy eigenvalues have been ascribed to the inadequacies of density functional potentials for the description of ground state electronic properties of semiconductors. 18,19,24 Also, other methods [46][47][48] that entirely go beyond the density functional theory (DFT) do not obtain the correct band gap values of most semiconductors without adjustment or fitting parameters. 49,50 This unsatisfactory situation is a key motivation for our work.…”

Section: Introductionmentioning

confidence: 99%

First principle electronic, structural, elastic, and optical properties of strontium titanate

et al. 2012

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We report self-consistent ab-initio electronic, structural, elastic, and optical properties of cubic SrTiO3 perovskite. Our non-relativistic calculations employed a generalized gradient approximation (GGA) potential and the linear combination of atomic orbitals (LCAO) formalism. The distinctive feature of our computations stem from solving self-consistently the system of equations describing the GGA, using the Bagayoko-Zhao-Williams (BZW) method. Our results are in agreement with experimental ones where the later are available. In particular, our theoretical, indirect band gap of 3.24 eV, at the experimental lattice constant of 3.91 Å, is in excellent agreement with experiment. Our predicted, equilibrium lattice constant is 3.92 Å, with a corresponding indirect band gap of 3.21 eV and bulk modulus of 183 GPa

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Ab‐initio theory of semiconductor band structures: New developments and progress

Cited by 124 publications

References 94 publications

First-principles modeling of localizeddstates with theGW@LDA+Uapproach

First-principles modeling of localizeddstates with theGW@LDA+Uapproach

Derivative discontinuity, bandgap and lowest unoccupied molecular orbital in density functional theory

First principle electronic, structural, elastic, and optical properties of strontium titanate

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