Efficient quasiparticle band-structure calculations for cubic and noncubic crystals (original) (raw)
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Physical Review B, 1993
We report state-of-the-art first-principles calculations of the quasiparticle energies of prototype homopolar and heteropolar covalent semiconductors described in terms of the electron self-energy operator. The wave functions are calculated within density-functional theory using the local-density approximation and employing nonlocal, norm-conserving pseudopotentials. The self-energy operator is evaluated in the GW approximation. Employing the plasmon-pole approximation for the frequency dependence of the dielectric matrix e& 6 (q, co), its static part is fully calculated within the random-phase approximation (RPA) as well as by using a number of different models. All calculations are carried out employing localized Gaussian orbital basis sets. This will turn out to be very useful for detailed studies of the quasiparticle properties of more complex systems such as bulk defects including lattice relaxation and reconstructed surfaces with large unit cells or interfaces, which are otherwise computationally too demanding. Using an s,p, d, s basis set of 40 Gaussian orbitals for Si, for example, yields already convergent results in excellent agreement with the results of a 350-plane-wave calculation in the corresponding plane-wave representation. Most of our results for Si, diamond, Ge, and GaAs are in very good agreement with experimental data and with available plane-wave G8'calculations. To our knowledge, our results for SiC are the first quasiparticle energies reported so far for this important material of high current technological interest. Also in this case we find very good agreement with the available experimental data except for E(L ").We believe that this deviation may be attributed to experimental uncertainties. In particular, we discuss and scrutinize the applicability of six different models for the static dielectric matrix eG G(q, 0) in the 68' approximation ranging from the simple Hartree-Fock expression over diagonal models to nondiagonal models that take the local fields within the inhomogeneous electronic charge density into account. Some of the nondiagonal models are shown to yield results in very good agreement with the full RPA results.
Ground-state electronic properties of diamond in the local-density formalism
We use our previously reported method for solving self-consistently the local-density one-particle equations in a numerical-basis-set linear combination of atomic orbitals expansion to study the ground-state charge density, x-ray structure factors, directional Compton profile, total energy, cohesive energy, equilibrium lattice constant, and behavior of one-electron properties under pressure of diamond. Good agreement is obtained with available experiment data. The results are compared with those obtained by the restricted Hartree-Fock model: the role of electron exchange and correlation on the binding mechanism, the charge density, and the momentum density is discussed. I. INTRODU(. 'TION The local density functional (LDF) formalism of Hohenberg, Kohn, and Sham, " and its recent extension as a local spin-density functional formalism , ' form the basis of a new approach to the study of electronic structure in that the effects of exchange and correlation are incorporated directly into a charge-density-dependent potential term that is determined self-consistently from the solution of an effective one-particle equation. Applications of the LDF formalism to atoms+' and molecules' have yielded encouraging results. Similar applications for solids are complicated by (i) the need to con sider both the short-range and the long-range multicenter crystal potential having nonspherical components, (ii) the difficulties in obtaining full self-consistency in a periodic system, and (iii) the need to provide a basis set with sufficient variational flexibility. Hence, theoretical. studies of ground-state electronic properties of solids in the LDF formalism have been mainly l.imited to muffin-tin models for the potential, " non-self-consistent schemes, ' treatments of simplified jellium models'0 or spherical cellular schemes We have recently proposed"" a general self-consistent method for solving the LDF formalism one-particle equation for realistic solids using a numerical-basis-set LCAO (linear combination of atomic orbitals) expansi. on and retaining all non-spherical parts of the crystal potential. We have demonstrated a rapid convergence of the self-consistent (SC) cycle when the treatment of the full crystal charge density is suitably apportioned between real-space and Fourier-transformed reciprocal-space parts and have indicated the large degree of variational flexibility offered by a nonlinearly optimized (exact) numerical atomic-like basis set. We have shown that all multi-center interactions as well as the nonconstant parts of the crystal potential are efficiently treated by a three-dimensional Diophantine integration scheme. The purpose of this paper is to illustrate the applicability of our method to real systems by studying the ground-state electronic properties of diamond. Diamond has been long considered as a prototype for covalently bonded insulators" and a great deal of experimental work has been done on its ground-state properties, including co-hensive energy, " lattice-constant studies, " x-ray scattering factors, "" charge density, " and directional Compton profile. O' In addition, theoretical studies on its ground-state properties within the restricted Hartree-Fock (RHF) model are available" " so comparison with the predictions of the LDF formalism is possible. Although the eigenvalue spectrum (band structure) of the local exchange Hamiltonian for diamond has been studied previously by a variety of first-principles techniques [augmented planes waves (APW), '" " orthogonalized plane waves (OPW), "" pseudo-potential OPW, " LCAO, " " and cellular methods "], the ground-state observables related to the ground-state crystal charge density have received much less attention. While our method was shown" to accurately reproduce the band structure of diamond as obtained by other tech-niques"'" (when correlation and self-consistency is omitted so as to be compatible with the previously published band-structure models and the full nonspherical components of the potential are retained in both calculations), we do not consider this as a stringent test since the LDF formalism in its "standard" form does not make any claim on the physical significance of the band eigen-values nor are these eigenvalues sensitive enough to the details of the basis set and potential. " In what follows we present our results for the x-ray scattering factors, charge density, directional Compton profile, total energy, and equilibrium lattice constant and discuss the role of exchange 5049
Quasiparticle band structure based on a generalized Kohn-Sham scheme
Physical Review B, 2007
We present a comparative full-potential study of generalized Kohn-Sham schemes (gKS) with explicit focus on their suitability as starting point for the solution of the quasiparticle equation. We compare G 0 W 0 quasiparticle band structures calculated upon LDA, sX, HSE03, PBE0, and HF functionals for exchange and correlation (XC) for Si, InN and ZnO. Furthermore, the HSE03 functional is studied and compared to the GGA for 15 non-metallic materials for its use as a starting point in the calculation of quasiparticle excitation energies. For this case, also the effects of selfconsistency in the GW self-energy are analysed. It is shown that the use of a gKS scheme as a starting point for a perturbative QP correction can improve upon the deficiencies found for LDA or GGA staring points for compounds with shallow d bands. For these solids, the order of the valence and conduction bands is often inverted using local or semi-local approximations for XC, which makes perturbative G 0 W 0 calculations unreliable. The use of a gKS starting point allows for the calculation of fairly accurate band gaps even in these difficult cases, and generally single-shot G 0 W 0 calculations following calculations using the HSE03 functional are very close to experiment.
Quasiparticle band structures of CuCl, CuBr, AgCl, and AgBr: The extreme case
Physical Review B, 2018
We present a systematic study of the quasiparticle band structures of transition metal halides CuCl, CuBr, AgCl, and AgBr. We show that GW calculations for cuprous halides are significantly more challenging computationally than ZnO, a much discussed extreme case. The local density approximation (LDA) within density functional theory severely underestimates the band gaps of CuCl and CuBr due to the inaccurate treatment of the semicore d electrons. As a result, many-body perturbation calculations within the G 0 W 0 approach fails to give accurate quasiparticle properties starting from the LDA mean-field solution. The LDA+U method (with the screened Coulomb and exchange parameters calculated using a constrained random phase approximation approach), on the other hand, provides a much better starting point for subsequent G 0 W 0 calculations. When properly converged, the G 0 W 0 /LDA+U approach is able to reproduce the experimental minimum band gaps of all four compounds to within 0.1 eV. These results, however, can only be achieved by applying extremely high cutoff parameters, which would be very difficult without using our recently developed accelerated GW approach. Our work demonstrates the applicability and accuracy of the G 0 W 0 /LDA+U method in predicting the quasiparticle band structure of these materials and other systems involving localized semicore states.
The electronic band structures for zincblende and wurtzite BeO
Journal of Physics C: Solid State Physics, 1983
The electronic band structures for zinc-blende and wurtzite CdS are calculated within the localdensity approximation with the use of first-principles pseudopotentials. Incorporating the d state into the valence band improves substantially the main-valence-band width, and yields valence-band features in good agreement with experiment. The maximum effect of the d band occurs at I » for zinc-blende CdS and at I «, I 6 for wurtzite CdS. We find that the local-density approximation does not predict accurately the position of localized Cd 4d state.
Bulk Electronic Structure of Quasicrystals
Physical Review Letters, 2012
We use hard x-ray photoemission to resolve a controversial issue regarding the mechanism for the formation of quasicrystalline solids, i.e., the existence of a pseudogap at the Fermi level. Our data from icosahedral fivefold Al-Pd-Mn and Al-Cu-Fe quasicrystals demonstrate the presence of a pseudogap, which is not observed in surface sensitive low energy photoemission because the spectrum is affected by a metallic phase near the surface. In contrast to Al-Pd-Mn, we find that in Al-Cu-Fe the pseudogap is fully formed; i.e., the density of states reaches zero at E F indicating that it is close to the metal-insulator phase boundary.
Quasiparticle band structure of silicon carbide polytypes
Physical Review B, 1995
The ab initio pseudopotential method within the local-density approximation and the quasiparticle approach have been used to investigate the electronic excitation properties of hexagonal (6H, 4H, 2H) and zinc-blende (3C) silicon carbide. The quasiparticle shifts added to the density-functional eigenvalues are calculated using a model dielectric function and an approximate treatment of the electron self-energy concerning local-field effects and dynamical screening. The inverse dielectric function and the auxiliary function are generalized to hexagonal crystals. Good agreement with the experimental results is obtained for the minimum indirect energy gaps. The k space location of the corresponding conduction-band minima is clarified. Other excitation energies are predicted. The in6uence of the quasiparticle effects on band discontinuities and the electron effective masses is studied.
Physical Review B, 1982
We introduce an ab initio self-consistent approachthe quasiband crystal-field (QBCF) methodto calculate the electronic structure of localized defect states in solids within a density-functional Green s-function approach. The method is simple, yet it produces very accurate self-consistent solutions both for s-p as well as for the hyperlocalized transitionatom d-electron impurities. This is made possible by four ideas: (1) Following the pioneering work (1929) of Bethe and Van Vleck and results of modern computations, it is recognized that whereas the defect and host wave functions may be extended and highly anisotropic in coordinate space, for deep defects the density and potential perturbations b p(r) and b, V(r) are considerably more localized and have a reduced directional anisotropy. We therefore describe the latter in a crystal-field one-center expansion +&I'~(~r~)KI(r), anchored at the defect site, with a separation of radial F~(~r~) and angular KI(r) variables. The defect problem, treated by contemporary Green's-function techniques as a multicenter scattering problem, is then transformed into a far simpler atomiclike problem, characterized by analytic angular integrals (Gaunt coefficients) and simple one-dimensional radial integrals. This permits a simple and highly precise treatment of self-consistency, incorporation of accurate (first-principles) nonlocal pseudopotentials, and the use of variationally flexible and computationally simple single-site basis functions introduced in chemistry in 1933 by Mulliken. (2) The standard Koster-Slater Green'sfunction approach to defects uses an expansion of the impurity wave functions in terms of (often chemically and physically unrelated) host-crystal Bloch eigenfunctions. It is shown that when the perturbation approaches a characteristic atomic length scale (or when the impurity is chemically sufficiently different from the host atom), such expansions converge exceedingly slowly. We have reformulated the Koster-Slater resolvent problem in terms of quasiband wave functions that incorporate from the outset not only aspects of the host, but also the characteristics of the defect. A large number of conduction-band wave functions, which would have been needed for an adequate representation of localized defect states, are renormalized into a much smaller number of quasiband wave functions. Expansion in terms of quasibands results in a rapidly convergent and efficient description even of very localized defect wave functions. (3) A new Newton-Raphson Jacobian update technique is used to establish self-consistency in the screening potential. It does not require any new information; it "remembers" information from all past iterations, but automatically discounts information from the distant past and is hence not confused by nonlinearities. The method is far more efficient than all standard selfconsistency methods and permits a precise assessment of charge-redistribution effects in the system. (4) The lengthy summations over the Brillouin zone encountered in spectral Green s-function methods are transformed into a simpler rapidly convergent series in a supercell representation. This allows one to treat impurities in large supercells (e.g. , 2662 atoms per cell) by treating only small matrices (36)& 36) whose sizes do not depend on the dimensions of the supercell. In this representation the poles of the Green's function are real and can be efficiently located using a new and fast algorithm introduced here. This paper describes these four ideas in physical terms. Full mathematical details are given in
Self-consistent band-gap corrections in density functional theory using modified pseudopotentials
Physical Review B, 2007
Density functional calculations based on the local density approximation or generalized gradient approximation have proven their value for predicting ground-state properties of materials. However, the corresponding band structures cannot be directly compared with experiment. We describe an approach based on a modification of pseudopotentials, in the spirit of a technique proposed by Christensen ͓Phys. Rev. B 30, 5753 ͑1984͔͒. These pseudopotentials still accurately describe structural properties and energetics, but they also produce band structures in better agreement with experiment. We establish reliability by performing extensive tests and comparisons with other methods, and illustrate the approach with applications to electronic stucture of bulk, point defects, and surfaces of nitride semiconductors.