Electron Self-energy Operator Research Articles

Electronic Excitations of Polythiophene within Many-Body Perturbation Theory with and without the Tamm-Dancoff Approximation.

Excited electronic states of small and large π-conjugated organic molecules can be described within ab initio many-body perturbation theory, notably by the GW approximation for the electron self-energy operator combined with the Bethe-Salpeter equation for correlated electron-hole excitations. In this context, the Tamm-Dancoff approximation is routinely employed to reduce the computational effort. It is known that the use of this approximation introduces errors of several 100 meV for small organic molecules but is negligible for extended systems. In this paper, we investigate how exactly the transition between these two regimes happens, by calculating the optical excitation energies of a series of polythiophene molecules of different sizes. We determine which parts of the electron-hole interaction are responsible for the deviation and show that the quantitative effects of the Tamm-Dancoff approximation depend sensitively on the size of the electronic system, in particular on the electronic conjugation length.

Enhanced static approximation to the electron self-energy operator for efficient calculation of quasiparticle energies

An enhanced static approximation for the electron self-energy operator is proposed for efficient calculation of quasiparticle energies. Analysis of the static Coulomb-hole screened-exchange (COHSEX) approximation originally proposed by Hedin shows that most of the error derives from the short-wavelength contributions of the assumed adiabatic accumulation of the Coulomb hole. A wave-vector-dependent correction factor can be incorporated as the basis for a new static approximation. This factor can be approximated by a single scaling function, determined from the homogeneous electron-gas model. The local field effect in real materials is captured by a simple ansatz based on symmetry consideration. As inherited from the COHSEX approximation, the new approximation presents a Hermitian self-energy operator and the summation over empty states is eliminated from the evaluation of the self-energy operator. Tests were conducted comparing the new approximation to GW calculations for diverse materials ranging from crystals, molecules, atoms and a carbon nanotube. The accuracy for the minimum gap is about 10% or better. Like in the COHSEX approximation, the occupied bandwidth is overestimated.

Electronic excitations of CO adsorbed on MgO(001)

We report ab initio calculations of the quasiparticle band structure and the optical excitation spectrum of bulk MgO, the MgO(001) surface, and CO molecules adsorbed on MgO(001). Many-body exchange and correlation effects are included within the GW approximation of the electron self-energy operator and the corresponding electron–hole interaction. The excited electron–hole states are obtained from the Bethe–Salpeter equation. At the clean MgO(001) surface exciton states are found with binding energies that are significantly stronger than in the bulk. The exciton spectrum of the adsorbate system CO : MgO is dominated by charge-transfer excitons, which couple strongly to the molecular excitations of CO.

Electron-hole excitations and optical spectra from first principles

We present a recently developed approach to calculate electron-hole excitations and the optical spectra of condensed matter from first principles. The key concept is to describe the excitations of the electronic system by the corresponding one- and two-particle Green's function. The method combines three computational techniques. First, the electronic ground state is treated within density-functional theory. Second, the single-particle spectrum of the electrons and holes is obtained within the $\mathrm{GW}$ approximation to the electron self-energy operator. Finally, the electron-hole interaction is calculated and a Bethe-Salpeter equation is solved, yielding the coupled electron-hole excitations. The resulting solutions allow the calculation of the entire optical spectrum. This holds both for bound excitonic states below the band gap, as well as for the resonant spectrum above the band gap. We discuss a number of technical developments needed for the application of the method to real systems. To illustrate the approach, we discuss the excitations and optical spectra of spatially isolated systems (atoms, molecules, and semiconductor clusters) and of extended, periodic crystals (semiconductors and insulators).

Excitonic Effects and the Optical Absorption Spectrum of Hydrogenated Si Clusters

We calculate the optical absorption spectrum of hydrogen-terminated silicon clusters by solving the Bethe-Salpeter equation for the two-particle Green{close_quote}s function using an {ital ab initio} approach. The one-particle Green{close_quote}s function and the electron-hole interaction kernel are calculated within the GW approximation for the electron self-energy operator. Very large exciton binding energies are observed. Our results for the one-particle properties and the optical absorption spectra of the clusters are in very good agreement with available experimental data. {copyright} {ital 1998} {ital The American Physical Society}

Self-energy effects on the surface-state energies of H-Si(111)1 x 1.

We have calculated the quasiparticle energy of the occupied surface states of the H-Si(111)1\ifmmode\times\else\texttimes\fi{}1 surface. The electron self-energy operator is expanded to first-order in the screened Coulomb interaction in the GW approximation. The results explain the data from recent high-resolution angle-resolved photoemission spectroscopy. Comparison of the quasiparticle surface-state energies with those from local-density-functional eigenvalues shows that the self-energy corrections are very large, typically two to three times larger than the corrections found in previous calculations on other semiconductor surface systems. We have also performed a frozen-phonon study of the stretching mode of the Si-H bond. As observed in several recent experiments and theoretical studies, a large anharmonicity is found.

Quasiparticle band-structure calculations for C, Si, Ge, GaAs, and SiC using Gaussian-orbital basis sets.

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 ${\mathrm{\ensuremath{\epsilon}}}_{\mathbf{G},\mathbf{G}\ensuremath{'}}$(q,\ensuremath{\omega}), 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 GW 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(${\mathrm{L}}_{1\mathrm{c}}$). 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 ${\mathrm{\ensuremath{\epsilon}}}_{\mathbf{G},\mathbf{G}\ensuremath{'}}$(q,0) in the GW 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.

Erratum: Pressure-induced insulator-metal transitions in solid xenon and hydrogen: A first-principles quasiparticle study

We report a quasiparticle study of the pressure-induced isostructural insulator-metal transition in solids by the mechanism of band-gap closure. Two examples are investigated: solid Xe and molecular solid hydrogen. The band gaps are calculated with a first-principles quasiparticle approach, in which the electron self-energy operator is expanded to first order in the screened Coulomb interaction, viz., the GW approximation. For the case of solid xenon, the crystal structure has been experimentally established to be hexagonal-close-packed (hcp) in the vicinity of the observed metallization pressure of 132(\ifmmode\pm\else\textpm\fi{}5) GPa. Our calculation for solid xenon yields a metallization pressure of 128 GPa, in good agreement with experiment. The theoretical results further quantitatively explain all the salient features observed in the experimental optical spectra at metallization. For molecular solid hydrogen the structure has yet to be determined definitively. Our calculations are carried out for structures in which hydrogen molecules assume an hcp arrangement. The quasiparticle results are compared with those from Hartree-Fock (HF) and local-density approximation (LDA) calculations.

Pressure-induced insulator-metal transitions in solid xenon and hydrogen: A first-principles quasiparticle study.

We report a quasiparticle study of the pressure-induced isostructural insulator-metal transition in solids by the mechanism of band-gap closure. Two examples are investigated: solid Xe and molecular solid hydrogen. The band gaps are calculated with a first-principles quasiparticle approach, in which the electron self-energy operator is expanded to first order in the screened Coulomb interaction, viz., the GW approximation. For the case of solid xenon, the crystal structure has been experimentally established to be hexagonal-close-packed (hcp) in the vicinity of the observed metallization pressure of 132(\ifmmode\pm\else\textpm\fi{}5) GPa. Our calculation for solid xenon yields a metallization pressure of 128 GPa, in good agreement with experiment. The theoretical results further quantitatively explain all the salient features observed in the experimental optical spectra at metallization. For molecular solid hydrogen the structure has yet to be determined definitively. Our calculations are carried out for structures in which hydrogen molecules assume an hcp arrangement. The quasiparticle results are compared with those from Hartree-Fock (HF) and local-density approximation (LDA) calculations.

Quasiparticle band structure of thirteen semiconductors and insulators.

By using a model dielectric matrix in electron self-energy evaluations the computational effort of a quasiparticle band-structure calculation for a semiconductor is greatly reduced. Applications to various systems with or without inversion symmetry, having narrow or wide band gaps, and semiconductor alloys demonstrate the reliability and accuracy of the method. Calculations have been performed for thirteen semiconducting or insulating materials: Si, LiCl, AlP, AlAs, AlSb, GaP, GaAs, GaSb, InP, InAs, InSb, and the Al{sub 0.5}Ga{sub 0.5}As and In{sub 0.53}Ga{sub 0.47}As alloys. Excellent agreement with experimental results is obtained for the quasiparticle energies for these materials. The only three exceptions, {ital E}({Gamma}{sub 1{ital c}}) of AlP, {ital E}({ital L}{sub 1{ital c}}) of AlAs, and {ital E}({ital L}{sub 1{ital c}}) of AlSb are discussed and attributed to various experimental uncertainties. Several other quasiparticle-excitation-related properties are also examined in this work. The many-body corrections to the eigenvalues of the valence-band-maximum states obtained from the local-density approximation are calculated for the zinc-blende-structure semiconductors, which are widely used in semiconductor-interface studies. In the present approach, the static screening of the Coulomb interaction between two electrons in a crystal is determined using a model that depends only on the local charge densities at these two points.more » Since a direct quantitative modeling of the electron self-energy operator has proven difficult, the successful application of the present model-dielectric-function scheme in self-energy calculations makes possible detailed studies of the quasiparticle properties of rather complex systems, which would be otherwise computationally too demanding.« less

Quasiparticle surface band structure and photoelectric threshold of Ge(111)-2 x 1.

The surface-state energies of the Ge(111)-2\ifmmode\times\else\texttimes\fi{}1 surface are calculated using a quasiparticle self-energy approach. The surface structural parameters are determined through a local-density-functional total-energy minimization resulting in a buckled \ensuremath{\pi}-bonded-chain geometry. The quasiparticle energies are computed using a first-order expansion of the electron self-energy operator in the screened Coulomb interaction with a model static dielectric matrix. Our calculated surface-state band gaps and dispersions of both the occupied and unoccupied surface states agree well with experiments. Further, the photoelectric threshold \ensuremath{\varphi} is found to be 4.73 eV, compared to 4.74--4.80 eV obtained experimentally.

Quasiparticle intepretation of photoemission spectra and optical properties of GaAs(110).

We investigate the quasiparticle band structure and optical properties of a relaxed GaAs(110) surface using a first-principles Green's-function approach. The local fields and the dynamical correlation are fully incorporated in the evaluation of the electron self-energy operator. The results provide a quantitative interpretation of the photoemission, inverse photoemission, and reflectivity spectra observed for this surface. Implications of our theoretical surface band structure for the current controversy between various experimental results for the position of the empty surface band are discussed.

Quasiparticle excitation spectrum for nearly-free-electron metals.

The quasiparticle excitation spectrum is calculated for the nearly-free-electron metals Li, Na, and Al by evaluation of the electron self-energy operator within the GW approximation and a generalized plasmon-pole model. The calculated quasiparticle energies for Na and Al are in excellent agreement with angle-resolved photoemission experiments. For Na in particular, the occupied-band width is significantly narrower than the free-electron value, as found in experiment. Inclusion of exchange and correlation effects in the dielectric matrix is shown to decrease the bandwidth relative to the random-phase-approximation result by a significant amount. Local-field effects, reflected in the off-diagonal elements of the dielectric matrix, are found to have little effect on the quasiparticle band structure of these simple metals.

Theory of quasiparticle surface states in semiconductor surfaces.

A first-principles theory of the quasiparticle surface-state energies on semiconductor surfaces is developed. The surface properties are calculated using a repeated-slab geometry. Many-body effects due to the electron-electron interaction are represented by the electron self-energy operator including the full surface Green's function and local fields and dynamical screening effects in the Coulomb interaction. Calculated surface-state energies for the prototypical Si(111):As and Ge(111):As surfaces are presented. The calculated energies and dispersions for the occupied surface states (resonances) are in excellent agreement with recent angle-resolved photoemission data. Predictions are made for the position of empty surface states on both surfaces which may be experimentally accessible. The resulting surface state gap at \ensuremath{\Gamma}\ifmmode\bar\else\textasciimacron\fi{} for Si(111):As agrees with recent scanning-tunneling-spectroscopy measurements. Comparison of the present results to eigenvalues from the local-density-functional calculation reveals substantial corrections for the gaps between empty and occupied surface states. This correction is found to depend on the character of the surface states involved.

Theory of quasiparticle energies: Band gaps and excitation spectra in solids

A first-principles theory for the band gaps and electronic excitation energies in crystals is described. Optical and photoemission spectra are properly interpreted as transitions between quasiparticle states of the many-electron system. The theory requires adequate treatment of the Coulomb interaction between the electrons, including exchange and dynamical correlation effects. The nonlocal energy-dependent electron self-energy operator is evaluated from first principles using the full dielectric matrix and the dressed Green's function. Quasiparticle energies for materials covering a wide range of metallicity and ionicity are presented. With no empirical input, the calculated band gaps, optical transition energies, and band dispersions are all within a few percent of experimental values. For semiconductors and insulators, we find that local field effects in the screening of the Coulomb interaction and dynamical renormalization are both crucial for accurate results. The present method also extends beyond the case of bulk crystals, e.g., to surfaces. Results on the surface state energies of the Ge (111): As and S(111):As surface are discussed and compared with experiment.

Electron correlation in semiconductors and insulators: Band gaps and quasiparticle energies.

We present a first-principles theory of the quasiparticle energies in semiconductors and insulators described in terms of the electron self-energy operator. The full dielectric matrix is used to evaluate the self-energy operator in the GW approximation: the first term in an expansion of the self-energy operator in terms of the dynamically screened Coulomb interaction (W) and the dressed Green's function (G). Quasiparticle energies are calculated for the homopolar materials diamond, Si, and Ge as well as for the ionic compound LiCl. The results are in excellent agreement with available experimental data. In particular, the indirect band gap is calculated as 5.5, 1.29, and 0.75 eV as compared with experimental gaps of 5.48, 1.17, and 0.744 eV for diamond, Si, and Ge, respectively. The Ge results include relativistic effects. The calculated direct gap for LiCl is within 5% of experiment. Viewed as a correction to the density-functional eigenvalues calculated with the local-density approximation, the present results show a correction dominated by a large jump at the gap. It is found that because of the charge inhomogeneity, the full dielectric screening matrix must be included, i.e., local-field effects are essential. The dynamical effects are also found to be crucial. The required dielectric matrices are obtained within the density-functional approach for the static case and extended to finite frequency with use of a generalized plasmon-pole model based on sum rules. The model reproduces the \ensuremath{\omega} and ${\ensuremath{\omega}}^{\mathrm{\ensuremath{-}}1}$ moments of the exact many-body response function. The qualitative features of the electron self-energy operator are discussed. Using the static Coulomb-hole--screened-exchange approximation for illustration, the role of local fields in the self-energy operator are explained. The role of dynamical renormalization is illustrated. The same qualitative features are observed in both the homopolar and ionic materials.

Electron correlation and the band gap in ionic crystals.

The band gap and quasiparticle energies in LiCl are calculated by evaluation of the electron self-energy operator including the effects of local fields and dynamic screening from first principles. Good agreement with available experimental data is obtained. In particular, the calculated band gap for bulk transitions (8.9 eV) is within 5% of the experimental result. Comparison with our previous study of homopolar materials shows that the same theoretical picture describes the electron correlation in both cases.

First-principles theory of quasiparticles: Calculation of band gaps in semiconductors and insulators.

We present a first-principles theory for the quasiparticle energies of semiconductors and insulators. The full dielectric matrix is used to evaluate the nonlocal, energy-dependent electron self-energy operator. Both local-field effects and dynamical screening are found to be essential for understanding quasiparticle energies. Results for the band gaps, optical transitions, and band dispersions for silicon and diamond are in excellent agreement with existing experimental data.