@article{18558, abstract = {{We present an implementation of the GW approximation for the electronic self-energy within the full-potential linearized augmented-plane-wave (FLAPW) method. The algorithm uses an all-electron mixed product basis for the representation of response matrices and related quantities. This basis is derived from the FLAPW basis and is exact for wave-function products. The correlation part of the self-energy is calculated on the imaginary-frequency axis with a subsequent analytic continuation to the real axis. As an alternative we can perform the frequency convolution of the Green function G and the dynamically screened Coulomb interaction W explicitly by a contour integration. The singularity of the bare and screened interaction potentials gives rise to a numerically important self-energy contribution, which we treat analytically to achieve good convergence with respect to the k-point sampling. As numerical realizations of the GW approximation typically suffer from the high computational expense required for the evaluation of the nonlocal and frequency-dependent self-energy, we demonstrate how the algorithm can be made very efficient by exploiting spatial and time-reversal symmetry as well as by applying an optimization of the mixed product basis that retains only the numerically important contributions of the electron-electron interaction. This optimization step reduces the basis size without compromising the accuracy and accelerates the code considerably. Furthermore, we demonstrate that one can employ an extrapolar approximation for high-lying states to reduce the number of empty states that must be taken into account explicitly in the construction of the polarization function and the self-energy. We show convergence tests, CPU timings, and results for prototype semiconductors and insulators as well as ferromagnetic nickel.}}, author = {{Friedrich, Christoph and Blügel, Stefan and Schindlmayr, Arno}}, issn = {{1550-235X}}, journal = {{Physical Review B}}, number = {{12}}, publisher = {{American Physical Society}}, title = {{{Efficient implementation of the GW approximation within the all-electron FLAPW method}}}, doi = {{10.1103/PhysRevB.81.125102}}, volume = {{81}}, year = {{2010}}, } @article{13573, abstract = {{Given the vast range of lithium niobate (LiNbO3) applications, the knowledge about its electronic and optical properties is surprisingly limited. The direct band gap of 3.7 eV for the ferroelectric phase – frequently cited in the literature – is concluded from optical experiments. Recent theoretical investigations show that the electronic band‐structure and optical properties are very sensitive to quasiparticle and electron‐hole attraction effects, which were included using the GW approximation for the electron self‐energy and the Bethe‐Salpeter equation respectively, both based on a model screening function. The calculated fundamental gap was found to be at least 1 eV larger than the experimental value. To resolve this discrepancy we performed first‐principles GW calculations for lithium niobate using the full‐potential linearized augmented plane‐wave (FLAPW) method. Thereby we use the parameter‐free random phase approximation for a realistic description of the nonlocal and energydependent screening. This leads to a band gap of about 4.7 (4.2) eV for ferro(para)‐electric lithium niobate.}}, author = {{Thierfelder, Christian and Sanna, Simone and Schindlmayr, Arno and Schmidt, Wolf Gero}}, issn = {{1610-1642}}, journal = {{Physica Status Solidi C}}, location = {{Weimar}}, number = {{2}}, pages = {{362--365}}, publisher = {{Wiley-VCH}}, title = {{{Do we know the band gap of lithium niobate?}}}, doi = {{10.1002/pssc.200982473}}, volume = {{7}}, year = {{2010}}, } @article{18562, abstract = {{The structural and electronic properties of strained silicon are investigated quantitatively with ab initio computational methods. For this purpose we combine densityfunctional theory within the local‐density approximation and the GW approximation for the electronic self‐energy. From the variation of the total energy as a function of applied strain we obtain the elastic constants, Poisson ratios and related structural parameters, taking a possible internal relaxation fully into account. For biaxial tensile strain in the (001) and (111) planes we then investigate the effects on the electronic band structure. These strain configurations occur in epitaxial silicon films grown on SiGe templates along different crystallographic directions. The tetragonal deformation resulting from (001) strain induces a valley splitting that removes the sixfold degeneracy of the conduction‐band minimum. Furthermore, strain in any direction causes the band structure to warp. We present quantitative results for the electron effective mass, derived from the curvature of the conduction band, as a function of strain and discuss the implications for the mobility of the charge carriers. The inclusion of proper self‐energy corrections within the GW approximation in our work not only yields band gaps in much better agreement with experimental measurements than the localdensity approximation, but also predicts slightly larger electron effective masses.}}, author = {{Bouhassoune, Mohammed and Schindlmayr, Arno}}, issn = {{1610-1642}}, journal = {{Physica Status Solidi C}}, location = {{Weimar}}, number = {{2}}, pages = {{460--463}}, publisher = {{Wiley-VCH}}, title = {{{Electronic structure and effective masses in strained silicon}}}, doi = {{10.1002/pssc.200982470}}, volume = {{7}}, year = {{2010}}, } @inbook{18549, abstract = {{We describe the software package SPEX, which allows first-principles calculations of quasiparticle and collective electronic excitations in solids using techniques from many-body perturbation theory. The implementation is based on the full-potential linearized augmented-plane-wave (FLAPW) method, which treats core and valence electrons on an equal footing and can be applied to a wide range of materials, including transition metals and rare earths. After a discussion of essential features that contribute to the high numerical efficiency of the code, we present illustrative results for quasiparticle band structures calculated within the GW approximation for the electronic self-energy, electron-energy-loss spectra with inter- and intraband transitions as well as local-field effects, and spin-wave spectra of itinerant ferromagnets. In all cases the inclusion of many-body correlation terms leads to very good quantitative agreement with experimental spectroscopies.}}, author = {{Schindlmayr, Arno and Friedrich, Christoph and Şaşıoğlu, Ersoy and Blügel, Stefan}}, booktitle = {{Modern and Universal First-Principles Methods for Many-Electron Systems in Chemistry and Physics}}, editor = {{Dolg, Franz Michael}}, isbn = {{978-3-486-59827-8}}, pages = {{67--78}}, publisher = {{Oldenbourg}}, title = {{{First-principles calculation of electronic excitations in solids with SPEX}}}, doi = {{10.1524/9783486711639.67}}, volume = {{3}}, year = {{2010}}, } @article{18560, abstract = {{We present a computational scheme to study spin excitations in magnetic materials from first principles. The central quantity is the transverse spin susceptibility, from which the complete excitation spectrum, including single-particle spin-flip Stoner excitations and collective spin-wave modes, can be obtained. The susceptibility is derived from many-body perturbation theory and includes dynamic correlation through a summation over ladder diagrams that describe the coupling of electrons and holes with opposite spins. In contrast to earlier studies, we do not use a model potential with adjustable parameters for the electron-hole interaction but employ the random-phase approximation. To reduce the numerical cost for the calculation of the four-point scattering matrix we perform a projection onto maximally localized Wannier functions, which allows us to truncate the matrix efficiently by exploiting the short spatial range of electronic correlation in the partially filled d or f orbitals. Our implementation is based on the full-potential linearized augmented-plane-wave method. Starting from a ground-state calculation within the local-spin-density approximation (LSDA), we first analyze the matrix elements of the screened Coulomb potential in the Wannier basis for the 3d transition-metal series. In particular, we discuss the differences between a constrained nonmagnetic and a proper spin-polarized treatment for the ferromagnets Fe, Co, and Ni. The spectrum of single-particle and collective spin excitations in fcc Ni is then studied in detail. The calculated spin-wave dispersion is in good overall agreement with experimental data and contains both an acoustic and an optical branch for intermediate wave vectors along the [100] direction. In addition, we find evidence for a similar double-peak structure in the spectral function along the [111] direction. To investigate the influence of static correlation we finally consider LSDA+U as an alternative starting point and show that, together with an improved description of the Fermi surface, it yields a more accurate quantitative value for the spin-wave stiffness constant, which is overestimated in the LSDA.}}, author = {{Şaşıoğlu, Ersoy and Schindlmayr, Arno and Friedrich, Christoph and Freimuth, Frank and Blügel, Stefan}}, issn = {{1550-235X}}, journal = {{Physical Review B}}, number = {{5}}, publisher = {{American Physical Society}}, title = {{{Wannier-function approach to spin excitations in solids}}}, doi = {{10.1103/PhysRevB.81.054434}}, volume = {{81}}, year = {{2010}}, } @article{18557, abstract = {{We describe the software package SPEX, which allows first-principles calculations of quasiparticle and collective electronic excitations in solids using techniques from many-body perturbation theory. The implementation is based on the full-potential linearized augmented-plane-wave (FLAPW) method, which treats core and valence electrons on an equal footing and can be applied to a wide range of materials, including transition metals and rare earths. After a discussion of essential features that contribute to the high numerical efficiency of the code, we present illustrative results for quasiparticle band structures calculated within the GW approximation for the electronic self-energy, electron-energy-loss spectra with inter- and intraband transitions as well as local-field effects, and spin-wave spectra of itinerant ferromagnets. In all cases the inclusion of many-body correlation terms leads to very good quantitative agreement with experimental spectroscopies.}}, author = {{Schindlmayr, Arno and Friedrich, Christoph and Şaşıoğlu, Ersoy and Blügel, Stefan}}, issn = {{2196-7156}}, journal = {{Zeitschrift für Physikalische Chemie}}, number = {{3-4}}, pages = {{357--368}}, publisher = {{Oldenbourg}}, title = {{{First-principles calculation of electronic excitations in solids with SPEX}}}, doi = {{10.1524/zpch.2010.6110}}, volume = {{224}}, year = {{2010}}, } @article{18632, abstract = {{We present measurements of the effective electron mass in biaxial tensile strained silicon on insulator (SSOI) material with 1.2 GPa stress and in unstrained SOI. Hall-bar metal oxide semiconductor field effect transistors on 60 nm SSOI and SOI were fabricated and Shubnikov–de Haas oscillations in the temperature range of T=0.4–4 K for magnetic fields of B=0–10 T were measured. The effective electron mass in SSOI and SOI samples was determined as mt=(0.20±0.01)m0. This result is in excellent agreement with first-principles calculations of the effective electron mass in the presence of strain.}}, author = {{Feste, Sebastian F. and Schäpers, Thomas and Buca, Dan and Zhao, Qing Tai and Knoch, Joachim and Bouhassoune, Mohammed and Schindlmayr, Arno and Mantl, Siegfried}}, issn = {{1077-3118}}, journal = {{Applied Physics Letters}}, number = {{18}}, publisher = {{American Institute of Physics}}, title = {{{Measurement of effective electron mass in biaxial tensile strained silicon on insulator}}}, doi = {{10.1063/1.3254330}}, volume = {{95}}, year = {{2009}}, } @inproceedings{18634, abstract = {{A computational method to obtain optical conductivities from first principles is presented. It exploits a relation between the conductivity and the complex dielectric function, which is constructed from the full electronic band structure within the random-phase approximation. In contrast to the Drude model, no empirical parameters are used. As interband transitions as well as local-field effects are properly included, the calculated spectra are valid over a wide frequency range. As an illustration I present quantitative results for selected simple metals, noble metals, and ferromagnetic transition metals. The implementation is based on the full-potential linearized augmented-plane-wave method.}}, author = {{Schindlmayr, Arno}}, booktitle = {{Theoretical and Computational Nanophotonics: Proceedings of the 2nd International Workshop}}, editor = {{Chigrin, Dmitry N.}}, isbn = {{978-0-7354-0715-2}}, issn = {{1551-7616}}, location = {{Bad Honnef}}, number = {{1}}, pages = {{157--159}}, publisher = {{American Institute of Physics}}, title = {{{Optical conductivity of metals from first principles}}}, doi = {{10.1063/1.3253897}}, volume = {{1176}}, year = {{2009}}, } @article{18636, abstract = {{We derive formulas for the Coulomb matrix within the full-potential linearized augmented-plane-wave (FLAPW) method. The Coulomb matrix is a central ingredient in implementations of many-body perturbation theory, such as the Hartree–Fock and GW approximations for the electronic self-energy or the random-phase approximation for the dielectric function. It is represented in the mixed product basis, which combines numerical muffin-tin functions and interstitial plane waves constructed from products of FLAPW basis functions. The interstitial plane waves are here expanded with the Rayleigh formula. The resulting algorithm is very efficient in terms of both computational cost and accuracy and is superior to an implementation with the Fourier transform of the step function. In order to allow an analytic treatment of the divergence at k=0 in reciprocal space, we expand the Coulomb matrix analytically around this point without resorting to a projection onto plane waves. Without additional approximations, we then apply a basis transformation that diagonalizes the Coulomb matrix and confines the divergence to a single eigenvalue. At the same time, response matrices like the dielectric function separate into head, wings, and body with the same mathematical properties as in a plane-wave basis. As an illustration we apply the formulas to electron-energy-loss spectra (EELS) for nickel at different k vectors including k=0. The convergence of the spectra towards the result at k=0 is clearly seen. Our all-electron treatment also allows to include transitions from 3s and 3p core states in the EELS spectrum that give rise to a shallow peak at high energies and lead to good agreement with experiment.}}, author = {{Friedrich, Christoph and Schindlmayr, Arno and Blügel, Stefan}}, issn = {{0010-4655}}, journal = {{Computer Physics Communications}}, number = {{3}}, pages = {{347--359}}, publisher = {{Elsevier}}, title = {{{Efficient calculation of the Coulomb matrix and its expansion around k=0 within the FLAPW method}}}, doi = {{10.1016/j.cpc.2008.10.009}}, volume = {{180}}, year = {{2009}}, } @article{18564, abstract = {{In the context of photoelectron spectroscopy, the GW approach has developed into the method of choice for computing excitation spectra of weakly correlated bulk systems and their surfaces. To employ the established computational schemes that have been developed for three-dimensional crystals, two-dimensional systems are typically treated in the repeated-slab approach. In this work we critically examine this approach and identify three important aspects for which the treatment of long-range screening in two dimensions differs from the bulk: (1) anisotropy of the macroscopic screening, (2) k-point sampling parallel to the surface, (3) periodic repetition and slab-slab interaction. For prototypical semiconductor (silicon) and ionic (NaCl) thin films we quantify the individual contributions of points (1) to (3) and develop robust and efficient correction schemes derived from the classic theory of dielectric screening.}}, author = {{Freysoldt, Christoph and Eggert, Philipp and Rinke, Patrick and Schindlmayr, Arno and Scheffler, Matthias}}, issn = {{1550-235X}}, journal = {{Physical Review B}}, number = {{23}}, publisher = {{American Physical Society}}, title = {{{Screening in two dimensions: GW calculations for surfaces and thin films using the repeated-slab approach}}}, doi = {{10.1103/PhysRevB.77.235428}}, volume = {{77}}, year = {{2008}}, } @inbook{18588, author = {{Schindlmayr, Arno}}, booktitle = {{Probing the Nanoworld }}, editor = {{Urban, Knut and Schneider, Claus Michael and Brückel, Thomas and Blügel, Stefan}}, isbn = {{978-3-89336-462-6}}, issn = {{1433-5506}}, location = {{Jülich}}, pages = {{A1.21--A1.36}}, publisher = {{Forschungszentrum Jülich}}, title = {{{Interaction of radiation with matter. Part II: Light and electrons}}}, volume = {{34}}, year = {{2007}}, } @article{18589, abstract = {{For the calculation of neutral excitations, time-dependent density functional theory (TDDFT) is an exact reformulation of the many-body time-dependent Schrödinger equation, based on knowledge of the density instead of the many-body wavefunction. The density can be determined in an efficient scheme by solving one-particle non-interacting Schrödinger equations—the Kohn–Sham equations. The complication of the problem is hidden in the—unknown—time-dependent exchange and correlation potential that appears in the Kohn–Sham equations and for which it is essential to find good approximations. Many approximations have been suggested and tested for finite systems, where even the very simple adiabatic local-density approximation (ALDA) has often proved to be successful. In the case of solids, ALDA fails to reproduce optical absorption spectra, which are instead well described by solving the Bethe–Salpeter equation of many-body perturbation theory (MBPT). On the other hand, ALDA can lead to excellent results for loss functions (at vanishing and finite momentum transfer). In view of this and thanks to recent successful developments of improved linear-response kernels derived from MBPT, TDDFT is today considered a promising alternative to MBPT for the calculation of electronic spectra, even for solids. After reviewing the fundamentals of TDDFT within linear response, we discuss different approaches and a variety of applications to extended systems.}}, author = {{Botti, Silvana and Schindlmayr, Arno and Del Sole, Rodolfo and Reining, Lucia}}, issn = {{1361-6633}}, journal = {{Reports on Progress in Physics}}, number = {{3}}, pages = {{357--407}}, publisher = {{IOP Publishing}}, title = {{{Time-dependent density-functional theory for extended systems}}}, doi = {{10.1088/0034-4885/70/3/r02}}, volume = {{70}}, year = {{2007}}, } @article{18591, abstract = {{Using density-functional theory, we investigate the stability of the half-metallic ground state of magnetite under different strain conditions. The effects of volume relaxation and internal degrees of freedom are fully taken into account. For hydrostatic compression, planar strain in the (001) plane and uniaxial strain along the [001] direction, we derive quantitative limits beyond which magnetite becomes metallic. As a major new result, we identify the bond length between the octahedrally coordinated iron atoms and their neighbouring oxygen atoms as the main characteristic parameter, and we show that the transition occurs if external strain reduces this interatomic distance from 2.06 Å in equilibrium to below a critical value of 1.99 Å. Based on this criterion, we also argue that planar strain due to epitaxial growth does not lead to a metallic state for magnetite films grown on (111)-oriented substrates.}}, author = {{Friák, Martin and Schindlmayr, Arno and Scheffler, Matthias}}, issn = {{1361-6633}}, journal = {{New Journal of Physics}}, number = {{1}}, publisher = {{IOP Publishing and Deutsche Physikalische Gesellschaft}}, title = {{{Ab initio study of the half-metal to metal transition in strained magnetite}}}, doi = {{10.1088/1367-2630/9/1/005}}, volume = {{9}}, year = {{2007}}, } @inbook{18593, abstract = {{We present a quantitative parameter-free method for calculating defect states and charge-transition levels of point defects in semiconductors. It combines the strength of density-functional theory for ground-state total energies with quasiparticle corrections to the excitation spectrum obtained from many-body perturbation theory. The latter is implemented within the G0W0 approximation, in which the electronic self-energy is constructed non-self-consistently from the Green’s function of the underlying Kohn–Sham system. The method is general and applicable to arbitrary bulk or surface defects. As an example we consider anion vacancies at the (110) surfaces of III–V semiconductors. Relative to the Kohn–Sham eigenvalues in the local-density approximation, the quasiparticle corrections open the fundamental band gap and raise the position of defect states inside the gap. As a consequence, the charge-transition levels are also pushed to higher energies, leading to close agreement with the available experimental data.}}, author = {{Schindlmayr, Arno and Scheffler, Matthias}}, booktitle = {{Theory of Defects in Semiconductors}}, editor = {{Drabold, David A. and Estreicher, Stefan K.}}, isbn = {{978-3-540-33400-2}}, issn = {{1437-0859}}, pages = {{165--192}}, publisher = {{Springer}}, title = {{{Quasiparticle calculations for point defects at semiconductor surfaces}}}, doi = {{10.1007/11690320_8}}, volume = {{104}}, year = {{2007}}, } @article{18595, abstract = {{Excited-state calculations, notably for quasiparticle band structures, are nowadays routinely performed within the GW approximation for the electronic self-energy. Nevertheless, certain numerical approximations and simplifications are still employed in practice to make the computations feasible. An important aspect for periodic systems is the proper treatment of the singularity of the screened Coulomb interaction in reciprocal space, which results from the slow 1/r decay in real space. This must be done without introducing artificial interactions between the quasiparticles and their periodic images in repeated cells, which occur when integrals of the screened Coulomb interaction are discretised in reciprocal space. An adequate treatment of both aspects is crucial for a numerically stable computation of the self-energy. In this article we build on existing schemes for isotropic screening and present an extension for anisotropic systems. We also show how the contributions to the dielectric function arising from the non-local part of the pseudopotentials can be computed efficiently. These improvements are crucial for obtaining a fast convergence with respect to the number of points used for the Brillouin zone integration and prove to be essential to make GW calculations for strongly anisotropic systems, such as slabs or multilayers, efficient.}}, author = {{Freysoldt, Christoph and Eggert, Philipp and Rinke, Patrick and Schindlmayr, Arno and Godby, Rex W. and Scheffler, Matthias}}, issn = {{0010-4655}}, journal = {{Computer Physics Communications}}, number = {{1}}, pages = {{1--13}}, publisher = {{Elsevier}}, title = {{{Dielectric anisotropy in the GW space–time method}}}, doi = {{10.1016/j.cpc.2006.07.018}}, volume = {{176}}, year = {{2007}}, } @inbook{18601, author = {{Friedrich, Christoph and Schindlmayr, Arno}}, booktitle = {{Computational Condensed Matter Physics}}, editor = {{Blügel, Stefan and Gompper, Gerhard and Koch, Erik and Müller-Krumbhaar, Heiner and Spatschek, Robert and Winkler, Roland G.}}, isbn = {{3-89336-430-7}}, issn = {{1433-5506}}, location = {{Jülich}}, pages = {{A5.1--A5.21}}, publisher = {{Forschungszentrum Jülich}}, title = {{{Many-body perturbation theory: The GW approximation}}}, volume = {{32}}, year = {{2006}}, } @inbook{18603, author = {{Schindlmayr, Arno}}, booktitle = {{Computational Condensed Matter Physics}}, editor = {{Blügel, Stefan and Gompper, Gerhard and Koch, Erik and Müller-Krumbhaar, Heiner and Spatschek, Robert and Winkler, Roland G.}}, isbn = {{3-89336-430-7}}, issn = {{1433-5506}}, location = {{Jülich}}, pages = {{A4.1--A4.19}}, publisher = {{Forschungszentrum Jülich}}, title = {{{Time-dependent density-functional theory}}}, volume = {{32}}, year = {{2006}}, } @inbook{18606, abstract = {{In this lecture we present many-body perturbation theory as a method to determine quasiparticle excitations in solids, especially electronic band structures, accurately from first principles. The main ingredient is the electronic self-energy that, in principle, contains all many-body exchange and correlation effects beyond the Hartree potential. As its exact mathematical expression is unknown, approximations must be used in practical calculations. The approximation is obtained using a systematic algebraic approach on the basis of Green function techniques. It constitutes an expansion of the self-energy up to linear order in the screened Coulomb potential, which describes the interaction between the quasiparticles and includes dynamic screening through the creation of exchange-correlation holes around the bare particles. The implementation of the approximation relies on a perturbative treatment starting from density functional theory. Besides a detailed mathematical discussion we focus on the underlying physical concepts and show some illustrative applications.}}, author = {{Friedrich, Christoph and Schindlmayr, Arno}}, booktitle = {{Computational Nanoscience: Do It Yourself!}}, editor = {{Grotendorst, Johannes and Blügel, Stefan and Marx, Dominik}}, isbn = {{3-00-017350-1}}, location = {{Jülich}}, pages = {{335--355}}, publisher = {{John von Neumann Institute for Computing}}, title = {{{Many-body perturbation theory: The GW approximation}}}, volume = {{31}}, year = {{2006}}, } @article{18597, abstract = {{We propose a new method for calculating optical defect levels and thermodynamic charge-transition levels of point defects in semiconductors, which includes quasiparticle corrections to the Kohn-Sham eigenvalues of density-functional theory. Its applicability is demonstrated for anion vacancies at the (110) surfaces of III–V semiconductors. We find the (+/0) charge-transition level to be 0.49 eV above the surface valence-band maximum for GaAs(110) and 0.82 eV for InP(110). The results show a clear improvement over the local-density approximation and agree closely with an experimental analysis.}}, author = {{Hedström, Magnus and Schindlmayr, Arno and Schwarz, Günther and Scheffler, Matthias}}, issn = {{1079-7114}}, journal = {{Physical Review Letters}}, number = {{22}}, publisher = {{American Physical Society}}, title = {{{Quasiparticle corrections to the electronic properties of anion vacancies at GaAs(110) and InP(110)}}}, doi = {{10.1103/PhysRevLett.97.226401}}, volume = {{97}}, year = {{2006}}, } @article{18599, abstract = {{This paper investigates the influence of the basis set on the GW self-energy correction in the full-potential linearized augmented-plane-wave (LAPW) approach and similar linearized all-electron methods. A systematic improvement is achieved by including local orbitals that are defined as second and higher energy derivatives of solutions to the radial scalar-relativistic Dirac equation and thus constitute a natural extension of the LAPW basis set. Within this approach linearization errors can be eliminated, and the basis set becomes complete. While the exchange contribution to the self-energy is little affected by the increased basis-set flexibility, the correlation contribution benefits from the better description of the unoccupied states, as do the quasiparticle energies. The resulting band gaps remain relatively unaffected, however; for Si we find an increase of 0.03 eV.}}, author = {{Friedrich, Christoph and Schindlmayr, Arno and Blügel, Stefan and Kotani, Takao}}, issn = {{1550-235X}}, journal = {{Physical Review B}}, number = {{4}}, title = {{{Elimination of the linearization error in GW calculations based on the linearized augmented-plane-wave method}}}, doi = {{10.1103/physrevb.74.045104}}, volume = {{74}}, year = {{2006}}, }