## Publications

Open list in Research Information System

## 2020

F. Schmidt, A. Kozub, T. Biktagirov, C. Eigner, C. Silberhorn, A. Schindlmayr, W.G. Schmidt, U. Gerstmann, Physical Review Research (2020), 2(4)

Polarons in dielectric crystals play a crucial role for applications in integrated electronics and optoelectronics. In this work, we use density-functional theory and Green's function methods to explore the microscopic structure and spectroscopic signatures of electron polarons in lithium niobate (LiNbO3). Total-energy calculations and the comparison of calculated electron paramagnetic resonance data with available measurements reveal the formation of bound polarons at Nb_Li antisite defects with a quasi-Jahn-Teller distorted, tilted configuration. The defect-formation energies further indicate that (bi)polarons may form not only at Nb_Li antisites but also at structures where the antisite Nb atom moves into a neighboring empty oxygen octahedron. Based on these structure models, and on the calculated charge-transition levels and potential-energy barriers, we propose two mechanisms for the optical and thermal splitting of bipolarons, which provide a natural explanation for the reported two-path recombination of bipolarons. Optical-response calculations based on the Bethe-Salpeter equation, in combination with available experimental data and new measurements of the optical absorption spectrum, further corroborate the geometries proposed here for free and defect-bound (bi)polarons.

## 2019

F. Schmidt, A. Riefer, W.G. Schmidt, A. Schindlmayr, M. Imlau, F. Dobener, N. Mengel, S. Chatterjee, S. Sanna, Physical Review Materials (2019), 3(5)

The cubic, tetragonal, and orthorhombic phase of potassium niobate (KNbO3) are studied based on density-functional theory. Starting from the relaxed atomic geometries, we analyze the influence of self-energy corrections on the electronic band structure within the GW approximation. We find that quasiparticle shifts widen the direct (indirect) band gap by 1.21 (1.44), 1.58 (1.55), and 1.67 (1.64) eV for the cubic, tetragonal, and orthorhombic phase, respectively. By solving the Bethe-Salpeter equation, we obtain the linear dielectric function with excitonic and local-field effects, which turn out to be essential for good agreement with experimental data. From our results, we extract an exciton binding energy of 0.6, 0.5, and 0.5 eV for the cubic, tetragonal, and orthorhombic phase, respectively. Furthermore, we investigate the nonlinear second-harmonic generation (SHG) both theoretically and experimentally. The frequency-dependent second-order polarization tensor of orthorhombic KNbO3 is measured for incoming photon energies between 1.2 and 1.6 eV. In addition, calculations within the independent-(quasi)particle approximation are performed for the tetragonal and orthorhombic phase. The novel experimental data are in excellent agreement with the quasiparticle calculations and resolve persistent discrepancies between earlier experimental measurements and ab initio results reported in the literature.

S. Neufeld, A. Bocchini, U. Gerstmann, A. Schindlmayr, W.G. Schmidt, Journal of Physics: Materials (2019), 2(4)

The KTiOPO4 (KTP) band structure and dielectric function are calculated on various levels of theory starting from density-functional calculations. Within the independent-particle approximation an electronic transport gap of 2.97 eV is obtained that widens to about 5.23 eV when quasiparticle effects are included using the GW approximation. The optical response is shown to be strongly anisotropic due to (i) the slight asymmetry of the TiO6 octahedra in the (001) plane and (ii) their anisotropic distribution along the [001] and [100] directions. In addition, excitonic effects are very important: The solution of the Bethe–Salpeter equation indicates exciton binding energies of the order of 1.5 eV. Calculations that include both quasiparticle and excitonic effects are in good agreement with the measured reflectivity.

## 2018

M. Friedrich, W.G. Schmidt, A. Schindlmayr, S. Sanna, Physical Review Materials (2018), 2(1)

A. Schindlmayr, Advances in Mathematical Physics (2018), 2018

The transverse dynamic spin susceptibility is a correlation function that yields exact information about spin excitations in systems with a collinear magnetic ground state, including collective spin-wave modes. In an ab initio context, it may be calculated within many-body perturbation theory or time-dependent density-functional theory, but the quantitative accuracy is currently limited by the available functionals for exchange and correlation in dynamically evolving systems. To circumvent this limitation, the spin susceptibility is here alternatively formulated as the solution of an initial-value problem. In this way, the challenge of accurately describing exchange and correlation in many-electron systems is shifted to the stationary initial state, which is much better understood. The proposed scheme further requires the choice of an auxiliary basis set, which determines the speed of convergence but always allows systematic convergence in practical implementations.

## 2017

M. Friedrich, W.G. Schmidt, A. Schindlmayr, S. Sanna, Physical Review Materials (2017), 1(3)

The optical properties of pristine and titanium-doped LiNbO3 are modeled from first principles. The dielectric functions are calculated within time-dependent density-functional theory, and a model long-range contribution is employed for the exchange-correlation kernel in order to account for the electron-hole binding. Our study focuses on the influence of substitutional titanium atoms on lithium sites. We show that an increasing titanium concentration enhances the values of the refractive indices and the reflectivity.

A. Riefer, N. Weber, J. Mund, D.R. Yakovlev, M. Bayer, A. Schindlmayr, C. Meier, W.G. Schmidt, Journal of Physics: Condensed Matter (2017), 29(21)

The electronic band structures of hexagonal ZnO and cubic ZnS, ZnSe, and ZnTe compounds are determined within hybrid-density-functional theory and quasiparticle calculations. It is found that the band-edge energies calculated on the G0W0 (Zn chalcogenides) or GW (ZnO) level of theory agree well with experiment, while fully self-consistent QSGW calculations are required for the correct description of the Zn 3d bands. The quasiparticle band structures are used to calculate the linear response and second-harmonic-generation (SHG) spectra of the Zn–VI compounds. Excitonic effects in the optical absorption are accounted for within the Bethe–Salpeter approach. The calculated spectra are discussed in the context of previous experimental data and present SHG measurements for ZnO.

F. Schmidt, M. Landmann, E. Rauls, N. Argiolas, S. Sanna, W.G. Schmidt, A. Schindlmayr, Advances in Materials Science and Engineering (2017), 2017

We perform a comprehensive theoretical study of the structural and electronic properties of potassium niobate (KNbO3) in the cubic, tetragonal, orthorhombic, monoclinic, and rhombohedral phase, based on density-functional theory. The influence of different parametrizations of the exchange-correlation functional on the investigated properties is analyzed in detail, and the results are compared to available experimental data. We argue that the PBEsol and AM05 generalized gradient approximations as well as the RTPSS meta-generalized gradient approximation yield consistently accurate structural data for both the external and internal degrees of freedom and are overall superior to the local-density approximation or other conventional generalized gradient approximations for the structural characterization of KNbO3. Band-structure calculations using a HSE-type hybrid functional further indicate significant near degeneracies of band-edge states in all phases which are expected to be relevant for the optical response of the material.

M. Friedrich, W.G. Schmidt, A. Schindlmayr, S. Sanna, Physical Review Materials (2017), 1(5)

The optical properties of congruent lithium niobate are analyzed from first principles. The dielectric function of the material is calculated within time-dependent density-functional theory. The effects of isolated intrinsic defects and defect pairs, including the NbLi4+ antisite and the NbLi4+−NbNb4+ pair, commonly addressed as a bound polaron and bipolaron, respectively, are discussed in detail. In addition, we present further possible realizations of polaronic and bipolaronic systems. The absorption feature around 1.64 eV, ascribed to small bound polarons [O. F. Schirmer et al., J. Phys.: Condens. Matter 21, 123201 (2009)], is nicely reproduced within these models. Among the investigated defects, we find that the presence of bipolarons at bound interstitial-vacancy pairs NbV−VLi can best explain the experimentally observed broad absorption band at 2.5 eV. Our results provide a microscopic model for the observed optical spectra and suggest that, besides NbLi antisites and Nb and Li vacancies, Nb interstitials are also formed in congruent lithium-niobate samples.

## 2016

A. Riefer, M. Friedrich, S. Sanna, U. Gerstmann, A. Schindlmayr, W.G. Schmidt, Physical Review B (2016), 93(7)

The influence of electronic many-body interactions, spin-orbit coupling, and thermal lattice vibrations on the electronic structure of lithium niobate is calculated from first principles. Self-energy calculations in the GW approximation show that the inclusion of self-consistency in the Green function G and the screened Coulomb potential W opens the band gap far stronger than found in previous G0W0 calculations but slightly overestimates its actual value due to the neglect of excitonic effects in W. A realistic frozen-lattice band gap of about 5.9 eV is obtained by combining hybrid density functional theory with the QSGW0 scheme. The renormalization of the band gap due to electron-phonon coupling, derived here using molecular dynamics as well as density functional perturbation theory, reduces this value by about 0.5 eV at room temperature. Spin-orbit coupling does not noticeably modify the fundamental gap but gives rise to a Rashba-like spin texture in the conduction band.

M. Friedrich, A. Schindlmayr, W.G. Schmidt, S. Sanna, Physica Status Solidi B (2016), 253(4), pp. 683-689

The phonon dispersions of the ferro‐ and paraelectric phase of LiTaO3 are calculated within density‐functional perturbation theory. The longitudinal optical phonon modes are theoretically derived and compared with available experimental data. Our results confirm the recent phonon assignment proposed by Margueron et al. [J. Appl. Phys. 111, 104105 (2012)] on the basis of spectroscopical studies. A comparison with the phonon band structure of the related material LiNbO3 shows minor differences that can be traced to the atomic‐mass difference between Ta and Nb. The presence of phonons with imaginary frequencies for the paraelectric phase suggests that it does not correspond to a minimum energy structure, and is compatible with an order‐disorder type phase transition.

## 2015

M. Bouhassoune, A. Schindlmayr, Advances in Condensed Matter Physics (2015), 2015

Using ab initio computational methods, we study the structural and electronic properties of strained silicon, which has emerged as a promising technology to improve the performance of silicon-based metal-oxide-semiconductor field-effect transistors. In particular, higher electron mobilities are observed in n-doped samples with monoclinic strain along the [110] direction, and experimental evidence relates this to changes in the effective mass as well as the scattering rates. To assess the relative importance of these two factors, we combine density-functional theory in the local-density approximation with the GW approximation for the electronic self-energy and investigate the effect of uniaxial and biaxial strains along the [110] direction on the structural and electronic properties of Si. Longitudinal and transverse components of the electron effective mass as a function of the strain are derived from fits to the quasiparticle band structure and a diagonalization of the full effective-mass tensor. The changes in the effective masses and the energy splitting of the conduction-band valleys for uniaxial and biaxial strains as well as their impact on the electron mobility are analyzed. The self-energy corrections within GW lead to band gaps in excellent agreement with experimental measurements and slightly larger effective masses than in the local-density approximation.

M. Friedrich, A. Riefer, S. Sanna, W.G. Schmidt, A. Schindlmayr, Journal of Physics: Condensed Matter (2015), 27(38)

The vibrational properties of stoichiometric LiNbO3 are analyzed within density-functional perturbation theory in order to obtain the complete phonon dispersion of the material. The phonon density of states of the ferroelectric (paraelectric) phase shows two (one) distinct band gaps separating the high-frequency (~800 cm−1) optical branches from the continuum of acoustic and lower optical phonon states. This result leads to specific heat capacites in close agreement with experimental measurements in the range 0–350 K and a Debye temperature of 574 K. The calculated zero-point renormalization of the electronic Kohn–Sham eigenvalues reveals a strong dependence on the phonon wave vectors, especially near Γ. Integrated over all phonon modes, our results indicate a vibrational correction of the electronic band gap of 0.41 eV at 0 K, which is in excellent agreement with the extrapolated temperature-dependent measurements.

## 2014

C. Friedrich, A. Schindlmayr, in: Computing Solids: Models, ab initio Methods and Supercomputing, Forschungszentrum Jülich, 2014, pp. A4.1-A4.21

C. Friedrich, E. Şaşıoğlu, M. Müller, A. Schindlmayr, S. Blügel, in: First Principles Approaches to Spectroscopic Properties of Complex Materials, Springer, 2014, pp. 259-301

Collective spin excitations form a fundamental class of excitations in magnetic materials. As their energy reaches down to only a few meV, they are present at all temperatures and substantially influence the properties of magnetic systems. To study the spin excitations in solids from first principles, we have developed a computational scheme based on many-body perturbation theory within the full-potential linearized augmented plane-wave (FLAPW) method. The main quantity of interest is the dynamical transverse spin susceptibility or magnetic response function, from which magnetic excitations, including single-particle spin-flip Stoner excitations and collective spin-wave modes as well as their lifetimes, can be obtained. In order to describe spin waves we include appropriate vertex corrections in the form of a multiple-scattering T matrix, which describes the coupling of electrons and holes with different spins. The electron–hole interaction incorporates the screening of the many-body system within the random-phase approximation. To reduce the numerical cost in evaluating the four-point T matrix, we exploit a transformation to maximally localized Wannier functions that takes advantage of the short spatial range of electronic correlation in the partially filled d or f orbitals of magnetic materials. The theory and the implementation are discussed in detail. In particular, we show how the magnetic response function can be evaluated for arbitrary k points. This enables the calculation of smooth dispersion curves, allowing one to study fine details in the k dependence of the spin-wave spectra. We also demonstrate how spatial and time-reversal symmetry can be exploited to accelerate substantially the computation of the four-point quantities. As an illustration, we present spin-wave spectra and dispersions for the elementary ferromagnet bcc Fe, B2-type tetragonal FeCo, and CrO2 calculated with our scheme. The results are in good agreement with available experimental data.

A. Schindlmayr, in: Many-Electron Approaches in Physics, Chemistry and Mathematics, Springer, 2014, pp. 343-357

Many-body perturbation theory is a well-established ab initio electronic-structure method based on Green functions. Although computationally more demanding than density functional theory, it has the distinct advantage that the exact expressions for all relevant observables, including the ground-state total energy, in terms of the Green function are known explicitly. The most important application, however, lies in the calculation of excited states, whose energies correspond directly to the poles of the Green function in the complex frequency plane. The accuracy of results obtained within this framework is only limited by the choice of the exchange-correlation self-energy, which must still be approximated in actual implementations. In this respect, the GW approximation has proved highly successful for systems governed by the Coulomb interaction. It yields band structures of solids, including the band gaps of semiconductors, as well as atomic and molecular ionization energies in very good quantitative agreement with experimental photoemission data.

S. Yanagisawa, Y. Morikawa, A. Schindlmayr, Japanese Journal of Applied Physics (2014), 53(5S1)

We investigate the band dispersion and related electronic properties of picene single crystals within the GW approximation for the electronic self-energy. The width of the upper highest occupied molecular orbital (HOMOu) band along the Γ–Y direction, corresponding to the b crystal axis in real space along which the molecules are stacked, is determined to be 0.60 eV and thus 0.11 eV larger than the value obtained from density-functional theory. As in our recent study of rubrene using the same methodology [S. Yanagisawa, Y. Morikawa, and A. Schindlmayr, Phys. Rev. B 88, 115438 (2013)], this increase in the bandwidth is due to the strong variation of the GW self-energy correction across the Brillouin zone, which in turn reflects the increasing hybridization of the HOMOu states of neighboring picene molecules from Γ to Y. In contrast, the width of the lower HOMO (HOMOl) band along Γ–Y remains almost unchanged, consistent with the fact that the HOMOl(Γ) and HOMOl(Y) states exhibit the same degree of hybridization, so that the nodal structure of the wave functions and the matrix elements of the self-energy correction are very similar.

## 2013

A. Riefer, S. Sanna, A. Schindlmayr, W.G. Schmidt, Physical Review B (2013), 87(19)

The frequency-dependent dielectric function and the second-order polarizability tensor of ferroelectric LiNbO3 are calculated from first principles. The calculations are based on the electronic structure obtained from density-functional theory. The subsequent application of the GW approximation to account for quasiparticle effects and the solution of the Bethe-Salpeter equation for the stoichiometric material yield a dielectric function that slightly overestimates the absorption onset and the oscillator strength in comparison with experimental measurements. Calculations at the level of the independent-particle approximation indicate that these deficiencies are, at least, partially related to the neglect of intrinsic defects typical for the congruent material. The second-order polarizability calculated within the independent-particle approximation predicts strong nonlinear coefficients for photon energies above 1.5 eV. The comparison with measured data suggests that the inclusion of self-energy effects in the nonlinear optical response leads to a better agreement with experiments. The intrinsic defects of congruent samples reduce the optical nonlinearities, in particular, for the 21 and 31 tensor components, further improving the agreement between experiments and theory.

A. Schindlmayr, Physical Review B (2013), 87(7)

The GW approximation for the electronic self-energy is an important tool for the quantitative prediction of excited states in solids, but its mathematical exploration is hampered by the fact that it must, in general, be evaluated numerically even for very simple systems. In this paper I describe a nontrivial model consisting of two electrons on the surface of a sphere, interacting with the normal long-range Coulomb potential, and show that the GW self-energy, in the absence of self-consistency, can in fact be derived completely analytically in this case. The resulting expression is subsequently used to analyze the convergence of the energy gap between the highest occupied and the lowest unoccupied quasiparticle orbital with respect to the total number of states included in the spectral summations. The asymptotic formula for the truncation error obtained in this way, whose dominant contribution is proportional to the cutoff energy to the power −3/2, may be adapted to extrapolate energy gaps in other systems.

A. Riefer, M. Rohrmüller, M. Landmann, S. Sanna, E. Rauls, N.J. Vollmers, R. Hölscher, M. Witte, Y. Li, U. Gerstmann, A. Schindlmayr, W.G. Schmidt, in: High Performance Computing in Science and Engineering ‘13, Springer, 2013, pp. 93-104

The frequency-dependent dielectric function and the second-order polarizability tensor of ferroelectric LiNbO3 are calculated from first principles. The calculations are based on the electronic structure obtained from density-functional theory. The subsequent application of the GW approximation to account for quasiparticle effects and the solution of the Bethe–Salpeter equation yield a dielectric function for the stoichiometric material that slightly overestimates the absorption onset and the oscillator strength in comparison with experimental measurements. Calculations at the level of the independent-particle approximation indicate that these deficiencies are at least partially related to the neglect of intrinsic defects typical for the congruent material. The second-order polarizability calculated within the independent-particle approximation predicts strong nonlinear coefficients for photon energies above 1.5 eV. The comparison with measured data suggests that self-energy effects improve the agreement between experiment and theory. The intrinsic defects of congruent samples reduce the optical nonlinearities, in particular for the 21 and 31 tensor components, further improving the agreement with measured data.

S. Yanagisawa, Y. Morikawa, A. Schindlmayr, Physical Review B (2013), 88(11)

We investigate the band dispersion and relevant electronic properties of rubrene single crystals within the GW approximation. Due to the self-energy correction, the dispersion of the highest occupied molecular orbital (HOMO) band increases by 0.10 eV compared to the dispersion of the Kohn-Sham eigenvalues within the generalized gradient approximation, and the effective hole mass consequently decreases. The resulting value of 0.90 times the electron rest mass along the Γ-Y direction in the Brillouin zone is closer to experimental measurements than that obtained from density-functional theory. The enhanced bandwidth is explained in terms of the intermolecular hybridization of the HOMO(Y) wave function along the stacking direction of the molecules. Overall, our results support the bandlike interpretation of charge-carrier transport in rubrene.

## 2012

C. Friedrich, M. Betzinger, M. Schlipf, S. Blügel, A. Schindlmayr, Journal of Physics: Condensed Matter (2012), 24(29)

We present recent advances in numerical implementations of hybrid functionals and the GW approximation within the full-potential linearized augmented-plane-wave (FLAPW) method. The former is an approximation for the exchange–correlation contribution to the total energy functional in density-functional theory, and the latter is an approximation for the electronic self-energy in the framework of many-body perturbation theory. All implementations employ the mixed product basis, which has evolved into a versatile basis for the products of wave functions, describing the incoming and outgoing states of an electron that is scattered by interacting with another electron. It can thus be used for representing the nonlocal potential in hybrid functionals as well as the screened interaction and related quantities in GW calculations. In particular, the six-dimensional space integrals of the Hamiltonian exchange matrix elements (and exchange self-energy) decompose into sums over vector–matrix–vector products, which can be evaluated easily. The correlation part of the GW self-energy, which contains a time or frequency dependence, is calculated on the imaginary frequency axis with a subsequent analytic continuation to the real axis or, alternatively, by a direct frequency convolution of the Green function G and the dynamically screened Coulomb interaction W along a contour integration path that avoids the poles of the Green function. Hybrid-functional and GW calculations are notoriously computationally expensive. We present a number of tricks that reduce the computational cost considerably, including the use of spatial and time-reversal symmetries, modifications of the mixed product basis with the aim to optimize it for the correlation self-energy and another modification that makes the Coulomb matrix sparse, analytic expansions of the interaction potentials around the point of divergence at k=0, and a nested density and density-matrix convergence scheme for hybrid-functional calculations. We show CPU timings for prototype semiconductors and illustrative results for GdN and ZnO.

## 2011

M. Wand, A. Schindlmayr, T. Meier, J. Förstner, Physica Status Solidi B (2011), 248(4), pp. 887-891

We present a nonequilibrium ab initio method for calculating nonlinear and nonlocal optical effects in metallic slabs with a thickness of several nanometers. The numerical analysis is based on the full solution of the time‐dependent Kohn–Sham equations for a jellium system and allows to study the optical response of metal electrons subject to arbitrarily shaped intense light pulses. We find a strong localization of the generated second‐harmonic current in the surface regions of the slabs.

M. Wand, A. Schindlmayr, T. Meier, J. Förstner, in: CLEO:2011 - Laser Applications to Photonic Applications , Optical Society of America, 2011

## 2010

A. Schindlmayr, C. Friedrich, E. Şaşıoğlu, S. Blügel, in: Modern and Universal First-Principles Methods for Many-Electron Systems in Chemistry and Physics, Oldenbourg, 2010, pp. 67-78

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.

A. Schindlmayr, C. Friedrich, E. Şaşıoğlu, S. Blügel, Zeitschrift für Physikalische Chemie (2010), 224(3-4), pp. 357-368

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.

E. Şaşıoğlu, A. Schindlmayr, C. Friedrich, F. Freimuth, S. Blügel, Physical Review B (2010), 81(5)

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.

C. Friedrich, S. Blügel, A. Schindlmayr, Physical Review B (2010), 81(12)

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.

C. Thierfelder, S. Sanna, A. Schindlmayr, W.G. Schmidt, Physica Status Solidi C (2010), 7(2), pp. 362-365

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.

M. Bouhassoune, A. Schindlmayr, Physica Status Solidi C (2010), 7(2), pp. 460-463

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.

## 2009

A. Schindlmayr, in: Theoretical and Computational Nanophotonics: Proceedings of the 2nd International Workshop, American Institute of Physics, 2009, pp. 157-159

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.

C. Friedrich, A. Schindlmayr, S. Blügel, Computer Physics Communications (2009), 180(3), pp. 347-359

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.

S.F. Feste, T. Schäpers, D. Buca, Q.T. Zhao, J. Knoch, M. Bouhassoune, A. Schindlmayr, S. Mantl, Applied Physics Letters (2009), 95(18)

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.

## 2008

C. Freysoldt, P. Eggert, P. Rinke, A. Schindlmayr, M. Scheffler, Physical Review B (2008), 77(23)

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.

## 2007

C. Freysoldt, P. Eggert, P. Rinke, A. Schindlmayr, R.W. Godby, M. Scheffler, Computer Physics Communications (2007), 176(1), pp. 1-13

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.

A. Schindlmayr, in: Probing the Nanoworld , Forschungszentrum Jülich, 2007, pp. A1.21-A1.36

S. Botti, A. Schindlmayr, R. Del Sole, L. Reining, Reports on Progress in Physics (2007), 70(3), pp. 357-407

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.

M. Friák, A. Schindlmayr, M. Scheffler, New Journal of Physics (2007), 9(1)

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.

A. Schindlmayr, M. Scheffler, in: Theory of Defects in Semiconductors, Springer, 2007, pp. 165-192

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.

## 2006

C. Friedrich, A. Schindlmayr, S. Blügel, T. Kotani, Physical Review B (2006), 74(4)

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.

A. Schindlmayr, in: Computational Condensed Matter Physics, Forschungszentrum Jülich, 2006, pp. A4.1-A4.19

M. Hedström, A. Schindlmayr, G. Schwarz, M. Scheffler, Physical Review Letters (2006), 97(22)

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.

C. Friedrich, A. Schindlmayr, in: Computational Nanoscience: Do It Yourself!, John von Neumann Institute for Computing, 2006, pp. 335-355

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.

C. Friedrich, A. Schindlmayr, in: Computational Condensed Matter Physics, Forschungszentrum Jülich, 2006, pp. A5.1-A5.21

## 2005

A. Schindlmayr, in: Magnetism goes Nano, Forschungszentrum Jülich, 2005, pp. D1.1-D1.20

## 2002

M. Hedström, A. Schindlmayr, M. Scheffler, Physica Status Solidi B (2002), 234(1), pp. 346-353

We discuss the implementation of quasiparticle calculations for point defects on semiconductor surfaces and, as a specific example, present an ab initio study of the electronic structure of the As vacancy in the +1 charge state on the GaAs(110) surface. The structural properties are calculated with the plane‐wave pseudopotential method, and the quasiparticle energies are obtained from Hedin's GW approximation. Our calculations show that the 1a″ vacancy state in the band gap is shifted from 0.06 to 0.65 eV above the valence‐band maximum after the self‐energy correction to the Kohn‐Sham eigenvalues. The GW result is in close agreement with a recent surface photovoltage imaging measurement.

## 2001

A. Schindlmayr, in: Recent Research Developments in Physics, Transworld Research Network, 2001, pp. 277-288

K. Tatarczyk, A. Schindlmayr, M. Scheffler, Physical Review B (2001), 63(23)

The performance of several common approximations for the exchange-correlation kernel within time-dependent density-functional theory is tested for elementary excitations in the homogeneous electron gas. Although the adiabatic local-density approximation gives a reasonably good account of the plasmon dispersion, systematic errors are pointed out and traced to the neglect of the wave-vector dependence. Kernels optimized for atoms are found to perform poorly in extended systems due to an incorrect behavior in the long-wavelength limit, leading to quantitative deviations that significantly exceed the experimental error bars for the plasmon dispersion in the alkali metals.

A. Schindlmayr, P. García-González, R.W. Godby, Physical Review B (2001), 64(23)

There is increasing interest in many-body perturbation theory as a practical tool for the calculation of ground-state properties. As a consequence, unambiguous sum rules such as the conservation of particle number under the influence of the Coulomb interaction have acquired an importance that did not exist for calculations of excited-state properties. In this paper we obtain a rigorous, simple relation whose fulfilment guarantees particle-number conservation in a given diagrammatic self-energy approximation. Hedin’s G0W0 approximation does not satisfy this relation and hence violates the particle-number sum rule. Very precise calculations for the homogeneous electron gas and a model inhomogeneous electron system allow the extent of the nonconservation to be estimated.

## 2000

A. Schindlmayr, Physical Review B (2000), 62(19), pp. 12573-12576

The decay properties of the one-particle Green function in real space and imaginary time are systematically studied for solids. I present an analytic solution for the homogeneous electron gas at finite and at zero temperature as well as asymptotic formulas for real metals and insulators that allow an analytic treatment in electronic-structure calculations based on a space-time representation. The generic dependence of the decay constants on known system parameters is used to compare the scaling of reciprocal-space algorithms for the GW approximation and the space-time method.

## 1999

A. Schindlmayr, American Journal of Physics (1999), 67(10), pp. 933-934

## 1998

A. Schindlmayr, R.W. Godby, Physical Review Letters (1998), 80(8), pp. 1702-1705

We present a general procedure for obtaining progressively more accurate functional expressions for the electron self-energy by iterative solution of Hedin's coupled equations. The iterative process starting from Hartree theory, which gives rise to the GW approximation, is continued further, and an explicit formula for the vertex function from the second full cycle is given. Calculated excitation energies for a Hubbard Hamiltonian demonstrate the convergence of the iterative process and provide further strong justification for the GW approximation.

T.J. Pollehn, A. Schindlmayr, R.W. Godby, Journal of Physics: Condensed Matter (1998), 10(6), pp. 1273-1283

We investigate the performance of the GW approximation by comparison to exact results for small model systems. The role of the chemical potentials in Dyson's equation as well as the consequences of numerical resonance broadening are examined, and we show how a proper treatment can improve computational implementations of many-body perturbation theory in general. Exchange-only and GW calculations are performed over a wide range of fractional band fillings and correlation strengths. We thus identify the physical situations where these schemes are applicable.

A. Schindlmayr, T.J. Pollehn, R.W. Godby, Physical Review B (1998), 58(19), pp. 12684-12690

With the aim of identifying universal trends, we compare fully self-consistent electronic spectra and total energies obtained from the GW approximation with those from an extended GWΓ scheme that includes a nontrivial vertex function and the fundamentally distinct Bethe-Goldstone approach based on the T matrix. The self-consistent Green’s function G, as derived from Dyson’s equation, is used not only in the self-energy but also to construct the screened interaction W for a model system. For all approximations we observe a similar deterioration of the spectrum, which is not removed by vertex corrections. In particular, satellite peaks are systematically broadened and move closer to the chemical potential. The corresponding total energies are universally raised, independent of the system parameters. Our results, therefore, suggest that any improvement in total energy due to self-consistency, such as for the electron gas in the GW approximation, may be fortuitous.

## 1997

A. Schindlmayr, European Journal of Physics (1997), 18(5), pp. 374-376

We present a simple analytic scheme for calculating the binding energy of excitons in semiconductors that takes full account of the existing anisotropy in the effective mass, as a complement to the qualitative treatment in most textbooks. Results obtained for excitons in gallium nitride form the basis for a discussion of the accuracy of this approach.

A. Schindlmayr, Physical Review B (1997), 56(7), pp. 3528-3531

We present a nontrivial model system of interacting electrons that can be solved analytically in the GW approximation. We obtain the particle number from the GW Green’s function strictly analytically, and prove that there is a genuine violation of particle number conservation if the self-energy is calculated non-self-consistently from a zeroth order Green’s function, as done in virtually all practical implementations. We also show that a simple shift of the self-energy that partially restores self-consistency reduces the numerical deviation significantly.

## 1995

A. Schindlmayr, R.W. Godby, Physical Review B (1995), 51(16), pp. 10427-10435

Inspired by earlier work on the band-gap problem in insulators, we reexamine the treatment of strongly correlated Hubbard-type models within density-functional theory. In contrast to previous studies, the density is fully parametrized by occupation numbers and overlap of orbitals centered at neighboring atomic sites, as is the local potential by the hopping matrix. This corresponds to a good formal agreement between density-functional theory in real space and second quantization. It is shown that density-functional theory is formally applicable to such systems and the theoretical framework is provided. The question of noninteracting v representability is studied numerically for finite one-dimnsional clusters, for which exact results are available, and qualitatively for infinite systems. This leads to the conclusion that the electron density corresponding to interacting systems of the type studied here is in fact not noninteracting v representable because the Kohn-Sham electrons are unable to reproduce the correlation-induced localization correctly.

##### Head

### Prof. Dr. Arno Schindlmayr

Many-Body Theory of Solids