Derivation of Miller's rule for the nonlinear optical susceptibility of a quantum anharmonic oscillator - Meyer, Maximilian Tim; Schindlmayr, Arno (Journal of Physics B: Atomic, Molecular and Optical Physics)
Miller's rule is an empirical relation between the nonlinear and linear optical coefficients that applies to a large class of materials but has only been rigorously derived for the classical Lorentz model with a weak anharmonic perturbation. In this work, we extend the proof and present a detailed derivation of Miller's rule for an equivalent quantum-mechanical anharmonic oscillator. For this purpose, the classical concept of velocity-dependent damping inherent to the Lorentz model is replaced by an adiabatic switch-on of the external electric field, which allows a unified treatment of the classical and quantum-mechanical systems using identical potentials and fields. Although the dynamics of the resulting charge oscillations, and hence the induced polarizations, deviate due to the finite zero-point motion in the quantum-mechanical framework, we find that Miller's rule is nevertheless identical in both cases up to terms of first order in the anharmonicity. With a view to practical applications, especially in the context of ab initio calculations for the optical response where adiabatically switched-on fields are widely assumed, we demonstrate that a correct treatment of finite broadening parameters is essential to avoid spurious errors that may falsely suggest a violation of Miller's rule, and we illustrate this point by means of a numerical example.

Electron polarons in lithium niobate: Charge localization, lattice deformation, and optical response - Schmidt, Falko; Kozub, Agnieszka L.; Gerstmann, Uwe; Schmidt, Wolf Gero; Schindlmayr, Arno (New Trends in Lithium Niobate: From Bulk to Nanocrystals)
Lithium niobate (LiNbO3), a material frequently used in optical applications, hosts different kinds of polarons that significantly affect many of its physical properties. In this study, a variety of electron polarons, namely free, bound, and bipolarons, are analyzed using first-principles calculations. We perform a full structural optimization based on density-functional theory for selected intrinsic defects with special attention to the role of symmetry-breaking distortions that lower the total energy. The cations hosting the various polarons relax to a different degree, with a larger relaxation corresponding to a larger gap between the defect level and the conduction-band edge. The projected density of states reveals that the polaron states are formerly empty Nb 4d states lowered into the band gap. Optical absorption spectra are derived within the independent-particle approximation, corrected by the GW approximation that yields a wider band gap and by including excitonic effects within the Bethe-Salpeter equation. Comparing the calculated spectra with the density of states, we find that the defect peak observed in the optical absorption stems from transitions between the defect level and a continuum of empty Nb 4d states. Signatures of polarons are further analyzed in the reflectivity and other experimentally measurable optical coefficients.

Programmierung und Computersimulationen - Schindlmayr, Arno (Kompetent Prüfungen gestalten: 60 Prüfungsformate für die Hochschullehre)
Dieses Format eignet sich, um zu prüfen, inwieweit Studierende Computersimulationen und eigene kleine Programme zur Lösung typischer Probleme ihres Fachs nutzen können. Wie bei Klausuren erfolgt die Bearbeitung in begrenzter Zeit und unter Aufsicht, wird aber am Computer durchgeführt und beinhaltet neben der Programmierung auch vor- und nachbereitende Aufgaben im Kontext der fachlichen Anwendung.

Quasiparticle energies and optical response of RbTiOPO4 and KTiOAsO4 - Neufeld, Sergej; Schindlmayr, Arno; Schmidt, Wolf Gero (Journal of Physics: Materials)
Many-body perturbation theory based on density-functional theory calculations is used to determine the quasiparticle band structures and the dielectric functions of the isomorphic ferroelectrics rubidium titanyl phosphate (RbTiOPO4) and potassium titanyl arsenide (KTiOAsO4). Self-energy corrections of more than 2 eV are found to widen the transport band gaps of both materials considerably to 5.3 and 5.2 eV, respectively. At the same time, both materials are characterized by strong exciton binding energies of 1.4 and 1.5 eV, respectively. The solution of the Bethe-Salpeter equation based on the quasiparticle energies results in onsets of the optical absorption within the range of the measured data.

A density-functional theory study of hole and defect-bound exciton polarons in lithium niobate - Schmidt, Falko; Kozub, Agnieszka L.; Gerstmann, Uwe; Schmidt, Wolf Gero; Schindlmayr, Arno (Crystals)
Hole polarons and defect-bound exciton polarons in lithium niobate are investigated by means of density-functional theory, where the localization of the holes is achieved by applying the +U approach to the oxygen 2p orbitals. We find three principal configurations of hole polarons: (i) self-trapped holes localized at displaced regular oxygen atoms and (ii) two other configurations bound to a lithium vacancy either at a threefold coordinated oxygen atom above or at a two-fold coordinated oxygen atom below the defect. The latter is the most stable and is in excellent quantitative agreement with measured g factors from electron paramagnetic resonance. Due to the absence of mid-gap states, none of these hole polarons can explain the broad optical absorption centered between 2.5 and 2.8 eV that is observed in transient absorption spectroscopy, but such states appear if a free electron polaron is trapped at the same lithium vacancy as the bound hole polaron, resulting in an exciton polaron. The dielectric function calculated by solving the Bethe–Salpeter equation indeed yields an optical peak at 2.6 eV in agreement with the two-photon experiments. The coexistence of hole and exciton polarons, which are simultaneously created in optical excitations, thus satisfactorily explains the reported experimental data.

Electron polarons in lithium niobate: Charge localization, lattice deformation, and optical response - Schmidt, Falko; Kozub, Agnieszka L.; Gerstmann, Uwe; Schmidt, Wolf Gero; Schindlmayr, Arno (Crystals)
Lithium niobate (LiNbO3), a material frequently used in optical applications, hosts different kinds of polarons that significantly affect many of its physical properties. In this study, a variety of electron polarons, namely free, bound, and bipolarons, are analyzed using first-principles calculations. We perform a full structural optimization based on density-functional theory for selected intrinsic defects with special attention to the role of symmetry-breaking distortions that lower the total energy. The cations hosting the various polarons relax to a different degree, with a larger relaxation corresponding to a larger gap between the defect level and the conduction-band edge. The projected density of states reveals that the polaron states are formerly empty Nb 4d states lowered into the band gap. Optical absorption spectra are derived within the independent-particle approximation, corrected by the GW approximation that yields a wider band gap and by including excitonic effects within the Bethe-Salpeter equation. Comparing the calculated spectra with the density of states, we find that the defect peak observed in the optical absorption stems from transitions between the defect level and a continuum of empty Nb 4d states. Signatures of polarons are further analyzed in the reflectivity and other experimentally measurable optical coefficients.

Lattice parameters and electronic band gap of orthorhombic potassium sodium niobate K0.5Na0.5NbO3 from density-functional theory - Bidaraguppe Ramesh, Nithin; Schmidt, Falko; Schindlmayr, Arno (The European Physical Journal B)
We perform a theoretical analysis of the structural and electronic properties of sodium potassium niobate K1-xNaxNbO3 in the orthorhombic room-temperature phase, based on density-functional theory in combination with the supercell approach. Our results for x=0 and x=0.5 are in very good agreement with experimental measurements and establish that the lattice parameters decrease linearly with increasing Na contents, disproving earlier theoretical studies based on the virtual-crystal approximation that claimed a highly nonlinear behavior with a significant structural distortion and volume reduction in K0.5Na0.5NbO3 compared to both end members of the solid solution. Furthermore, we find that the electronic band gap varies very little between x=0 and x=0.5, reflecting the small changes in the lattice parameters.

Erratum: Efficient implementation of the GW approximation within the all-electron FLAPW method [Phys. Rev. B 81, 125102 (2010)] - Friedrich, Christoph; Blügel, Stefan; Schindlmayr, Arno (Physical Review B)

Polaronic enhancement of second-harmonic generation in lithium niobate - Kozub, Agnieszka L.; Schindlmayr, Arno; Gerstmann, Uwe; Schmidt, Wolf Gero (Physical Review B)
Density-functional theory within a Berry-phase formulation of the dynamical polarization is used to determine the second-order susceptibility χ(2) of lithium niobate (LiNbO3). Defect trapped polarons and bipolarons are found to strongly enhance the nonlinear susceptibility of the material, in particular if localized at NbV–VLi defect pairs. This is essentially a consequence of the polaronic excitation resulting in relaxation-induced gap states. The occupation of these levels leads to strongly enhanced χ(2) coefficients and allows for the spatial and transient modification of the second-harmonic generation of macroscopic samples.

Free and defect-bound (bi)polarons in LiNbO3: Atomic structure and spectroscopic signatures from ab initio calculations - Schmidt, Falko; Kozub, Agnieszka L.; Biktagirov, Timur; Eigner, Christof; Silberhorn, Christine; Schindlmayr, Arno; Schmidt, Wolf Gero; Gerstmann, Uwe (Physical Review Research)
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.

Quasiparticle and excitonic effects in the optical response of KNbO3 - Schmidt, Falko; Riefer, Arthur; Schmidt, Wolf Gero; Schindlmayr, Arno; Imlau, Mirco; Dobener, Florian; Mengel, Nils; Chatterjee, Sangam; Sanna, Simone (Physical Review Materials)
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.

Potassium titanyl phosphate (KTP) quasiparticle energies and optical response - Neufeld, Sergej; Bocchini, Adriana; Gerstmann, Uwe; Schindlmayr, Arno; Schmidt, Wolf Gero (Journal of Physics: Materials)
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.

Exact formulation of the transverse dynamic spin susceptibility as an initial-value problem - Schindlmayr, Arno (Advances in Mathematical Physics)
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.

Erratum: Optical properties of titanium-doped lithium niobate from time-dependent density-functional theory [Phys. Rev. Materials 1, 034401 (2017)] - Friedrich, Michael; Schmidt, Wolf Gero; Schindlmayr, Arno; Sanna, Simone (Physical Review Materials)

Zn–VI quasiparticle gaps and optical spectra from many-body calculations - Riefer, Arthur; Weber, Nils; Mund, Johannes; Yakovlev, Dmitri R.; Bayer, Manfred; Schindlmayr, Arno; Meier, Cedrik; Schmidt, Wolf Gero (Journal of Physics: Condensed Matter)
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.

Polaron optical absorption in congruent lithium niobate from time-dependent density-functional theory - Friedrich, Michael; Schmidt, Wolf Gero; Schindlmayr, Arno; Sanna, Simone (Physical Review Materials)
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.

Optical properties of titanium-doped lithium niobate from time-dependent density-functional theory - Friedrich, Michael; Schmidt, Wolf Gero; Schindlmayr, Arno; Sanna, Simone (Physical Review Materials)
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.

Consistent atomic geometries and electronic structure of five phases of potassium niobate from density-functional theory - Schmidt, Falko; Landmann, Marc; Rauls, Eva; Argiolas, Nicola; Sanna, Simone; Schmidt, Wolf Gero; Schindlmayr, Arno (Advances in Materials Science and Engineering)
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.

LiNbO3 electronic structure: Many-body interactions, spin-orbit coupling, and thermal effects - Riefer, Arthur; Friedrich, Michael; Sanna, Simone; Gerstmann, Uwe; Schindlmayr, Arno; Schmidt, Wolf Gero (Physical Review B)
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.

LiTaO3 phonon dispersion and ferroelectric transition calculated from first principles - Friedrich, Michael; Schindlmayr, Arno; Schmidt, Wolf Gero; Sanna, Simone (Physica Status Solidi B)
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.