TY - JOUR AB - 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. AU - Meyer, Maximilian Tim AU - Schindlmayr, Arno ID - 52723 JF - Journal of Physics B: Atomic, Molecular and Optical Physics SN - 0953-4075 TI - Derivation of Miller's rule for the nonlinear optical susceptibility of a quantum anharmonic oscillator ER - TY - CHAP AB - 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. AU - Schmidt, Falko AU - Kozub, Agnieszka L. AU - Gerstmann, Uwe AU - Schmidt, Wolf Gero AU - Schindlmayr, Arno ED - Corradi, Gábor ED - Kovács, László ID - 30288 SN - 978-3-0365-3340-7 T2 - New Trends in Lithium Niobate: From Bulk to Nanocrystals TI - Electron polarons in lithium niobate: Charge localization, lattice deformation, and optical response ER - TY - JOUR AB - 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. AU - Neufeld, Sergej AU - Schindlmayr, Arno AU - Schmidt, Wolf Gero ID - 26627 IS - 1 JF - Journal of Physics: Materials TI - Quasiparticle energies and optical response of RbTiOPO4 and KTiOAsO4 VL - 5 ER - TY - CHAP AB - 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. AU - Schindlmayr, Arno ED - Gerick, Julia ED - Sommer, Angela ED - Zimmermann, Germo ID - 29808 SN - 9783825258597 T2 - Kompetent Prüfungen gestalten: 60 Prüfungsformate für die Hochschullehre TI - Programmierung und Computersimulationen ER - TY - JOUR AB - 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. AU - Schmidt, Falko AU - Kozub, Agnieszka L. AU - Gerstmann, Uwe AU - Schmidt, Wolf Gero AU - Schindlmayr, Arno ID - 44088 IS - 11 JF - Crystals TI - A density-functional theory study of hole and defect-bound exciton polarons in lithium niobate VL - 12 ER - TY - JOUR AB - 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. AU - Schmidt, Falko AU - Kozub, Agnieszka L. AU - Gerstmann, Uwe AU - Schmidt, Wolf Gero AU - Schindlmayr, Arno ID - 21946 JF - Crystals TI - Electron polarons in lithium niobate: Charge localization, lattice deformation, and optical response VL - 11 ER - TY - JOUR AB - 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. AU - Bidaraguppe Ramesh, Nithin AU - Schmidt, Falko AU - Schindlmayr, Arno ID - 22960 IS - 8 JF - The European Physical Journal B SN - 1434-6028 TI - Lattice parameters and electronic band gap of orthorhombic potassium sodium niobate K0.5Na0.5NbO3 from density-functional theory VL - 94 ER - TY - JOUR AU - Friedrich, Christoph AU - Blügel, Stefan AU - Schindlmayr, Arno ID - 22761 IS - 3 JF - Physical Review B SN - 2469-9950 TI - Erratum: Efficient implementation of the GW approximation within the all-electron FLAPW method [Phys. Rev. B 81, 125102 (2010)] VL - 104 ER - TY - JOUR AB - 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. AU - Kozub, Agnieszka L. AU - Schindlmayr, Arno AU - Gerstmann, Uwe AU - Schmidt, Wolf Gero ID - 23418 JF - Physical Review B SN - 2469-9950 TI - Polaronic enhancement of second-harmonic generation in lithium niobate VL - 104 ER - TY - JOUR AB - 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. AU - Schmidt, Falko AU - Kozub, Agnieszka L. AU - Biktagirov, Timur AU - Eigner, Christof AU - Silberhorn, Christine AU - Schindlmayr, Arno AU - Schmidt, Wolf Gero AU - Gerstmann, Uwe ID - 19190 IS - 4 JF - Physical Review Research TI - Free and defect-bound (bi)polarons in LiNbO3: Atomic structure and spectroscopic signatures from ab initio calculations VL - 2 ER -