08 Fakultät Mathematik und Physik
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Item Open Access From ground state properties to high energy spectroscopy : extending the application of DMFT for correlated quantum materials(2020) Schmid, Michael; Daghofer, Maria (Prof. Dr.)Strongly correlated electron systems exhibit rich physical phenomena reaching from superconductivity, Kondo- and, Mott physics to novel magnetic phases, which lie beyond most single-particle approaches such as density functional theory (DFT) or static mean-field theory. For many transition metal oxides (TMOs) such as Ca2RuO4 or LiV2O4 this is often a result of the partially filled d shells, leading to many-body wave functions, which cannot expressed as a single-slater determinant. Moreover, within this compounds there is often no clear hierarchy of energy scales, e.g. strong spin-orbit coupling, Hund’s coupling, and crystal-field splitting, making the description with minimal models difficult. The breakdown of the single-particle picture triggered the development of numerous numerical methods (DMFT, DMRG, VCA, . . . ) within the last decades, all aimed at tackling the aforementioned phenomena with complementary approximations. One of the most prominent methods for describing real compounds has become dynamical mean-field theory (DMFT), which in many cases has proven to describe local electronic phenomena in good agreement with experimental results. In this thesis we perform state of the art DFT+DMFT calculations in its single shot approach to complement theoretical k-resolved one-particle spectral functions to neutron and x-ray diffraction experiments on Ca2RuO4 . In the experiment small DC currents were applied to a Ca2RuO4 single-crystal resulting in the stabilization of new nonequilibrium phases. Based on experimentally refined structures, DFT calculations are performed to extract a tight binding model by projecting the correlated t2g -subspace onto maximally localized Wannier orbitals. Within our DMFT calculations spin-orbit coupling (SOC) and the spherical invariant Coulomb interaction are added to calculate spectral functions. The results indicate a semimetalic state with partially gapped Fermi surface in the nonequilibrium phases with elongated RuO6 octahedra. Additionally, we extend the DFT+DMFT scheme by a discretization scheme to obtain core-level spectroscopy data, such as XAS or RIXS spectra. This concept is based on the discretization of the DMFT hybridization function to construct an Anderson impurity model of finite bath sites. The discretized model is then extended by the core levels and core-valence interaction. To include sufficiently large amounts of bath sites, despite using an exact diagonalization (ED) solver, we choose the natural orbital basis as the single particle basis of choice to compute RIXS and XAS spectra.Item Open Access NMR investigations on alkali intercalated carbon nanotubes(2005) Schmid, Michael; Mehring, Michael (Prof.)In the present work, nuclear magnetic resonance (NMR) experiments were carried out on Lithium and Cesium intercalated single-walled carbon nanotube (SWNT) bundles. The alkali metals were intercalated in raw SWNT as starting material. The raw nanotubes are supposed to possess closed end caps whereby possible alkali adsorption sites are only provided by the interstitial channels as well as the surface of a carbon nanotube bundle. The interior space of the present SWNT is supposed to be predominantly inaccessible for penetration by alkali atoms. Lithium was chemically intercalated in SWNT bundles by using solutions of aromatic hydrocarbons, the solving agent tetrahydrofuran (THF) and SWNT. 13C NMR measurements enabled to follow the density of states at the Fermi level for various Li intercalation stoichiometries. Generally, pristine SWNT consist of a mixture of metallic and semiconducting SWNT. Upon intercalation and subsequent Li-C electron charge transfer the Fermi level is tuned. The intercalated system reveals a pure metallic behavior and a signature for semiconducting SWNT cannot be found any more. However, at higher Li intercalation stoichiometries an incomplete electron charge transfer is observed. 7Li NMR experiments show the presence of two types of Li-nuclei with different environments in the SWNT bundles: at low intercalation levels first, completely ionized alpha-type Li ions are intercalated, whereas at higher stoichiometries a second type of partially ionized beta-type Li is adsorbed by the SWNT host. The above sketched charge transfer limitation is explained by the presence of partially ionized Li(beta)+ ions, which show a hybridization of the Li(2s) orbitals with the SWNT C(2p) orbitals. 7Li NMR demonstrates a remarkable Knight shift for these beta-type Li nuclei as well as a strong hyperfine coupling to SWNT conduction electrons. The alpha-type Li+ ions exhibit a high-temperature dynamical process which is interpreted as a Li(alpha)+ cation diffusion along the interstitial channels of the SWNT bundles. 1H NMR investigations were carried out in order to investigate the role of the THF solvent molecules. The experiments provide evidence for the existence of two types of inequivalent THF solvent molecules. They are most likely coupled by a thermally activated exchange process. At temperatures below 300 K, THF molecules are perpendicularly arranged in between adjacent SWNT and exhibit an axial rotation around their dipolar axis. The Li+ cations are located halfway between adjacent SWNT and pin the oxygen-(THF) atoms to their immediate neighborhood. Above room temperature, THF molecules detach from the SWNT and start to isotropically rotate and diffuse along the interstitial channels of the SWNT bundles. Remarkable diamagnetic shifts of the 1H NMR lines can be explained with an extremely large diamagnetic shielding of the carbon nanotube bundles since the SWNT exhibit highly anisotropic diamagnetic susceptibilities. Various stoichiometries of vapor phase Cs intercalated SWNT bundles were investigated. 13C NMR MAS and MAT experiments show the presence of two different types of carbon environments in all intercalated samples. The two carbon environments can be explained with the finite size effect and therewith the bulk- and surface susceptibility of the SWNT bundles as well as a localized density of states due to Cs ions located close to SWNT. Comparable to Li intercalation in SWNT, 13C NMR spin-lattice relaxation measurements enabled to determine the density of states at the Fermi level. The increase of the density of states upon intercalation enhances the metallicity of the SWNT system and no semiconducting SWNT are observable any more. However, at higher intercalation levels a Cs-C electron charge transfer limitation is observed. 133Cs NMR measurements indicate the presence of two coexisting types of Cs ions intercalated in the SWNT bundle. At low intercalation levels fully ionized Cs(alpha)+ ions are exclusively intercalated, whereas at higher Cs stoichiometries a second type of Cs(beta)+ ions is additionally intercalated in the SWNT bundle. The Cs(alpha)+ ions exhibit a thermally activated slow-motion diffusion process along the interstitial channels of the SWNT bundle as well as an inter-channel diffusion perpendicular to the SWNT bundle. The Cs(beta)+ ions are only subject to a weakly temperature dependence of the electric field gradient at the site of the Cs nuclei which suggests a highly structural molecular Cs. Possibly the Cs+ ions occupy well defined atom positions relative to the carbon lattice covering the SWNT fragmentarily. 133Cs NMR Korringa relaxation behavior and Knight shifts suggest a Cs(6s) - C(2p) hybridization for the Cs(beta)+ ions which explains the observed charge transfer limitation at higher Cs stoichiometries.