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In this thesis we study strongly correlated electron systems within the Density Functional Theory (DFT) in combination with the Dynamical Mean-Field Theory (DMFT).
First, we give an introduction into the theoretical methods and then apply them to study realistic materials. We present results on the hole-doped 122-family of the iron-based superconductors and the transition-metal oxide SrVO3. Our investigations show that a proper treatment of strong electronic correlations is necessary to describe the experimental observations.

One of the most challenging problems in solid state systems is the microscopic analysis of electronic correlations. A paramount minimal model that encodes correlation effects is the Hubbard Hamiltonian, which—regardless of its simplicity—is exactly solvable only in a few limiting cases and approximate many-body methods are required for its solution. In this review, an overview on the non-perturbative two-particle self-consistent method (TPSC), which was originally introduced to describe the electronic properties of the single-band Hubbard model, is presented. A detailed derivation of the multi-orbital generalization of TPSC is introduced here and particular features of the method on exemplary interacting models in comparison to dynamical mean-field theory results are discussed.

Formation of Hubbard-like bands as a fingerprint of strong electron-electron interactions in FeSe
(2017)

We use angle-resolved photo-emission spectroscopy (ARPES) to explore the electronic structure of single crystals of FeSe over a wide range of binding energies and study the effects of strong electron-electron correlations. We provide evidence for the existence of "Hubbard-like bands" at high binding energies consisting of incoherent many-body excitations originating from Fe 3d states in addition to the renormalized quasiparticle bands near the Fermi level. Many high energy features of the observed ARPES data can be accounted for when incorporating effects of strong local Coulomb interactions in calculations of the spectral function via dynamical mean-field theory, including the formation of a Hubbard-like band. This shows that over the energy scale of several eV, local correlations arising from the on-site Coulomb repulsion and Hund's coupling are essential for a proper understanding of the electronic structure of FeSe and other related iron based superconductors.

Recent density functional theory (DFT) calculations for KFe2As2 have been shown to be insufficient to satisfactorily describe angle-resolved photoemission (ARPES) measurements as well as observed de Haas–van Alphen (dHvA) frequencies. In the present work, we extend DFT calculations based on the full-potential linear augmented plane-wave method by dynamical mean field theory (DFT+DMFT) to include correlation effects beyond the local density approximation. We present results for two sets of reported crystal structures. Our calculations indicate that KFe2As2 is a moderately correlated metal with a mass renormalization factor of the Fe $3{\rm d}$ orbitals between 1.6 and 2.7. Furthermore, the obtained shape and size of the Fermi surface are in good agreement with ARPES measurements and we observe some topological changes with respect to DFT calculations such as the opening of an inner hole cylinder at the Z point. As a result, our calculated dHvA frequencies differ greatly from existing DFT results and qualitatively agree with experimental data. On this basis, we argue that correlation effects are important to understand the -presently under debate- nature of the superconducting state in KFe2As2.

Electronic and magnetic properties of the RuX3 (X=Cl, Br, I) family: two siblings - and a cousin?
(2022)

Motivated by reports of metallic behavior in the recently synthesized RuI3, in contrast to the Mott-insulating nature of the actively discussed α-RuCl3, as well as RuBr3, we present a detailed comparative analysis of the electronic and magnetic properties of this family of trihalides. Using a combination of first-principles calculations and effective-model considerations, we conclude that RuI3, similarly to the other two members, is most probably on the verge of a Mott insulator, but with much smaller magnetic moments and strong magnetic frustration. We predict the ideal pristine crystal of RuI3 to have a nearly vanishing conventional nearest-neighbor Heisenberg interaction and to be a quantum spin liquid candidate of a possibly different kind than the Kitaev spin liquid. In order to understand the apparent contradiction to the reported resistivity ρ, we analyze the experimental evidence for all three compounds and propose a scenario for the observed metallicity in existing samples of RuI3. Furthermore, for the Mott insulator RuBr3, we obtain a magnetic Hamiltonian of a similar form to that in the much-discussed α-RuCl3 and show that this Hamiltonian is in agreement with experimental evidence in RuBr3.

Motivated by recent reports of a quantum-disordered ground state in the triangular lattice compound NaRuO2, we derive a jeff = 1/2 magnetic model for this system by means of first-principles calculations. The pseudospin Hamiltonian is dominated by bond-dependent off-diagonal Γ interactions, complemented by a ferromagnetic Heisenberg exchange and a notably antiferromagnetic Kitaev term. In addition to bilinear interactions, we find a sizable four-spin ring exchange contribution with a strongly anisotropic character, which has been so far overlooked when modeling Kitaev materials. The analysis of the magnetic model, based on the minimization of the classical energy and exact diagonalization of the quantum Hamiltonian, points toward the existence of a rather robust easy-plane ferromagnetic order, which cannot be easily destabilized by physically relevant perturbations.