Cette thèse traite de la structure électronique de supraconducteurs telle que déterminée par la théorie de la fonctionnelle de la densité. Une brève explication de cette théorie est faite dans l’introduction. Le modèle de Hubbard est présenté pour pallier à des problèmes de cette théorie face à certains matériaux, dont les cuprates. L’union de deux théories donne la DFT+U, une méthode permettant de bien représenter certains systèmes ayant des électrons fortement corrélés. Par la suite, un article traitant du couplage électron- phonon dans le supraconducteur NbC1−xNx est présenté. Les résultats illustrent bien le rôle de la surface de Fermi dans le mécanisme d’appariement électronique menant à la supraconductivité. Grâce à ces résultats, un modèle est développé qui permet d’expliquer comment la température de transition critique est influencée par le changement des fré- quences de vibration du cristal. Ensuite, des résultats de calcul d’oscillations quantiques obtenus par une analyse approfondie de surfaces de Fermi, permettant une comparaison directe avec des données expérimentales, sont présentés dans deux articles. Le premier traite d’un matériau dans la famille des pnictures de fer, le LaFe2P2. L’absence de su- praconductivité dans ce matériau s’explique par la différence entre sa surface de Fermi obtenue et celle du supraconducteur BaFe2As2. Le second article traite du matériau à fermions lourds, le YbCoIn5. Pour ce faire, une nouvelle méthode efficace de calcul des fréquences de Haas-van Alphen est développée. Finalement, un dernier article traitant du cuprate supraconducteur à haute température critique YBa2Cu3O6.5 est présenté. À l’aide de la DFT+U, le rôle de plusieurs ordres magnétiques sur la surface de Fermi est étudié. Ces résultats permettent de mieux comprendre les mesures d’oscillations quan- tiques mesurées dans ce matériau. / In this thesis, the electronic structure of different kinds of superconductors is explored with the density functional theory. A brief explanation of this theory is done in the in- troduction. The Hubbard model is also presented as it can be used to solve shortcomings of the theory in some materials such as cuprates. The blend of the two theories is the DFT+U which is used to describe materials with strongly correlated electrons. After- ward, a paper describing the electron-phonon coupling in the superconductor NbC1−xNx is presented. Results from this work show the role of the Fermi surface in the electron pairing mechanism leading to superconductivity. Based on these results, a model is de- veloped explaining how the critical temperature is influenced by the change in frequency of the vibration modes. Then, quantum oscillation results based on a detailed analysis of Fermi surfaces, allowing a direct comparison with experimental data, are presented within two papers. The first one is about a material in the iron pnictide family, the LaFe2P2. Our calculations show that the Fermi surface of this material is different from the superconducting doped BaFe2As2 which explains why this material shows no sign of superconductivity. The second paper is about the heavy fermion system YbCoIn5. To do this, a new efficient method to calculate de Haas-van Alphen frequencies is developed. Finally, a paper on superconducting YBa2Cu3O6.5 is presented. Using DFT+U, the role of various magnetic orders on the Fermi surface are studied. The results allow a better understanding of the measured quantum oscillations in this material.

Cette thèse traite de la structure électronique de supraconducteurs telle que déterminée par la théorie de la fonctionnelle de la densité. Une brève explication de cette théorie est faite dans l’introduction. Le modèle de Hubbard est présenté pour pallier à des problèmes de cette théorie face à certains matériaux, dont les cuprates. L’union de deux théories donne la DFT+U, une méthode permettant de bien représenter certains systèmes ayant des électrons fortement corrélés. Par la suite, un article traitant du couplage électron- phonon dans le supraconducteur NbC1−xNx est présenté. Les résultats illustrent bien le rôle de la surface de Fermi dans le mécanisme d’appariement électronique menant à la supraconductivité. Grâce à ces résultats, un modèle est développé qui permet d’expliquer comment la température de transition critique est influencée par le changement des fré- quences de vibration du cristal. Ensuite, des résultats de calcul d’oscillations quantiques obtenus par une analyse approfondie de surfaces de Fermi, permettant une comparaison directe avec des données expérimentales, sont présentés dans deux articles. Le premier traite d’un matériau dans la famille des pnictures de fer, le LaFe2P2. L’absence de su- praconductivité dans ce matériau s’explique par la différence entre sa surface de Fermi obtenue et celle du supraconducteur BaFe2As2. Le second article traite du matériau à fermions lourds, le YbCoIn5. Pour ce faire, une nouvelle méthode efficace de calcul des fréquences de Haas-van Alphen est développée. Finalement, un dernier article traitant du cuprate supraconducteur à haute température critique YBa2Cu3O6.5 est présenté. À l’aide de la DFT+U, le rôle de plusieurs ordres magnétiques sur la surface de Fermi est étudié. Ces résultats permettent de mieux comprendre les mesures d’oscillations quan- tiques mesurées dans ce matériau. / In this thesis, the electronic structure of different kinds of superconductors is explored with the density functional theory. A brief explanation of this theory is done in the in- troduction. The Hubbard model is also presented as it can be used to solve shortcomings of the theory in some materials such as cuprates. The blend of the two theories is the DFT+U which is used to describe materials with strongly correlated electrons. After- ward, a paper describing the electron-phonon coupling in the superconductor NbC1−xNx is presented. Results from this work show the role of the Fermi surface in the electron pairing mechanism leading to superconductivity. Based on these results, a model is de- veloped explaining how the critical temperature is influenced by the change in frequency of the vibration modes. Then, quantum oscillation results based on a detailed analysis of Fermi surfaces, allowing a direct comparison with experimental data, are presented within two papers. The first one is about a material in the iron pnictide family, the LaFe2P2. Our calculations show that the Fermi surface of this material is different from the superconducting doped BaFe2As2 which explains why this material shows no sign of superconductivity. The second paper is about the heavy fermion system YbCoIn5. To do this, a new efficient method to calculate de Haas-van Alphen frequencies is developed. Finally, a paper on superconducting YBa2Cu3O6.5 is presented. Using DFT+U, the role of various magnetic orders on the Fermi surface are studied. The results allow a better understanding of the measured quantum oscillations in this material.

The physics of iron pnictides has been the subject of intense research for half a decade since the discovery of superconductivity in doped LaFeAsO in 2008. By now there exists a large number of different materials that are summarized under the term "pnictides'' with significant differences in their crystal structure, electronic properties, and their phase diagrams. This thesis is concerned with the investigation of the various phase transitions that are observed in the underdoped compounds of the pnictide subgroups RFeAsO, where R is a rare-earth element, and AFe_2As_2, where A is an alkaline-earth element. These compounds display two closely bound transitions from a tetragonal to an orthorhombic phase and from a paramagnetic to an antiferromagnetic metal. Both symmetry-broken phases are suppressed by doping or pressure and close to their disappearance superconductivity sets in. The superconducting state is stabilized until some optimal doping or pressure is reached and gets suppressed thereafter. The central goal of this thesis is to improve our understanding of the interplay between these three phases and to describe the various phase transitions. We start from an itinerant picture that explains the magnetism as a result of an excitonic instability and show how the other phases can be included into this picture. This approach is based on the the observation that the compounds we are interested in have a Fermi surface with multiple nested electron and hole pockets and that they have small to intermediate interaction strengths. The thesis starts with a study of the doping dependence of the antiferromagnetic phase transition in four different five-orbital models. We use the random-phase approximation to determine the transition temperature, the dominant ordering vector, and the contribution of the different orbitals to the ordering. This allows us to identify the more realistic models, which give results that are in good agreement with experimental observations. In addition to the frequently made assumption of orbital-independent interaction potentials we study the effect of a reduction of the interaction strengths that involve the d_{xy} orbital. We find that this tunes the system between two different nesting instabilities. A reduction of the interactions that involve the d_{xy} orbital also enhances the tendency towards incommensurate (IC) order. For a weak reduction this tendency is compensated by the presence of the orthorhombic phase. However, for a reduction of 30%, as it is suggested by constrained random-phase-approximation calculations, we always find large doping ranges, where a state with IC order has the highest transition temperature. We continue the investigation of the magnetic phase transition by studying the competition of different possible types of antiferromagnetic order that arises from the presence of two degenerate nesting instabilities with the ordering vectors (pi,0) and (0,pi). We derive a Ginzburg-Landau free energy from a microscopic two-band model and find that the presence of the experimentally observed stripe phase strongly depends on the number and size of the hole pockets in the system and on the doping. We show that within the picture of a purely magnetically driven nematic phase transition, which breaks the C_4 symmetry and induces the orthorhombic distortion, the nematic phase displays exactly the same dependence on the model parameters as the magnetic stripe phase. We propose that in addition to the purely magnetically driven nematic instability there is a ferro-orbital instability in the system that stabilizes the nematic transition and, thus, explains the experimentally observed robustness of the orthorhombic transition. We argue that including a ferro-orbital instability into the picture may also be necessary to reproduce the transition from simultaneous first-order transitions into an orthorhombic antiferromagnetic state to two separate second-order transitions, which is observed as a function of doping. Finally, a study of the superconducting phase transition inside the antiferromagnetic phase that is observed in some pnictide compounds is presented. We present an approach to calculate the fluctuation-mediated pairing interaction in the spin-density-wave phase of a multiband system, which is based on the random-phase approximation. This approach is applied to a minimal two-band model for the pnictides to study the effect of the various symmetry-allowed bare on-site interactions on the gap symmetry and structure. We find a competition between various even- and odd-parity states and over a limited parameter range a p_x-wave state is the dominant instability. The largest part of the parameter space is dominated by even parity states but the gap structure sensitively depends on the bare interactions. We propose that the experimentally observed transition from a nodeless to a nodal gap can be due to changes in the on-site interaction potentials.

In this thesis the charge dynamics of correlated electron systems, in which a metallic phase lies in close proximity to an ordered phase, are investigated by means of angle resolved photoemission spectroscopy (ARPES). The analysis of the experimental data is complemented by electronic structure calculations within the framework of density functional theory (DFT). First the charge dynamics of the colossal magnetoresistant bilayer manganites are studied. The analysis of the ARPES spectra based on DFT calculations and a Peierls type charge density wave model, suggests that charge, orbital, spin and lattice degrees of freedom conspire to form a fluctuating two dimensional local order that produces a large pseudo gap of about 450 meV in the ferromagnetic metallic phase and that reduces the expected bilayer splitting. Next, the interplay of Kondo physics and (magnetic) order in the heavy fermion superconductor URu2Si2 is investigated. The low energy electronic structure undergoes strong changes at 17.5 K, where a second order phase transition occurs whose phenomenology is well characterized, but whose order parameter could not yet be unambigeously identified. Below THO, non-dispersive quasi particles with a large scattering rate suddenly acquire dispersion and start to hybridize with the conduction band electrons. Simultaniously the scattering rate drops sinificantly and a large portion of the Fermi surface vanishes due to the opening of a gap within the band of heavy quasi particles. The observed behaviour is in stark contrast to conventional heavy fermion systems where the onset of hybridization between localized and itinerant carriers happens in a crossover type transition rather than abruptly. These experimental results suggest that Kondo screening and the hidden order parameter work together to produce the unusual thermodynamic signatures observed in this compound. Finally, the influence of charge doping and impurity scattering on the superconducting porperties of the transition metal substituted iron pnictide superconductor Ba(Fe1-xTMx)2As2 (TM = Co, Ni) is studied. Here, resonant soft X-ray ARPES is applied to see element selective the contribution of the 3d states of the TM substitute to the Fe 3d host bands. The spectroscopic signatures of the substitution are found to be well reproduced by DFT supercell and model impurity calculations. Namely, the hybridization of the dopant with the host decreases with increasing impurity potential and the electronic states of the impurtiy become increasingly localized. Simultaniously, in all simulated cases a shift of the Fermi level due to electron doping is observed. The magnitude of the shift in the chemical potential that accurs in BaFe2As2, however, is in stark contrast to the marginal doping values obtained for the impurity model, where the shift of the chemical potential is largely compensated by the influence of the increasing impurity potential. This suggests that the rigid band behaviour of TM substituded BaFe2As2 is a peculiarity of the compound, which has strong implications for the developement of superconductivity. / In dieser Arbeit wird die Ladungstraegerdynamik in korrelierten Elektronensystemen, in denen eine metallische Phase in direkter Nachbarschaft zu einer geordneten Phase liegt, mit Hilfe von winkelaufgeloester Photoelektronenspektroskopie (ARPES) untersucht. Die Analyse der experimentellen Daten wird ergaenzt durch lektronenstrukturrechnungen im Rahmen der Dichtefunktionaltheorie (DFT). Zuerst wird die Ladungstraegerdynamik in gemischtvalenten zweischichtmanganaten mit kolossalem Magnetiwiderstand studiert. Die Analyse der Photoemissionsspektren basierend auf DFT Rechnungen und einem Peierls artigem Ladungsdichtewellenmodell, legt nahe, dass die Freiheitsgrade von Ladung, Orbitalen, Spin und des Ionengitters konspirieren, um eine fluktuierende zweidimensionale lokale Ordnung zu bilden, die verantwortlich ist fuer die beobachtete Pseudobandluecke von 450 meV, und die zur Reduktion der erwarteten Zweischichtaufspaltung beitraegt. Als naechstes wird das Zusammenspiel von Kondo Physik und (magnetischer) Ordung im Schwerfermionensupraleiter URu2Si2 untersucht. Die iedrigenergetische elektronische Struktur zeigt starke Veraenderungen bei 17.5 K, wo ein Phasenuebergang zweiter Ordnungstattfindet, der phenomenologisch gut charakterisiert ist, aber dessen Ordungsparameter nocht nicht eindeutig identifiziert werden konnte. Unterhalb von THOerlangen nicht dispergierende Quasiteilchen mit gro en Streuraten abrupt Dispersion und hybridisieren mit den Leitungselektronen. Gleichzeitig sinkt die Streurate und ein gro er Teil der Fermiflaeche verschwindet durch das Oeffnen einer Bandluecke innehalb des Bandes schwerer Quasiteilchen. Das beobachtete Verhalten steht in starkem Kontrast zu dem von konventionellen Schwerfermionensystemen, in denen die Hybridisierung zwischen lokalisierten und itineranten Ladungstraegern in einem kontinuierlichen Uebergang ablaeuft, anstatt abrubt. Diese experimentellen Befunde lassen den Schluss zu, dass das zusammenspiel zwischen Kondo Abschirmung und dem unbekannten Ordnungsparameter die ungewoehnlichen thermodynamischen Signaturen in dieser Verbindung hervorruft. Abschliessend wird das Zusammenwirken von Ladungstraegerdotierung und Streuung an Stoeratomen auf die Supraleitung uebergangsmetalldotierter Eisenpniktid Supraleiter Ba(Fe1-xTMx)2As2 (TM = Co, Ni) untersucht. Mit Hilfe von resonantem Weichenroentgen ARPES gelingt es, elementselektiv den Beitrag der 3d Zustaende des TM Substituenten zu den Eisen 3d Wirtsbaendern zu beobachten. Die spektroskopischen Signaturen der Substitution sind mit Hilfe von DFT Rechnungen und Modelrechnungen mit zufaellig verteilten Stoeratomen gut zu reproduzieren. Insbesondere nimmt die Hybridisierung des dotierten Uebergangsmetalls und der Eisenbaender mit zunehmender Kernladungszahl ab und die elektronischen Zustaende der Stoeratome werden zunehmen lokalisiert. Gleichzeitig wird in allen gerechneten Faellen eine Verschiebung des Fermi Niveaus durch Elektronendotierung beobachtet. Der Betrag der Verschiebung des chemischen Potentials in BaFe2As2 steht allerdings in starkem Kontrast zu den Werten, die man im Falle der Modellrechnungen erhaelt, wo die Verschiebung des Fermi Niveaus durch den Einfluss des Potentials der Stoeratome groesstenteils kompensiert wird. Dies legt nahe, dass das beobachtete "rigid band" Verhalten von TM substituiertem BaFe2As2 eine Besonderheit dieser Verbindung ist, welches starke Auswirkungen auf die Ausbildung von Supraleitung hat.

The capability to probe the dispersion of elementary spin, charge, orbital, and lattice excitations has positioned resonant inelastic x-ray scattering (RIXS) at the forefront of photon science. In this work, we will investigate how RIXS can contribute to a deeper understanding of the orbital properties and of the pairing mechanism in unconventional high-temperature superconductors. In particular, we will show how direct RIXS spectra of magnetic excitations can reveal long-range orbital correlations in transition metal compounds, by discriminating different kind of orbital order in magnetic and antiferromagnetic systems. Moreover, we will show how RIXS spectra of quasiparticle excitations in superconductors can measure the superconducting gap magnitude, and reveal the presence of nodal points and phase differences of the superconducting order parameter on the Fermi surface. This can reveal the properties of the underlying pairing mechanism in unconventional superconductors, in particular cuprates and iron pnictides, discriminating between different superconducting order parameter symmetries, such as s, d (singlet pairing) and p wave (triplet pairing).

The discovery of superconductivity in iron-based pnictides in 2008 gave rise to a high advance in the research of high-temperature superconductors. But up to now there is no generally admitted theory of the non-BCS mechanism of these superconductors. The electron and hole doped Ba122 (BaFe2As2) compounds investigated in this thesis are supposed to be suitable model systems for studying the electronic behavior in order to shed light on the superconducting mechanisms. The 3d-transiton metal doped Ba122 compounds are investigated using the X-ray photoelectron spectroscopy (XPS), X-ray absorption spectroscopy (XAS), X-ray emission spectroscopy (XES) and X-ray magnetic circular dichroism (XMCD), while the completely hole doped K122 is observed using XPS. The experimental measurements are complemented by theoretical calculations. A further new class of superconductors is represented by the electride 12CaO*7Al2O3: Here superconductivity can be realized by electrons accommodated in the crystallographic sub-nanometer-sized cavities, while the mother compound is a wide band gap insulator. Electronic structure investigations, represented by XPS, XAS and resonant X-ray photoelectron spectroscopy (ResPES), carried out in this work, should help to illuminate this unconventional superconductivity and resolve a debate of competing models for explaining the existence of superconductivity in this compound.

La découverte en 2008 de supraconductivité à relativement haute température (Tc,max = 56K) dans les pnictures de Fer a ravivé les questions fondamentales sur l’origine et la nature de la supraconductivité posés par les supraconducteurs non conventionnels. En particulier, la présence d’une phase antiferromagnétique à proximité de celle supraconductrice dans leur diagramme de phase pose la question du lien entre magnétisme et supraconductivité. Ces supraconducteurs à base de Fe présentent un diagramme de phase générique, mais quelques exceptions remettent en question une description qui se voudrait universelle. Nous avons choisi d’étudier ces cas particuliers grâce à une sonde locale, la résonance magnétique nucléaire (RMN). Nos observations nous ont non seulement permis de comprendre la raison de ces exceptions, mais aussi de s’en servir pour mieux sonder les corrélations magnétiques dans ces matériaux, un ingrédient clé pour la compréhension de la supraconductivité. Premier sujet, la coexistence de supraconductivité et de magnétisme : celle-ci a été observée dans la plupart des supraconducteurs à base de Fer de façon homogène ou inhomogène, mais toujours pour des états magnétiques à faible TN et faibles moments en accord avec des descriptions itinérantes à faibles corrélations. Pourtant un nouveau composé au Sélénium est venu remettre en cause ces conclusions en présentant une apparente coexistence homogène entre une forte supraconductivité macroscopique (Tc ≈ 30K) et un très fort antiferromagnétisme (TN ≈ 600K, moments magnétiques de valeur élevée de 3.3µB). Cette observation suggère donc une description ici plutôt en terme d’isolants de Mott contrairement aux autres supraconducteurs à base de Fer. Nos mesures RMN permettent de montrer en fait l’existence d’une séparation de phase et de statuer sur la stœchiométrie et les propriétés électroniques des différentes phases, pour finalement réconcilier ce composé et les autres familles. Deuxième exception : dans la famille archétype BaFe₂As₂, tous les dopages sur site Fer ou Arsenic ou même l’application de pression mènent à la supraconductivité, sauf dans le cas du dopage au Manganèse ou au Chrome en site Fer, qui ne provoquent pas l’apparition de la supraconductivité. Nos mesures RMN nous ont permis de sonder la nature de la transition magnétique, mais aussi l’état métallique de ces composés substitués. Nous montrons en particulier que le trou supplémentaire du Manganèse substitué à la place du Fer reste en fait localisé sur son site et se manifeste alors par un moment magnétique localisé. Cette étude du dopage par le Manganèse ouvre la voie à l’idée d’utiliser le Manganèse en faible concentration comme source de moments localisés qui polarisent magnétiquement leur environnement. Cette polarisation permet en effet de caractériser la nature même des corrélations de spin. Nous avons donc utilisé la RMN ainsi que la magnétométrie-SQUID pour mesurer cette polarisation dans des composés supraconducteurs pour sonder les corrélations de spins de ces systèmes. Nous concluons que ces corrélations sont plutôt faibles et indépendantes de la température dans les composés dopés en électrons. / The discovery in 2008 of superconductivity at a rather high temperature in the iron pnictides (Tc,max = 56K) has revived the fundamental questions about the existence and the nature of the superconducting phase raised by the unconventional superconductors. In particular, the existence of an antiferromagnetic phase that is in vicinity of the superconducting phase in the phase diagram raises questions about the link between magnetism and superconductivity. These Iron based superconductors have a generic phase diagram, but some exceptions are questioning a description that would be universal. We chose to study these cases through a local probe, nuclear magnetic resonance (NMR). Our observations have not only allowed us to understand the reasons for these exceptions, but also be used to better probe the magnetic correlations in these materials, a key ingredient for the understanding of superconductivity. First subject, the coexistence of superconductivity and magnetism: it was observed in most superconductors based on iron homogeneously or inhomogeneously, but always for magnetic states at low TN and low magnetic moments in accordance with nesting descriptions with low correlations. Yet a new compound Selenium came to question these conclusions with an apparent homogeneous coexistence between a strong macroscopic superconductivity (Tc ≈ 30K) and a very strong antiferromagnetism (TN ≈ 600K, magnetic moments of high value of 3.3μB). This observation suggests a description rather in terms of Mott insulators, unlike other iron-based superconductors. Our NMR measurements show the existence of an effective phase separation and determine the stoichiometry and the electronic properties of the different phases, eventually reconciling this compound and other families. Second exception : in the archetype family BaFe₂As₂, all iron or arsenic on-site doping or even application of pressure leads to superconductivity, except in the case of Chrome or Manganese doping in Iron site, which does not cause the onset of superconductivity. Our NMR measurements have allowed us to probe the nature of the magnetic transition, but also the metallic state of the substituted compounds. We show in particular that the extra hole Manganese substituted in place of the iron is actually located on its atom and then manifested by a localized magnetic moment. This study of Manganese doping opens up the idea of using Manganese in low concentrations as a source of localized moments which magnetically polarize their environment. This polarization makes it possible to characterize the nature of the spin correlations. We used NMR and SQUID magnetometry, to measure the polarization in superconducting compounds to probe the spin correlations of these systems. We conclude that these correlations are rather low and independent of temperature in electrons doped compounds.

In dieser Arbeit werden niederfrequente optische Messungen an vier neuartigen Supraleitern vorgestellt. Im Bereich von 100 GHz bis 3 THz zeigen die vier untersuchten Systeme – LuNi2B2C, Ba(Fe0,9Co0,1)2As2, T’-Pr2CuO4 und Si:Ga – ein sehr unterschiedliches Verhalten. Die beiden erst genannten Supraleiter sind Mehrbandsupraleiter, bei denen die Cooper-Paarkopplung unterschiedlich für verschiedene Fermiflächen ist. T’-Pr2CuO4 ist ein undotierter Kupratsupraleiter, der nach bisheriger Lehrmeinung nicht existieren dürfte. Mit THz-Spektroskopie konnte erstmals die Bildung einer Meißner-Phase in T’-Pr2CuO4 mit optischen Methoden beobachtet werden. Eine gewisse Sonderstellung nimmt Si:Ga als amorpher Supraleiter ein. Si:Ga wird durch Ionenimplantation von Gallium in einen Siliziumwafer hergestellt. Es besteht die Hoffnung, mit Si:Ga halb- und supraleitende Logikblöcke in großem Maßstab auf einem Chip vereinen zu können, da die Ionenimplantation mit den Produktionsprozessen der Halbleiterindustrie kompatibel ist.

In this thesis, quantum cluster methods are used to calculate electronic properties of correlated-electron systems. A special focus lies in the determination of the ground state properties of a 3/4 filled triangular lattice within the one-band Hubbard model. At this filling, the electronic density of states exhibits a so-called van Hove singularity and the Fermi surface becomes perfectly nested, causing an instability towards a variety of spin-density-wave (SDW) and superconducting states. While chiral d+id-wave superconductivity has been proposed as the ground state in the weak coupling limit, the situation towards strong interactions is unclear. Additionally, quantum cluster methods are used here to investigate the interplay of Coulomb interactions and symmetry-breaking mechanisms within the nematic phase of iron-pnictide superconductors. The transition from a tetragonal to an orthorhombic phase is accompanied by a significant change in electronic properties, while long-range magnetic order is not established yet. The driving force of this transition may not only be phonons but also magnetic or orbital fluctuations. The signatures of these scenarios are studied with quantum cluster methods to identify the most important effects. Here, cluster perturbation theory (CPT) and its variational extention, the variational cluster approach (VCA) are used to treat the respective systems on a level beyond mean-field theory. Short-range correlations are incorporated numerically exactly by exact diagonalization (ED). In the VCA, long-range interactions are included by variational optimization of a fictitious symmetry-breaking field based on a self-energy functional approach. Due to limitations of ED, cluster sizes are limited to a small number of degrees of freedom. For the 3/4 filled triangular lattice, the VCA is performed for different cluster symmetries. A strong symmetry dependence and finite-size effects make a comparison of the results from different clusters difficult. The ground state in the weak-coupling limit is superconducting with chiral d+id-wave symmetry, in accordance to previous renormalization group approaches. In the regime of strong interactions SDW states are preferred over superconductivity and a collinaer SDW state with nonuniform spin moments on a quadrupled unit cell has the lowest grand potential. At strong coupling, inclusion of short-range quantum fluctuations turns out to favor this collinear state over the chiral phase predicted by mean-field theory. At intermediate interactions, no robust conclusion can be drawn from the results. Symmetry-breaking mechanisms within the nematic phase of the iron-pnictides are studied using a three-band model for the iron planes on a 4-site cluster. CPT allows a local breaking of the symmetry within the cluster without imposing long-range magnetic order. This is a crucial step beyond mean-field approaches to the magnetically ordered state, where such a nematic phase cannot easily be investigated. Three mechanisms are included to break the fourfold lattice symmetry down to a twofold symmetry. The effects of anisotropic magnetic couplings are compared to an orbital ordering field and anisotropic hoppings. All three mechanisms lead to similar features in the spectral density. Since the anisotropy of the hopping parameters has to be very large to obtain similar results as observed in ARPES, a phonon-driven transition is unlikely.

The physics of iron pnictides has been the subject of intense research for half a decade since the discovery of superconductivity in doped LaFeAsO in 2008. By now there exists a large number of different materials that are summarized under the term "pnictides'' with significant differences in their crystal structure, electronic properties, and their phase diagrams. This thesis is concerned with the investigation of the various phase transitions that are observed in the underdoped compounds of the pnictide subgroups RFeAsO, where R is a rare-earth element, and AFe_2As_2, where A is an alkaline-earth element. These compounds display two closely bound transitions from a tetragonal to an orthorhombic phase and from a paramagnetic to an antiferromagnetic metal. Both symmetry-broken phases are suppressed by doping or pressure and close to their disappearance superconductivity sets in. The superconducting state is stabilized until some optimal doping or pressure is reached and gets suppressed thereafter. The central goal of this thesis is to improve our understanding of the interplay between these three phases and to describe the various phase transitions. We start from an itinerant picture that explains the magnetism as a result of an excitonic instability and show how the other phases can be included into this picture. This approach is based on the the observation that the compounds we are interested in have a Fermi surface with multiple nested electron and hole pockets and that they have small to intermediate interaction strengths. The thesis starts with a study of the doping dependence of the antiferromagnetic phase transition in four different five-orbital models. We use the random-phase approximation to determine the transition temperature, the dominant ordering vector, and the contribution of the different orbitals to the ordering. This allows us to identify the more realistic models, which give results that are in good agreement with experimental observations. In addition to the frequently made assumption of orbital-independent interaction potentials we study the effect of a reduction of the interaction strengths that involve the d_{xy} orbital. We find that this tunes the system between two different nesting instabilities. A reduction of the interactions that involve the d_{xy} orbital also enhances the tendency towards incommensurate (IC) order. For a weak reduction this tendency is compensated by the presence of the orthorhombic phase. However, for a reduction of 30%, as it is suggested by constrained random-phase-approximation calculations, we always find large doping ranges, where a state with IC order has the highest transition temperature. We continue the investigation of the magnetic phase transition by studying the competition of different possible types of antiferromagnetic order that arises from the presence of two degenerate nesting instabilities with the ordering vectors (pi,0) and (0,pi). We derive a Ginzburg-Landau free energy from a microscopic two-band model and find that the presence of the experimentally observed stripe phase strongly depends on the number and size of the hole pockets in the system and on the doping. We show that within the picture of a purely magnetically driven nematic phase transition, which breaks the C_4 symmetry and induces the orthorhombic distortion, the nematic phase displays exactly the same dependence on the model parameters as the magnetic stripe phase. We propose that in addition to the purely magnetically driven nematic instability there is a ferro-orbital instability in the system that stabilizes the nematic transition and, thus, explains the experimentally observed robustness of the orthorhombic transition. We argue that including a ferro-orbital instability into the picture may also be necessary to reproduce the transition from simultaneous first-order transitions into an orthorhombic antiferromagnetic state to two separate second-order transitions, which is observed as a function of doping. Finally, a study of the superconducting phase transition inside the antiferromagnetic phase that is observed in some pnictide compounds is presented. We present an approach to calculate the fluctuation-mediated pairing interaction in the spin-density-wave phase of a multiband system, which is based on the random-phase approximation. This approach is applied to a minimal two-band model for the pnictides to study the effect of the various symmetry-allowed bare on-site interactions on the gap symmetry and structure. We find a competition between various even- and odd-parity states and over a limited parameter range a p_x-wave state is the dominant instability. The largest part of the parameter space is dominated by even parity states but the gap structure sensitively depends on the bare interactions. We propose that the experimentally observed transition from a nodeless to a nodal gap can be due to changes in the on-site interaction potentials.