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Strong electron-electron correlations and lattice frustration are two physical interactions that pose serious challenges to condensed matter physics. A variety of exotic physical phenomena, for example, charge ordering, spin liquid, and unconventional superconductivity, are believed to arise from the interplay of the two interactions. In this dissertation, I examine two families of systems which exhibit both electron-electron correlations and lattice frustration – charge transfer solids and layered cobaltates. The half-filled band Hubbard model on the triangular lattice has been proposed by mean-field theories as the minimal model for the superconductivity in the charge transfer solids. In the first part of this dissertation, by using exact calculations, I prove the absence of superconductivity in this model. This result calls for a new theoretical approach to describe the rich physics in charge transfer solids. In the second part of this dissertation, I study charge transfer solids by focusing on its real bandfilling ¼. I show that a new kind of insulating phase, paired electron crystal, emerges from antiferromagnetism as the frustration is increased. The paired electron crystal state can explain the various insulating states adjacent to the superconducting state, thus provides a new avenue towards the understanding of the unconventional superconductivity in charge transfer solids and other ¼ filled systems. In the third part of this dissertation, I investigate the carrier concentration-dependent electronic behavior in layered cobaltates. I provide a natural yet simple explanation for this behavior. I show that it can be described within correlated-electron Hamiltonians with finite on-site and significant nearest neighbor hole-hole Coulomb repulsions. I also point out the similarities between organic charge transfer solids and layered cobaltates, which may involve superconductivity.

High-pressure techniques have become increasingly important in the synthesis of ceramic and metallic solids allowing the discovery of new materials with interesting properties. In this research dense solid oxides have been synthesised at high pressures, and structural investigations have been conducted using x-ray and neutron diffraction. The perovskite LaPdO3 has been synthesised at pressures of 6{10GPa. Neutron diffraction studies have been carried out from 7{260K to investigate any structural distortions, particularly related to the possibility of charge order at low temperatures. No reduction in symmetry associated with charge ordering has been observed; the material appears to remain metallic with only one unique Pd site down to 7K. LaPdO3 adopts the GdFeO3-type Pbnm structure. The PdO6 octahedra exhibit a tetragonal distortion throughout the temperature range with a shortening of the apical Pd{O bonds of 2:5% relative to the equatorial bonds. Attempts to prepare analogues of the perovskite containing smaller rare earths have resulted in multi-phase samples, and further RPdO3 perovskites remain inaccessible although there is evidence for a small amount of the perovskite phase in the products of synthesis attempts with neodymium. Three new oxypnictide superconductors, RFeAsO1 xFx (R = Tb, Dy and Ho) have been synthesised at 7{12GPa. The materials are isostructural with other recently discovered iron arsenide superconductors and have Tc's of 52:8 K, 48:5K and 36:2K respectively, demonstrating a downturn in Tc in the series for smaller R. Systematic studies on TbFeAsO0.9F0.1 and HoFeAsO0.9F0.1 show negative values of dTc=dV in contrast to those reported for early R containing materials. Low-temperature neutron diffraction measurements on both materials, and synchrotron studies on HoFeAsO0.9F0.1 reveal no tetragonal to orthorhombic transitions as observed in early R-containing materials with lower doping levels. Magnetic reflections are evident but they are shown to be from R2O3 and RAs impurities with TN's of 5:5K for Tb2O3, 6:5K for HoAs and 1:7K < TN < 4K for Ho2O3. The implications of these results for superconductivity in the iron arsenides are discussed.

This thesis describes inelastic neutron scattering (INS) experiments on several iron-based materials. The experiments were primarily designed to investigate the link between magnetic dynamics and superconductivity. The work contributes to evidence that magnetic fluctuations influence or are influenced by superconductivity. It is demonstrated that the INS response of a material, in conjunction with theoretical models, can provide valuable information about both superconductivity and magnetism. I measured the magnetically ordered parent-compound SrFe2As2 to investigate the nature of magnetism in iron-based systems. Comparison of the data to models based on both itinerant and localised magnetism showed that an itinerant model offers the best description of the data. LiFeAs is a superconductor that shows no magnetic order, however I was able to distinguish a magnetic signal in its INS spectrum. The signal is consistent with the magnetic resonance observed in several other iron-based superconductors. This indicates that LiFeAs likely hosts an s± gap symmetry. I investigated two iron-phosphide systems, LaFePO and Sr2ScO3FeP, and in this case I was unable to identify any magnetic scattering. Comparison to LiFeAs showed that any signal in LaFePO is at least 7 times weaker. These results suggest that magnetic fluctuations are not as influential to the electronic properties of iron-phosphide systems as they are in other iron-based superconductors. In CsxFe2−ySe2 I found two independent signals that appear to be related to phase-separated magnetic and superconducting regions of the sample. I showed that fluctuations associated with the magnetically ordered phase are consistent with localised magnetism, and do not respond to superconductivity. The second signal, however, increases in intensity below the superconducting transition temperature Tc = 27K, consistent with a magnetic resonance. This could be indicative of a pairing symmetry in CsxFe2−ySe2 that is distinct from most other iron-based superconductors. Finally, the molecular intercalated FeSe compound Li0.6(ND2)0.2(ND3)0.8Fe2Se2 revealed strong magnetic fluctuations. Again the signal was consistent with a magnetic resonance responding to Tc = 43 K. The results suggest that Lix(ND2)y(ND3)1−yFe2Se2 is similar to the superconducting phase of CsxFe2−ySe2, placing constraints on theoretical models to describe the molecular intercalated FeSe compounds.

One of the most central concepts in condensed matter physics is the electronic band structure. Although band theory was established more than 80 years ago, recent developments have led to new insights that are formulated in the framework of topological band theory. In this thesis a subset of topological band theory is presented, with particular focus on topological supercon- ductors and accompanying Majorana fermions. While simple models are used to introduce basic concepts, a physically more realistic model is also studied intensely in the papers. Through self- consistent tight-binding calculations it is confirmed that Majorana fermions appear in vortex cores and at wire end points when the superconductor is in the topologically non-trivial phase. Many other properties such as the topological invariant, experimental signatures in the local density of states and spectral function, unconventional and odd-frequency pairing, the precense of spin-polarized currents and spin-polarization of the Majorana fermions, and a local π-phase shift in the order parameter at magnetic impurities are also investigated.

The physics of the series Pr_yY_1-yBa₂Cu₃O_6&plus;x, and ability of Pr to suppress superconductivity, has been a subject of frequent discussions in the literature for more than a decade. This thesis describes a polarised neutron diffraction (PND) experiment performed on PrBa₂Cu₃O_6.24 designed to find out something about the electron structure. This experiment pushed the limits of what can be done using the PND technique. The problem is one of a limited number of measured Fourier components that need to be inverted to form a real space image. To accomplish this inversion the maximum entropy technique has been employed. In some cases, the maximum entropy technique has the ability to increase the resolution of ‘inverted’ data immensely, but this ability is found to depend critically on the choice of constants used in the method. To investigate this a Bayesian robustness analysis of the maximum entropy method is carried out, resulting in an improvement of the maximum entropy technique for analysing PND data. Some results for nickel in the literature have been re-analysed and a comparison is made with different maximum entropy algorithms. Equipped with an improved data analysis technique and carefully measured PND data for PrBa₂Cu₃O_6.24 a number of new interesting features are observed, putting constraints on existing theoretical models of Pr_yY_1-yBa₂Cu₃O_6&plus;x and leaving room for more questions to be answered.

This thesis reports the synthesis and characterisation of the layered oxypnictides Sr₂MO₃FeAs (M = Sc, V and Cr) and CeOMnAs. In these materials the choice of transition metal cation at the tetrahedral site in the arsenide layer chiefly dictates the physical properties that are observed. The bulk of this work has focussed on the development of a new family of iron arsenide superconductor with the general formula Sr₂MO₃FeAs (M = Sc, V, Cr). This structure is comprised of anti-PbO-type [FeAs]^- layers which alternate with insulating [Sr₂MO₃]⁺ oxide fragments that resemble a portion of the K₂NiF₄ structure. In contrast to other FeAs parent materials, no member of the Sr₂MO₃FeAs family exhibits any strong evidence for long range Fe order or a tetragonal to orthorhombic distortion upon cooling. Attempts to electron and hole dope Sr₂ScO₃FeAs into the superconducting regime have as yet been unsuccessful. Although Sr₂ScO₃FeAs shows no evidence for Fe ordering, a checkerboard arrangement of Cr³⁺ spins in the ab-plane is observed below 40 K (k = (½, ½, 0)) analogous to that seen in Pr₂CuO₄. The partial substitution of Fe²⁺ (d⁶) by Co²⁺ (d⁷) in Sr₂CrO₃Fe_1-xCo_xAs has been shown to be a fruitful strategy for electron-doping this material into the superconducting regime with T_c maximised at 18 K in Sr₂CrO₃Fe_0.92Co_0.08As. It is also established that this substitution influences the ordering on the Cr sub-lattice with a doubling in the size of the magnetic cell along the c axis (k = (½, ½, ½)). Sr₂VO₃FeAs, a rare example of an “undoped” superconductor (T_c = 25 K), is shown to be electron-doped by mixed valence vanadium +3.13(5). Magnetometry measurements also reveal a series of magnetic transitions in Sr₂VO₃FeAs, however μSR and powder neutron diffraction studies suggest that this system is some way from commensurate long range order. In contrast to Sr₂CrO₃FeAs, electron-doping strategies in Sr₂VO₃FeAs have the effect of decreasing T_c and ultimately suppressing superconductivity entirely as Sr₂V_1-xTi_xO₃FeAs and Sr₂VO₃Fe_1-xCo_xAs materials are over electron-doped. Sr₂V_1-xMg_xO₃FeAs samples were also prepared, but rather than this strategy hole-doping the FeAs layer it preferentially oxidises vanadium towards V⁴⁺. This substitution also has a considerable effect on the superconducting critical temperature (T_c) which is raised as high as 31 K in Sr₂V_0.775Mg_0.225O₃FeAs. The isovalent substitution of Sr²⁺ by Ca²⁺ in Sr_2-xCa_xVO₃FeAs has been shown to strongly influence the superconducting properties of this material and a clear correlation between the evolution of T_c and the shape of the FeAs₄ tetrahedron has been established. These results demonstrate that superconductivity in iron-based superconductors is extremely sensitive to both electron count and the crystal structure. Finally, investigations into the manganese oxide arsenide CeOMnAs reveal room temperature ordering of Mn²⁺ spins and a spin reorientation transition of Mn moments at 36 K. This transition is concomitant with Ce ordering and an apparent weak structural distortion, demonstrating that f electrons are able to dictate the orientation of Mn moments.

Despite over 100 years of scientific research, a full understanding of superconductivity remains elusive. While it is known that the electron-phonon interaction is responsible for the formation of Cooper pairs in conventional superconductors, many superconductors exhibit behaviour suggestive of more exotic pairing mechanisms. In this thesis, two novel superconducting materials are considered, monolayer transition metal dichalcogenide, MoS₂, and iron-based superconductor, LaFeAsO_1−xF_x. The former is ideal for the study of the electron-phonon interaction, as it not only has potential applications as an atomically thin transistor, but also displays a dome-shaped superconductive state as a function of electron doping. In the latter, the superconductive state emerges from a magnetic parent compound upon flourine doping. Its high critical temperature is thought to be enhanced by magnetic fluctuation rather than being purely phonon-mediated. By using novel first-principles techniques, the electron-phonon interaction in electron doped single-layer MoS₂ is investigated. The superconducting gap is calculated using the Migdal-Eliashberg theory, and by considering the electronic structure and lattice dynamics in this material, an explanation is provided for the experimentally observed doping-dependent critical temperature in this material. The origin of the doping-induced transition from a magnetic phase to a nonmagnetic phase in LaFeAsO_1−xF_x is determined. A new model to capture the effects of the fluorine dopants is developed, which has implications for the electron-phonon interaction in this material.

Dans cette thèse intitulé "Dynamique quantique de la phase et de la charge dans des chaînes des jonctionsJosephson", une étude expérimentale et une description théorique des effets quantiques des phases et descharges dans les chaînes de jonctions Josephson est présenté.La dynamique des chaînes de jonctions est dominé par deux échelles d'energie: l'energie Josephsonrelié a la superposition des fonctions d'ondes de deux électrodes et l'energie de charge relié a l'énergieélectrostatique des charges sur les deux électrodes. La réalisation d'un état quasi-classique de la chargenécessite une énergie de charge importante pour diminuer lesfluctuation quantique de la charge. En plus,le temps de relaxations de la jonctions dois être augmenté par un environnement a haute impédance.Un état de charges localisé a été réalisé sur une jonctions Josephson dans un environnement inductiveréalisé par une chaîne de jonction Josephson. L'état de charge localisé se manifeste par l'apparition d'undomaine a haute résistances dans les caractéristques courant-tension.Une chaînes des jonctions n'est pas une inductances parfaite. Des résonances electro-magnétique lié a lacapacité vers la masse des îlots supra-conducteurs altèrent la localisation de charge.Une characterisation des effets de pertes et des non-lineartés de ces résonances a été effectué. / In this thesis entitled ' Quantum phase and charge dynamics in Josephson junction chains ' an experimental study and theoretical description of quantum effects of phases and charges in chains of Josephsonjunctions is presented.The dynamics of Josephson junction chains are dominated by two different energy scales: the Josephsonenergy, which is related to the overlap of the superconducting wave functions of the two superconductorsforming the junction and the charging energy that is related to the electrostatic energy of the Cooper-pairs on the islands. The realization of a well-defined charge state on a Josephson junction requires a highcharging energy to suppress the quantumfluctuations of the charge. In addition, the charge relaxationtimes must be increased by inserting the junction in a high impedance environment.We have realized such a well-defined charge state on a Josephson junction in an inductive environmentthat is formed by a Josephson junction chain. The localized charge state manifest itself by the appearanceof a high resistive regime in the current-voltage characteristic.A Josephson junction chain is however not a perfect inductor. Electromagnetic resonances related withthe finite ground capacitance of the superconducting islands influence the charge localization.We have characterized the effect of losses and nonlinearities on the electromagnetic resonances of Josephson junction chains in microwave spectroscopy measurements.