This thesis is devoted to a study of the effect of disorder on strongly correlated electrons. For non-interacting electrons, Anderson localization occurs if the amount of disorder is sufficient. For disorder-free systems, a Mott metal-insulator transition may occur if the electron-electron interactions are strong enough. The question we ask in this thesis is what happens when both disorder and interactions are present. We study the Anderson-Hubbard model, which is the simplest model to include both interactions and disorder, using a Gutzwiller variational wave function approach. We then study Anderson localization of electrons from the response of the Anderson-Hubbard Hamiltonian to an external magnetic field. An Aharonov-Bohm flux induces a persistent current in mesoscopic rings. Strong interactions result in two competing tendencies: they tend to suppress the current because of strong correlations, and they also screen the disorder potential and making the system more homogenous. We find that, for strongly interacting electrons, the localization length may be large, even though the current is suppressed by strong correlations. This unexpected result highlights how strongly correlated materials can be quiet di erent from weakly correlated ones. / Thesis (Ph.D, Physics, Engineering Physics and Astronomy) -- Queen's University, 2011-08-31 09:51:47.155

The design and construction of a state-of-the-art ultra-high vacuum spectrometer for the performance of angle-resolved inverse photoemission spectroscopy is presented. Detailed descriptions of its most important components are included, especially the Geiger-Muller ultraviolet photodetectors. By building on recent developments in the literature, we expect our spectrometer to achieve resolution comparable or superior to that of other prominent groups, and in general be one of the foremost apparatus for studying the momentum dependence of the unoccupied states in strongly correlated materials. Summaries of the theory of angle-resolved inverse photoemission spectroscopy and the basics of ultra-high vacuum science are also included.

Within condensed matter physics, systems with strong electronic correlations give rise to fascinating phenomena which characteristically require a physical description beyond a one-electron theory, such as high temperature superconductivity, or Mott metal-insulator transitions. In this thesis, a class of strongly correlated electron systems is considered. These systems exhibit fractionally charged excitations with charge +e/2 or -e/2 in two dimensions (2D) and three dimensions (3D), a consequence of both strong correlations and the geometrical frustration of the interactions on the underlying lattices. Such geometrically frustrated systems are typically characterized by a high density of low-lying excitations, leading to various interesting physical effects. This thesis constitutes a study of a model of spinless fermions on the geometrically frustrated kagome lattice. Focus is given in particular to the regime in which nearest-neighbour repulsions V are large in comparison with hopping t between neighbouring sites, the regime in which excitations with fractional charge occur. In the classical limit t = 0, the geometric frustration results in a macroscopically large ground-state degeneracy. This degeneracy is lifted by quantum fluctuations. A low-energy effective Hamiltonian is derived for the spinless fermion model for the case of 1/3 filling in the regime where |t| << V . In this limit, the effective Hamiltonian is given by ring-exchange of order ~ t^3/V^2, lifting the degeneracy. The effective model is shown to be equivalent to a corresponding hard-core bosonic model due to a gauge invariance which removes the fermionic sign problem. The model is furthermore mapped directly to a Quantum Dimer model on the hexagonal lattice. Through the mapping it is determined that the kagome lattice model exhibits plaquette order in the ground state and also that fractional charges within the model are linearly confined. Subsequently a doped version of the effective model is studied, for the case where exactly one spinless fermion is added or subtracted from the system at 1/3 filling. The sign of the newly introduced hopping term is shown to be removable due to a gauge invariance for the case of hole doping. This gauge invariance is a direct result of the bipartite nature of the hole hopping and is confirmed numerically in spectral density calculations. For further understanding of the low-energy physics, a derivation of the model gauge field theory is presented and discussed in relation to the confining quantum electrodynamic in two dimensions. Exact diagonalization calculations illustrate the nature of the fractional charge confinement in terms of the string tension between a bound pair of defects. The calculations employ topological symmetries that exist for the manifold of ground-state configurations. Dynamical calculations of the spectral densities are considered for the full spinless fermion Hamiltonian and compared in the strongly correlated regime with the doped effective Hamiltonian. Calculations for the effective Hamiltonian are then presented for the strongly correlated regime where |t| << V . In the limit g << |t|, the fractional charges are shown to be effectively free in the context of the finite clusters studied. Prominent features of the spectral densities at the Gamma point for the hole and particle contributions are attributed to approximate eigenfunctions of the spinless fermion Hamiltonian in this limit. This is confirmed through an analytical derivation. The case of g ~ t is then considered, as in this case the confinement of the fractional charges is observable in the spectral densities calculated for finite clusters. The bound states for the effectively confined defect pair are qualitatively estimated through the solution of the time-independent Schroedinger equation for a potential which scales linearly with g. The double-peaked feature of spectral density calculations over a range of g values can thus be interpreted as a signature of the confinement of the fractionally charged defect pair. Furthermore, the metal-insulator transition for the effective Hamiltonian is studied for both t > 0 and t < 0. Exact diagonalization calculations are found to be consistent with the predictions of the effective model. Further calculations confirm that the sign of t is rendered inconsequential due to the gauge invariance for g in the regime |t| << V . The charge-order melting metal-insulator transition is studied through density-matrix renormalization group calculations. The opening of the energy gap is found to differ for the two signs of t, reflecting the difference in the band structure at the Fermi level in each case. The qualitative nature of transition in each case is discussed. As a step towards a realization of the model in experiment, density-density correlation functions are introduced and such a calculation is shown for the plaquette phase for the effective model Hamiltonian at 1/3 filling in the absence of defects. Finally, the open problem of statistics of the fractional charges is discussed.

This Ph.D. thesis in mathematical physics concerns systems of interacting fermions with strong correlations. For these systems the physical properties can only be described in terms of the collective behavior of the fermions. Moreover, they are often characterized by a close competition between fermion localization versus delocalization, which can result in complex and exotic physical phenomena. Strongly correlated fermion systems are usually modelled by many-body Hamiltonians for which the kinetic- and interaction energy have the same order of magnitude. This makes them challenging to study as the application of conventional computational methods, like mean field- or perturbation theory, often gives unreliable results. Of particular interest are Hubbard-type models, which provide minimal descriptions of strongly correlated fermions. The research of this thesis focuses on such models defined on two-dimensional square lattices. One motivation for this is the so-called high-Tc problem of the cuprate superconductors. A main hypothesis is that there exists an underlying Fermi surface with nearly flat parts, i.e. regions where the surface is straight. It is shown that a particular continuum limit of the lattice system leads to an effective model amenable to computations. This limit is partial in that it only involves fermion degrees of freedom near the flat parts. The result is an effective quantum field theory that is analyzed using constructive bosonization methods. Various exactly solvable models of interacting fermions in two spatial dimensions are also derived and studied. / QC 20111207

The design and construction of a state-of-the-art ultra-high vacuum spectrometer for the performance of angle-resolved inverse photoemission spectroscopy is presented. Detailed descriptions of its most important components are included, especially the Geiger-Muller ultraviolet photodetectors. By building on recent developments in the literature, we expect our spectrometer to achieve resolution comparable or superior to that of other prominent groups, and in general be one of the foremost apparatus for studying the momentum dependence of the unoccupied states in strongly correlated materials. Summaries of the theory of angle-resolved inverse photoemission spectroscopy and the basics of ultra-high vacuum science are also included.

The objective of this thesis is to reach theoretical understanding of the unusual relationship between charge-ordering and superconductivity in correlated-electron systems. The competition between these broken symmetries and magnetism in the cuprate high temperature superconductors has been extensively discussed, but exists also in many other correlated-electron superconductors, including quasi-two-dimensional organic charge-transfer solids. It has been suggested that the same attractive interaction is responsible for both charge-order and superconductivity. We propose that the specific interaction is the tendency in correlated-electron systems to form spin-singlet bonds, which is strongly enhanced at the commensurate carrier density p of ½ a charge carrier per site, characteristic of all superconducting charge-transfer solids. To probe superconductivity driven by electron correlations, a necessary condition is that electron-electron interactions enhance superconducting pair-pair correlations, relative to the non-interacting limit. We have performed state of the art numerical calculations on the two-dimensional Hubbard model on different triangular lattices, as well as other lattices corresponding to K-BEDT-TTF based organic charge transfer solids, for the complete range of carrier densities per site p (0 ≤ p ≤ 1). We have shown that pair-pair correlation for each cluster is enhanced by electron-electron interaction only for p ≃ 0.5, far away from the density range thought to be important for superconductivity. Although initial focus is on charge-transfer solids, the results of the research will impact the field of correlated electrons as a whole. We believe our calculations will provide fundamental and fresh insight to the theory of superconductivity in strongly correlated systems.

Transition metal oxides and chalcogenides are an ideal platform for demonstrating and investigating many interesting electronic phases of matter. These phases emerge as a result of collective many body interactions among the electrons. The omnipresent electron, depending on its interaction with other electrons and with the underlying lattice, can generate diverse phases of matter with exotic physical properties. The ultimate objective of Materials Science is to provide a complete microscopic understanding of these myriad electronic phases of matter. A proper understanding of the collective quant-tum behaviour of electrons in different system can also help in designing and tuning new electronic phases of matter that may have strong impact in the field of microelectronics, well beyond that predicted by Moore s law. Strong electron correlation effects produce a wide spectrum of ground state prop-retires like superconductivity, Metal Insulator Transition (MIT), charge-orbital ordering and many more. Similarly, different spin interactions among electrons, essentially due to various kinds of exchange coupling, give rise to varying magnetic ground state prop-retires like ferromagnetism, anti-ferromagnetism, spin glass, among others. The main objective of this thesis is to understand and rationalize diverse electronic and magnetic phases of matter in some selected strongly correlated systems. In chapter 1 we have provided an overview of various electronic and magnetic phases of matter which are relevant and necessary for understanding the chapters that follow. The first part of this chapter describes the fundamental concepts of the so called Metal Insulator Transition (MIT). A small section is dedicated to the subtle interactions among electrons and lattice that actually drive a system from a highly conducting metallic state to a strongly resistive insulating state. The second part of this chapter offers a compilation of different magnetic ground states which are discussed in detail in the last two chapters. In Chapter 2, we have explained various methodologies and experimental tech-antiques that have been used in the work reported in this thesis. In Chapter 3, we have provided a detailed understanding of the MIT in different polymorphic forms of Vanadium dioxide (VO2). Although VO2 exhibits a number of polymorphic forms, only the rutile/monoclinic VO2 phase has been studied extensively compared to other polymorphic forms. This phase shows a well-established MIT across ∼340 K, which has been extensively investigated in order to understand the relative importance of many body electron correlation effects arising primarily from on-site Coulomb interactions within the Vanadium 3d manifold, and single electron effects flounced by the dimerization of Vanadium atoms. Unlike the rutile phase of VO2, little is known about the MIT appearing across 212 K in the metastable B-phase of VO2. This phase shows dimerization of only half of the Vanadium atoms in the insulating state, in contrast to rutile/monoclinic VO2, which show complete dimerization. There is a long standing debate about the origin of the MIT in the rutile/monoclinic phase, that contrasts the role of the many-body Hubbard U term, with single particle effects of the dimerization. In light of this debate, the MIT in the B-phase offers a unique opportunity to understand and address the competition between many body and single particle effects, that has been unresolved over several decades. In this chapter we have investigated different polymorphs of VO2 to understand the underlying electronic structure and the nature of the MIT in these polymorphic forms. The MIT in VO2 B phase is very broad in nature. X-ray photoemission and optical conductivity data indicate that in case of VO2 B phase both correlation effects and dimerization is necessary to drive the MIT. We have also established that the correlation effects are more prominent for VO2 B phase compared to rutile/monoclinic phase. In Chapter 4, we have discussed the electronic structure of LaTiO3 (LTO)-SrTiO3 (STO) system. At the interface between polar LTO and non-polar (STO) oxides, an unique two dimensional electron gas (2DEG) like state appears, that exhibits a phenomenal range of unexpected transport, magnetic, and electronic properties. Thus, this interface stands as a prospective candidate for not only fundamental scientific investigation, but also application in technological and ultimately commercial frontiers. In this chapter, using variable energy Hard X-ray photoemission spectroscopy (HAXPES), we have experimentally investigated the layer resolved evolution of electronic structure across the interface in LTO-STO system. HAXPES results suggest that the interface is more coherent in nature and the coherent to incoherent feature ratio changes significantly as we probe deeper into the layer In chapter 5, we have investigated the electronic structure of the chemically exfoliated trigonal phase of MoS2. This elusive trigonal phase exists only as small patches on chemically exfoliated MoS2, and is believed to control functioning of MoS2 based devices. Its electronic structure is little understood, with total absence of any spec-troscopic data, and contradictory claims from theoretical investigations. We have ad-dressed this issue experimentally by studying the electronic structure of few layered chemically exfoliated MoS2 systems using spatially resolved X-ray photoemission spec-otoscopy and micro Raman spectroscopy in conjunction with electronic structure calculations. We have established that the ground state of this unique trigonal phase is actually a small gap (∼90 meV) semiconductor. This is in contrast with most of the claims in existing literature. In chapter 6, we have re-examined and revaluated the electronic structure of the late 3d transition metal monoxides (NiO, FeO, and CoO) using a combination of HAX-PES and state-of-the-art theoretical calculations. We have observed a strong evolution in the valence band spectra as a function of excitation energy. Theoretical results show that a combined GW+LDA+DMFT scheme is essential for explaining the observed experimental findings. Additionally, variable temperature HAXPES measurement In chapter 8, we have differentiated the surface and the bulk electronic structure in Sr2FeMoO6 and also have provided a new route to increase the Curie temperature of this material. Sr2FeMoO6 is well known for its high Curie temperature (Tc ∼410 K), half-metallic ferromagnetism, and a spectacularly large tunnelling magnetoresistance. The surface electronic structure of Sr2FeMoO6 is believed to be different from the bulk; leading to a Spin-Valve type Magnetoresistance. We have carried out variable energy HAXPES on Sr2FeMoO6 to probe electronic structure as a function of surface depth. Our experimental results indicate that surface is more Mo6+ rich. We have also demonstrated what we believe is the first direct experimental evidence of hard ferro-magnetism in the surface layer using X Ray Magnetic Circular Dichroism (XMCD) with dual detection mode. In the second part of this chapter we have designed a new route to increase the Curie temperature and have been successfully able to achieve a Curie temperature as high as 515 K.

In a many-body fermionic system, the suppression of continuous transitions to absolute zero can result in a low temperature quantum fluid which deviates strongly from typical metallic behaviour; unconventional superconductivity can be induced by the strange metal region surrounding the zero-temperature phase transition. In this thesis we focus on three systems which demonstrate a highly tunable phase transition, with the aim of pushing them toward the border of a zero-temperature phase transition, and potentially superconductivity. CeAgSb2 is a uniaxial 4f ferromagnet, where physical pressure or a transverse field may be used to tune the magnetic transition towards T = 0 K. Our investigations, however, did not reveal the presence of superconductivity. It is likely that the field tuned transition does not correspond to a true critical point, whilst the high pressure region may be occupied by an antiferromagnetic phase, with the true critical point at higher pressures. However, other interesting features emerge in the electrical resistivity and AC-susceptibility, along with novel thermodynamic signatures linking the magnetisation to the specific heat. The doping series Lu(1-x)YxFe2Ge2 shows an antiferromagnetic transition which is suppressed to absolute zero at a critical concentration x_c=0.2. YFe2Ge2 displays anomalous low temperature behaviour consistent with the proximity to quantum critical fluctuations, along with a superconducting transition which appears in the electrical resistivity beneath a critical temperature of T_c ~ 1.7 K. Using low temperature DC magnetisation measurements, we show that this is a bulk effect, and that the superconductivity in YFe2Ge2 is of type-II. The thermodynamic and BCS properties of the superconducting phase are analysed in line with the parameters we extract experimentally. The superconducting 3-4-13 stannides (Ca,Sr)3Ir4Sn13 show a high temperature structural transition which may be suppressed by the application of hydrostatic pressure or effective chemical pressure. A superconducting dome is found, which appears to peak near where the structural transition extrapolates to zero temperature. Anomalous exponents are seen in the electrical resistivity over a wide temperature range. We investigate the influence of pressure on the superconducting critical temperature in Ca3Ir4Sn13 and the related compound Co3Ca4Sn13, along with an analysis of the upper critical field and flux-line phenomena in Ca3Ir4Sn13 and Sr3Ir4Sn13.

Les systèmes à électrons fortement corrélés sont d’intérêt particulier pour le calcul ab initio, cherchant à modéliser ces systèmes à partir des premiers principes. La théorie de la fonctionnelle de la densité associée à une prise en compte des corrélations locales en DFT+U ou en DFT+DMFT, permet de reproduire qualitativement la physique de ces systèmes. Cependant, ces méthodes font intervenir les paramètres d’interaction effective de Hubbard U et de Hund J. Ces derniers peuvent eux-mêmes être calculés de manière ab initio, notamment avec l’approximation de phase aléatoire contrainte (cRPA), ouvrant la voie au développement de schémas de calcul les plus prédictifs possible. Nous utilisons un schéma DFT+U/cRPA, dont le principe consiste à calculer les paramètres U et J en cRPA et la structure électronique en DFT+U de manière auto-cohérente. Nous appliquons ce schéma aux lanthanides allant du cérium au lutétium (en détaillant le cas du cérium dans ses phases gamma et alpha), et aux dioxydes des actinides allant de l'uranium au curium. Nous effectuons d'abord une étude de l'état fondamental en DFT+U en fonction de U, en détaillant l'influence des états métastables. Nous étudions le rôle de la localisation des orbitales corrélées sur l'interaction effective dans un cas particulier. Nous détaillons ensuite les valeurs de U obtenues en cRPA en fonction de celles utilisées pour le calcul DFT+U. Nous nous intéressons plus particulièrement aux effets des processus d’écrantage sur les valeurs de U obtenues. Nous montrons que les limitations du schéma observées (multiplicité des valeurs auto-cohérentes de U obtenues et/ou incompatibilité de ces valeurs avec les spectres de photoémission expérimentaux) sont causées par certains processus d’écrantage spécifiques. Cela suggère d'améliorer la description de ces processus d'écrantage en modifiant le modèle. / Strongly correlated electron systems are particularly interesting for ab initio calculus, which aims to model these systems from first principles. Density functional theory, improved by taking into account local correlations within DFT+U or DFT+DMFT, enables to reproduce qualitatively the physics of these systems. Nonetheless, these methods require the Hubbard and Hund effective interaction parameters U and J. These can be computed from first principles as well, within the constrained random phase approximation (cRPA), paving the way for numerical schemes as predictive as possible. Here, we use a DFT+U/cRPA scheme, which aims to compute self-consistently the U and J parameters with cRPA and the DFT+U electronic structure. We apply this scheme to lanthanides from cerium to lutetium (insisting on cerium and its gamma and alpha phases), and dioxides of actinides from uranium to curium. We study the DFT+U ground state in function of U, giving more details about the influence of metastable states. We study as well the influence of the localization of correlated orbitals on the effective interaction in a particular case. We then detail the values of U obtained with cRPA, in function of those used for the DFT+U calculation. We study more particularly the effects of screening processes on the obtained values of U. We show that the limitations of the scheme (multiplicity of self-consistent values of U and/or their incompatibility with experimental photoemission spectra) are caused by specific screening processes. This suggests to improve the description of these screening processes by modifying the model.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第21550号 / 理博第4457号 / 新制||理||1640(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)准教授 戸塚 圭介, 教授 川上 則雄, 教授 前野 悦輝 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM