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京都大学 / 新制・課程博士 / 博士(理学) / 甲第23696号 / 理博第4786号 / 新制||理||1685(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)教授 松田 祐司, 教授 柳瀬 陽一, 教授 石田 憲二 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

Transition metal oxides (TMO) have proven to exhibit novel properties such as high temperature superconductivity, magnetic ordering, charge and spin density waves, metal to insulator transitions and colossal magnetoresistance. Among these are a spin-orbit coupling (SOC) induced Mott insulator Sr2IrO4. The electric transport properties of this material remain finite even at cryogenic temperatures enabling its complex electronic structure to be investigated by a scanning tunneling microscope. At T = 77 K, we observed two features which represent the Mott gap with a value of 2D ~ 615 meV. Additionally an inelastic loss feature was observed inside this gap due to a single magnon excitation at an energy of ~ 125 meV. These features are consistent with similar measurements with other probes. In addition to these features, at T = 4.2 K lower energy features appear which are believed to be due to additional magnetic ordering. Another material that exhibits a unique physical behavior is the sliding charge density wave (CDW) material TaS3. It is a quasi-one dimensional material that forms long narrow ribbon shaped crystals. It exhibits anomalies including non-ohmic conductivity, a decrease in the Young’s modulus, a decrease in the shear modulus and voltage induced changes in the crystal’s overall length. In addition, we have observed the torsional piezo-like response, voltage induced torsional strain (VITS), in TaS3 which was first discovered by Pokrovskii et. al. in 2007. Our measurements were conducted with a helical resonator. The VITS response has a huge effective piezoelectric coefficient of ~ 104 cm/V. In addition we have concluded that the VITS is a very slow response with time constants of ~ 1 s near the CDW depinning threshold, that these time constants are dependent on the CDW current, and we suggest that the VITS is due to residual twists being initially present in the crystal.

In this thesis we employ various mean-field approaches to study the shortrange interaction effects in topological insulators. We start with the Kane-Mele model on the decorated honeycomb lattice and study the stability of topological insulator phase against different perturbations. We establish an adiabatic connection between a noninteracting topological insulator and a strongly interacting spin liquid in its Majorana fermion representation. We use the Hartree-Fock mean-field approach, slave-rotor approach and slave-boson approach to study correlation effects related to topological insulators. With the spontaneous symmetry breaking mechanism, we can have an interaction driven topological insulator with extended Hubbard models on the kagome lattice and decorated honeycomb lattice. For the interplay among spin-orbit coupling, distortion and correlation effect in transition metal oxides, we use the slave-rotor mean-field approach to study its phase transition. We identify regimes where a strong topological Mott insulator and a weak topological insulator reside due to the strong Coulomb interaction and distortion. This is relevant to experiments with the transition metal oxides as they hold promise to realize topological insulators. To study the doping effects and a possible spin liquid in Kane-Mele-Hubbard model on the honeycomb lattice, we employ the slave-boson mean-field approach which is appropriate for the intermediate interaction strength. We compare our results with those obtained from other methods. / text

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Les oxydes de métaux de transition (Ti, Fe, Mn, Cu, etc) présentent une multitude de fonctionnalités tout en cristallisant dans un nombre réduit de structures. C’est le cas par exemple dans la famille des pérovskites qui arborent de nombreux ordres électroniques (isolants, métaux, supraconducteurs) et magnétiques (ferro- et antiferromagnétiques). La compatibilité structurale de ces différents composés permet de les combiner au sein d'hétérostructures multifonctionnelles mais aussi, dans certains cas, de faire émerger de nouvelles propriétés aux interfaces. Un exemple typique découvert en 2004 est celui du gaz électronique bidimensionnel se formant à l'interface entre deux isolants de bande, LaAlO₃ et SrTiO₃ .S’inspirant de ce résultat majeur, ce travail de thèse a pour but de générer de nouvelles phases électroniques et magnétiques aux interfaces, non à partir d'isolants de bande mais d'isolants de Mott et d'isolants à transfert de charge. A l'interface entre ces deux types de composés, l’alignement de bande est rendu plus complexe par la présence de fortes corrélations électroniques.Ainsi, les reconstructions d’interface peuvent donner lieu à une déstabilisation de l'état fondamental, et à la génération de nouvelles phases magnétiques, conductrices ou supraconductrices absentes du diagramme de phase du matériau massif.Dans un premier temps, lors de ce travail nous avons synthétisé, par ablation laser pulsé des couches minces d'isolants de Mott, les titanates de terre-rare (RTiO₃ ). Nous avons caractérisé leurs propriétés magnétiques, optiques et électroniques.Dans un second temps, nous avons également optimisé des couches minces d’isolants à transfert de charge, les nickelates de terre-rare (RNiO₃ ). Nous avons étudié en détail l’effet du rayon ionique de la terre-rare sur la structure électronique à basse température de ces composés.Le cœur de ce travail de thèse a été l'étude des propriétés de l’interface formée par ces deux constituants via une combinaison de plusieurs techniques de spectroscopie (absorption de rayonnement synchrotron, XAS, dichroïsme linéaire et circulaire, XMCD, et spectroscopie de perte d’énergie, STEM-EELS) en lien avec des calculs ab-initio.Après avoir démontré l’apparition d’une nouvelle phase ferromagnétique dans les nickelates, nous discutons du rôle des corrélations dans les nickelates sur le transfert de charge et sur la reconstruction magnétique, observés à l’interface avec GdTiO₃ .Enfin, nous mettons en évidence la possibilité d’utiliser un paramètre de contrôle externe comme la lumière pour altérer le niveau de covalence dans les nickelates sans modifier la terre-rare. Ces résultats ouvrent la voie à de nouveaux dispositifs tirant partie du contrôle actif du niveau de covalence dans les isolants à transfert de charge. / Transition metal oxides (Ti, Fe, Mn, Cu, etc.) display a multitude of features while crystallizing in a reduced number of structures. This is the case for example of perovskites which exhibit many electronic (insulators, metals, superconductors) and magnetic (ferro- and antiferromagnetic) orders. Their structural compatibility offers a unique playground for combining them in the search for new interfacial properties. A typical example discovered in 2004 is LaAlO₃ and SrTiO₃ whose interface reveals a high-mobility electron gas although the parent constituents are two conventional band insulators.Following-up on this major achievement, this thesis aims at generating new electronic interfacial phases, not from band insulators but rather from Mott and charge transfer insulators. At the interface between these types of compounds, band alignment is made more complex by the presence of strong correlations between electrons.Hence, interfacial reconstructions can destabilize the ground state, and generate new phases absent from the phase diagrams of the two building blocks.Initially, we synthetized, by pulsed laser deposition, a typical Mott insulator, rare earth titanates (RTiO₃ ) in the form of thin layers, which were optimized and characterized on different substrates.Secondly, we also grew charge transfer insulators, rare earth nickelates (RNiO₃ ). We specifically studied the effect of the ionic radius of the rare earth on the electronic structure of these compounds at low temperature.The core of this thesis is to study the interface formed by these two constituents via a combination of spectroscopic techniques (synchrotron radiation-based absorption, XAS, linear and circular dichroism XMCD and energy loss spectroscopy, STEM-EELS) in connection with ab-initio calculations.After demonstrating the emergence of a new ferromagnetic phase in nickelates, absent of the bulk phase diagram, we discuss in particular the role of correlations in nickelates on the charge transfer and magnetic reconstruction, observed at the interface with GdTiO₃ .Finally, we will propose a new external knob, light, to alter the level of covalence in nickelates without changing the rare earth. These results open the way for new devices taking advantage of the active control of the level of covalence in charge transfer insulators.

J'étudie en détail la solution d'un modèle simplifié d'électrons fortement corrélés, à savoir le modèle de Hubbard dimérisé. Ce modèle est la réalisation la plus simple d'un problème de cluster DMFT. Je fournis une description détaillée des solutions dans une région de coexistence où l'on trouve deux états (méta) stables des équations DMFT, l'un métallique et l'autre isolant. De plus, je décris en détail comment ces états disparaissent à leurs lignes critiques respectives. Je clarifie le rôle clé joué par la corrélation intra-dimère, qui agit ici en complément des corrélations de Coulomb.Je passe en revue la question importante du passage continue entre unisolant Mott et un isolant Peierls où je caractérise une variété de régimes physiques. Dans un subtil changement de la structure électronique, lesbandes de Hubbard évoluent des bandes purement incohérentes (Mott) à desbandes purement cohérentes (Peierls) à travers un état inattendu au caractère mixte. Je trouve une température d'appariement singulet T* en-dessous de laquelle les électrons localisés à chaque site atomique peuvent se lier dans un singulet et minimiser leur entropie. Ceci constitue un nouveau paradigme d'un isolant de Mott paramagnétique.Enfin, je discute la pertinence de mes résultats pour l'interprétation de différentes études expérimentales sur VO₂. Je présente plusieurs arguments qui me permettent d'avancer la conclusion que la phase métallique, à vie longue (métastable) induite dans les expériences pompe-sonde, et l'état métallique métastable M₁, thermiquement activé dans des nano-domaines, sont identiques. De plus, ils peuvent tous être qualitativement décrits, dans le cadre de notre modèle, par un métal corrélé dimérisé. / We study in detail the solution of a basic strongly correlated model,namely, the dimer Hubbard model. This model is the simplest realization ofa cluster DMFT problem.We provide a detailed description of the solutions in the ``coexistentregion'' where two (meta)stable states of the DMFT equations are found, onea metal and the other an insulator. Moreover, we describe in detail howthese states break down at their respective critical lines. We clarify thekey role played by the intra-dimer correlation, which here acts in additionto the onsite Coulomb correlations.We review the important issue of the Mott-Peierls insulator crossoverwhere we characterize a variety of physical regimes. In a subtle change inthe electronic structure the Hubbard bands evolve from purely incoherent(Mott) to purely coherent (Peierls) through a state with unexpected mixedcharacter. We find a singlet pairing temperature T* below which thelocalized electrons at each atomic site can bind into a singlet and quenchtheir entropy, this uncovers a new paradigm of a para-magnetic Mottinsulator.Finally, we discuss the relevance of our results for the interpretation ofvarious experimental studies in VO₂. We present a variety of argumentsthat allow us to advance the conclusion that the long-lived (meta-stable)metallic phase, induced in pump-probe experiments, and the thermallyactivated M₁ meta-stable metallic state in nano-domains are the same.In fact, they may all be qualitatively described by the dimerizedcorrelated metal state of our model.

Nesta dissertação estudaremos sistemas de bósons ultrafrios armadilhados em uma rede ótica quadrada bidimensional sem levar em consideração o confinamento harmônico. A dinâmica desses sistemas é bem descrita pelo modelo de Bose-Hubbard, que prevê uma transição de fase quântica de um superfluido para um isolante de Mott a temperaturas baixas, e pode ser induzida variando a profundidade do potencial da rede ótica. Apresentaremos o diagrama de fases dessa transição construído a partir de uma aproximação de campo médio e também com um cálculo numérico usando um algoritmo de Monte Carlo Quântico, denominado algoritmo Worm. Encontramos o ponto crítico para o primeiro lobo de Mott em ambos os casos, concordando com trabalhos anteriores. / This work study the two-dimensional ultracold bosonic atoms loaded in a square optical lattice, without harmonic confinement. The dynamics of this system is described by the Bose-Hubbard model, which predicts a quantum phase transition from a superfluid to a Mott-insulator at low temperatures that can be induced by varying the depth of the optical potential. We present here the phase diagram of this transition built from a mean field approach and from a numerical calculation using a Quantum Monte Carlo algorithm, namely the Worm algorithm. We found the critical transition point for the first Mott lobe in both cases, in agreement with the standard literature.

We discuss the appearance of quantum orders in the Hubbard model for interacting electrons, at half-filling. Such phases do not have local order parameters and need to be characterized by the quantum mechanical properties of their ground state. On one hand, we study the Mott transition from a metal to a spin liquid insulator in two dimensions, of potential relevance to some layered organic compounds. The correlation-driven transition occurs at fixed filling and involves fractionalization of the electron: upon entering the insulator, a Fermi surface of neutral spinons coupled to an internal gauge field emerges. We focus on the transport properties near the quantum critical point and find that the emergent gauge fluctuations play a key role in determining the universal scaling. Second, motivated by a class of three-dimensional transition metal oxides, the pyrochlore iridates, we study the interplay of non-trivial band topology and correlations. Building on the strong spin orbit coupling in these compounds, we construct a general microscopic Hubbard model and determine its mean-field phase diagram, which contains topological insulators, Weyl semimetals, axion insulators and various antiferromagnets. We also discuss the effects many-body correlations on theses phases. We close by examining a fractionalized topological insulator that combines the two main themes of the thesis: fractionalization and non-trivial band topology. Specifically, we study how the two-dimensional protected surface states of a topological Mott insulator interact with a three-dimensional emergent gauge field. Various correlation effects on observables are identified.

We discuss the appearance of quantum orders in the Hubbard model for interacting electrons, at half-filling. Such phases do not have local order parameters and need to be characterized by the quantum mechanical properties of their ground state. On one hand, we study the Mott transition from a metal to a spin liquid insulator in two dimensions, of potential relevance to some layered organic compounds. The correlation-driven transition occurs at fixed filling and involves fractionalization of the electron: upon entering the insulator, a Fermi surface of neutral spinons coupled to an internal gauge field emerges. We focus on the transport properties near the quantum critical point and find that the emergent gauge fluctuations play a key role in determining the universal scaling. Second, motivated by a class of three-dimensional transition metal oxides, the pyrochlore iridates, we study the interplay of non-trivial band topology and correlations. Building on the strong spin orbit coupling in these compounds, we construct a general microscopic Hubbard model and determine its mean-field phase diagram, which contains topological insulators, Weyl semimetals, axion insulators and various antiferromagnets. We also discuss the effects many-body correlations on theses phases. We close by examining a fractionalized topological insulator that combines the two main themes of the thesis: fractionalization and non-trivial band topology. Specifically, we study how the two-dimensional protected surface states of a topological Mott insulator interact with a three-dimensional emergent gauge field. Various correlation effects on observables are identified.