京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第18445号 / 理博第4005号 / 新制||理||1577(附属図書館) / 31323 / 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 前野 悦輝, 教授 石田 憲二, 教授 田中 耕一郎 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

Cette thèse présente l'étude de la coexistence métal isolant dans deux systèmes très différents pour la communauté scientifique de la matière condensée : l'isolant topologique 3D Bi2Te3 et le composé prototype de la transition de Mott V2O3. Ces deux systèmes ont été étudiés par des techniques basées sur la spectroscopie de photoélectrons. La première technique utilisée est le TR-ARPES (time and angle resolved photoemission spectroscopy), avec une résolution temporelle de 80 fs, appliquée à l'isolant topologique 3D Bi2Te3 pour distinguer la dynamique ultra-rapide des états métalliques de la surface de celle des états isolants du volume. Cette mesure a permet de comprendre les différents mécanismes de diffusion entre la surface et le volume, ainsi que l'amélioration de la relaxation du cône de Dirac par la préexistence à la sous-surface d'une bande de flexion. La seconde technique utilisée dans cette thèse est le SPEM (scanning photoelectron microscopy), avec une résolution spatiale de 150 nm, permettant d'étudier la coexistence des domaines métalliques et isolants à la transition de Mott dans V2O3 ; cette coexistence a pour origine le caractère 1 er ordre de la transition. La mesure montre une coexistence métal-isolant dans le Cr-dopé : les domaines métalliques sont dus à des centres de nucléations < 150 nm et la forme des domaines est clairement liée à la forme des marches de clivage. / This thesis presents the study of metal-insulator coexistence in two very different systems for the scientific community of condensed matter: the 3D topological insulator Bi2Te3 and the prototype compound of the Mott transition V2O3. Both systems were studied by techniques based on photoelectron spectroscopy. The first technique is the TR- ARPES (time and angle resolved photoemission spectroscopy), with a temporal resolution of 80 fs, applied to the 3D topological insulator Bi2Te3 to distinguish the ultrafast dynamics of metallic surface states from that of the insulating bulk states. This allows us to understand the different mechanisms of scattering between the surface and the bulk, as well as the amelioration on the Dirac cone relaxation due to the preexistence of subsurface band bending. The second technique used in this thesis is the SPEM (scanning photoelectron microscopy), with a spatial resolution of 150 nm, which was used to study the coexistence of metallic and insulating domains at the Mott transition on V2O3. This coexistence takes its origin from the first order character of the transition. The measurement shows the metal-insulator coexistence on the Cr-doped: metal domains are due to nucleation centers < 150 nm and the shape of the domains is clearly linked to the shape of the cleavage steps.

No description available.

Cette thèse se concentre sur des aspects multiorbitales des systèmes fermioniques fortement corrélés. En particulier, sur l'existence d'une différentiation orbitale dans laquelle la coexistence de caractère itinérant et localisé peut être associée à différentes orbitales. Cette problématique est examinée dans le contexte des atomes froids et des matériaux, offrant un pont entre les deux communautés.Dans la première partie de la thèse, nous donnons un aperçu du problème des corrélations fortes dans les matériaux, et nous introduisons le concept de 'transition de Mott sélective en orbitales'. Nous fournissons également les principaux outils pour comprendre comment les matériaux peuvent être simulés avec des atomes froids, et nous présentons des résultats importants liés à la transition métal-isolant de Mott. Les aspects techniques, basées sur la théorie du champ moyen dynamique sont également discutés, et la solution de deux principaux modèles de systèmes fermioniques fortement corrélés, à savoir le modèle d'Hubbard (HM) et le modèle de Falicov-Kimball (FKM), sont passés en revue.Ensuite, nous étudions en détail la physique de deux espèces fermioniques en interaction forte avec des masses différentes dans un réseau optique. Nous établissons les différentes phases (avec et sans ordre à longue portée) en termes de la force des interactions (U), du rapport des masses et de la température (T), et aussi nous discutons les variables thermodynamiques, qui sont pertinentes pour les expériences d'atomes froids. Nous montrons que dans la phase métallique (U inférieure à une valeur critique) et avec un certain degré de différence de masses, un 'crossover' apparaît entre un état métallique du type de liquide de Fermi à basse T, et un état avec différentiation orbital à haute T, où les fermions lourds se localisent tandis que les fermions légers restent itinérant. Par conséquent, nous proposons ce modèle minimal pour étudier la physique des systèmes qui présentent une différentiation orbitale avec des expériences d'atomes froids.Basé sur les propriétés du modèle étudié, nous proposons la 'chromatographie entropique' comme une nouvelle méthode pour refroidir des atomes fermioniques dans les réseaux optiques. Nous discutons son efficacité et ses limites, et fournissons quelques idées afin de les surmonter.Dans la dernière partie de la thèse, nous généralisons le modèle précédent aux matériaux corrélés à plusieurs bandes qui permet d'afficher la différentiation orbitale. Nous montrons que l'état de Mott sélectif en orbital peut être stable sous les distorsions du réseau, modélisées par une hybridation locale entre les orbitales. Cependant, l'état de Mott est caractérisé par un pseudo-gap, où les fluctuations de charge sont brusquement réduites, mais l'état reste compressible. En relation au modèle précédent, nous discutons le 'crossover' entre l'état métallique et l'état sélectif induit par des effets température, nous comparons nos résultats avec les expériences de photoémission, et nous prédisons ce qui se passerait dans les matériaux qui présentent une hybridation locale entre les bandes. / This thesis focuses on multiorbital aspects of strongly correlated fermionic systems. In particular, it focuses on the existence of orbital differentiation in which coexistence of itinerant and localized character can be associated to different orbitals. This subject is discussed in the context of cold atoms and materials, providing a bridge between both communities.In the first part of the thesis, we give an insight into the problem of strong correlations in materials, and we introduce the concept of 'orbital-selective Mott transition'. We also provide the main tools to understand how materials can be simulated with cold atoms experiments, and we present important related results in the context of the metal-Mott insulator transition. The technical aspects, based on dynamical mean-field theory are also discussed, and the solution of two key models of strongly correlated fermionic systems, i.e., the Hubbard model (HM) and the Falicov-Kimball model (FKM), are reviewed.Then we study in detail the physics of two interacting fermionic species with different masses in an optical lattice. We establish the different phases (with and without long-range order) in terms of the interactions strength (U), mass ratio and temperature (T), and also discuss the thermodynamic variables, which are relevant in cold atoms experiments. We show that in the metallic phase (U below a critical value) and for some degree of mass imbalance, a crossover appears between a Fermi-liquid metallic state at low T, and an 'orbital-selective' state at higher T, where the heavy fermions effectively localize while the light species remain itinerant. Hence, we propose this minimal model for addressing orbital-selective physics with cold atoms experiments.Based on the properties of the studied model, we propose the 'entropic chromatography' as a new method for cooling fermionic atoms in optical lattices. We discuss its efficiency and limitations, and provide some ideas in order to overcome them.In the last part of the thesis we generalize the previous model to a model relevant for multiband correlated materials that can display orbital differentiation. We show that the orbital-selective Mott state can be stable under lattice distortions modeled by local hybridization between the orbitals. However, the Mott state is characterized by a pseudogap, where charge fluctuations abruptly reduce, but the state remains compressible. In connection with the previous model, we discuss the temperature-induced orbital-selective crossover in this problem, we compare our results with photoemission experiments, and predict what would happen in materials that display local hybridization between the bands.

The vicinity of continuous quantum phase transitions displays unique properties such as scaling behavior and incoherent excitation spectra which are not found in any stable phase of matter. This fascinating quantum critical regime is crucial for progress on key problems of modern condensed matter physics. The three research projects of this thesis challenge and refine our understanding of quantum criticality in different ways. Part I concerns unexpected quantum critical behavior near the Mott transition. The bandwidth-controlled Mott transition in the half-filled one-band Hubbard model is one of the most paradigmatic phenomena of strongly correlated physics. Within the approximation of dynamical mean-field theory (DMFT) this metal-insulator transition is of first order at low temperatures, with the transition line ending at a critical temperature. Surprisingly, numerical calculations with DMFT and experiments in organic salts consistently found quantum critical scaling of the resistivity above the critical temperature. The aim of this project is to explain this unexpected scaling in the absence of a quantum critical point in the phase diagram. To this end, we perform extensive DMFT simulations with the numerical renormalization group as a state-of-the-art impurity solver. We find that the quantum critical scaling can be traced back to the metastable insulator at the boundary of the coexistence region at T = 0 which exhibits previously unknown scale-invariance on the frequency axis. In Part II we study how magnetic quantum criticality is affected by the coupling to additional non-critical degrees of freedom. Considering typical electronic energy scales the study of quantum critical phenomena in magnets requires very low temperatures in the sub-100mK range. In this regime additional effects which are typically neglected in the theoretical modeling may become important. Here we focus on one particular example, which is the hyperfine coupling to nuclear spins. We investigate the fate of the quantum critical behavior at lowest temperatures and determine crossover scales below which a purely electronic description is no longer sufficient. Explicit calculations for paradigmatic models on the level of mean-field theory plus Gaussian fluctuations reveal that the quantum phase transition can be shifted or smeared in the presence of nuclear spins. More exotic effects of nuclear spins, e.g. in spin liquids, are discussed on a qualitative level. Part III is devoted to the discussion of domain-driven phase transitions in easy-axis ferromagnets.This work is motivated by an experimental study of LiHoF4, a dipolar easy-axis ferromagnet that displays a well-studied quantum phase transition from a ferromagnetic to a paramagnetic phase as function of a transverse field. Measurements of the ac susceptibility found a well-defined phase transition even in tilted fields where the Ising symmetry is explicitly broken and Landau theory of the microscopic order parameter predicts a crossover. We are able to explain and model the transition in tilted fields by the inclusion of domain effects, i.e., by taking into account the spontaneous breaking of translational symmetry by mesoscale pattern formation in the ferromagnetic phase. The modeling of stray-field energies as effective antiferromagnetic couplings between magnetization components in different domains is in excellent quantitative agreement with the experimental results.:1 Phases and their transitions . . . . . . . . . . . . . . . . . . . . 4 1.1 Thermal and quantum phase transitions . . . . . . . . . . . . . . . . . . . . 4 1.2 Theoretical description of phase transitions . . . . . . . . . . . . . . . . . . 8 1.3 Project overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 I Mott quantum criticality in the one-band Hubbard model . . . . . . . . . . .15 2 Introduction to the Mott transition . . . . . . . . . . . . . . . . . . . . 16 2.1 Metal-insulator transitions and the Hubbard model . . . . . . . . . . . . . . 16 2.2 A local perspective: the idea of dynamical mean-field theory . . . . . . . . . 19 2.3 Quantum critical scaling near the Mott transition . . . . . . . . . . . . . . . 21 3 Dynamical mean-field theory (DMFT) . . . . . . . . . . . . . . . . . . . . 25 3.1 Single-impurity Anderson model . . . . . . . . . . . . . . . . . . . . . . . . 25 3.2 Theoretical foundations of DMFT . . . . . . . . . . . . . . . . . . . . . . . 28 3.3 Wilson's numerical renormalization group . . . . . . . . . . . . . . . . . . . 32 3.4 Implementation and choice of parameters . . . . . . . . . . . . . . . . . . . 36 4 Power-law spectra and quantum critical scaling . . . . . . . . . . . . . . . . . . 38 4.1 Scale-invariant solutions of DMFT . . . . . . . . . . . . . . . . . . . . . . . 38 4.2 Spectral power laws at T=0 in the metastable insulator . . . . . . . . . . . 40 4.3 Finite-temperature crossovers in the spectral function . . . . . . . . . . . . 47 4.4 Resistivity scaling driven by spectral power laws . . . . . . . . . . . . . . . 50 4.5 Scaling analysis of the dynamic susceptibility . . . . . . . . . . . . . . . . . 58 4.6 Ideas and obstacles towards an analytical understanding . . . . . . . . . . . 62 4.7 Conclusions and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 II Limits on magnetic quantum criticality from nuclear spins . . . . . . . . . . . . .65 5 Stability of magnetic transitions to hyperfine coupling . . . . . . . . . . . . . . . .66 5.1 Nuclear spins near quantum criticality . . . . . . . . . . . . . . . . . . . . . 66 5.2 Introduction to nuclear spins and hyperfine coupling . . . . . . . . . . . . . 67 5.3 Magnetic phases in the presence of nuclear spins . . . . . . . . . . . . . . . 69 5.4 Two scenarios for magnetic quantum criticality plus nuclear spins . . . . . . 70 6 Paradigmatic models for magnetic quantum phase transitions . . . . . . . . . 73 6.1 Transverse-field Ising model . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 6.2 Coupled-dimer model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 6.3 Frustrated spin models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 7 Crossover scales introduced by nuclear spins . . . . . . . . . . . . . . . . . . .83 7.1 Shifted transitions: transverse-field Ising magnets . . . . . . . . . . . . . . . 83 7.2 Smeared transitions: coupled-dimer magnets . . . . . . . . . . . . . . . . . . 90 7.3 Additional transitions due to nuclear spins . . . . . . . . . . . . . . . . . . . 98 7.4 Exotic magnetic quantum phase transitions plus nuclear spins . . . . . . . . 101 7.5 Conclusions and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 III Domain-driven phase transitions in easy-axis ferromagnets . . . . . . . . 105 8 Easy-axis ferromagnet LiHoF4 . . . . . . . . . . . . . . . . . . . . 106 8.1 Easy-axis ferromagnets in tilted fields . . . . . . . . . . . . . . . . . . . . . 106 8.2 LiHoF4 and its phase transitions . . . . . . . . . . . . . . . . . . . . . . . . 109 9 Modeling of microscopic degrees of freedom in LiHoF4 . . . . . . . . . . . . 112 9.1 Landau theory in tilted fields . . . . . . . . . . . . . . . . . . . . . . . . . . 112 9.2 Crystal field effects and microscopic Hamiltonian . . . . . . . . . . . . . . . 113 9.3 Crossovers in the microscopic model . . . . . . . . . . . . . . . . . . . . . . 118 10 Modeling of mesoscopic degrees of freedom in LiHoF4 . . . . . . . . . . . . . . .123 10.1 Domains in ferromagnets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 10.2 Modeling of domain effects as effective interactions . . . . . . . . . . . . . . 127 10.3 Combined mean-field Hamiltonian and domain optimization . . . . . . . . . 130 10.4 Nature of the phase transition in tilted fields . . . . . . . . . . . . . . . . . 132 10.5 Domain-driven phase transition at T = 0 . . . . . . . . . . . . . . . . . . . . 135 10.6 Domain-driven phase transition at finite temperatures . . . . . . . . . . . . 141 10.7 Comparison with experimental results . . . . . . . . . . . . . . . . . . . . . 146 10.8 Conclusions and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 IV Summary & Outlook . . . . . . . . . . . . . . . . . . . . 151 V Appendices . . . . . . . . . . . . . . . . . . . . 155 A Part I: NRG level spectra . . . . . . . . . . . . . . . . . . . . 156 B Part I: Analytical properties of scale-invariant DMFT solutions . . . . . . . . . . .159 B.1 Kondo perturbation theory as an impurity solver . . . . . . . . . . . . . . . 159 B.2 Analytical properties of a power-law self-energy . . . . . . . . . . . . . . . . 166 C Part I: Scaling analysis of the resistivity . . . . . . . . . . . . . . . . . . 168 D Part II: Solution of the transverse-field Ising model with nuclear spins . . . . . . 172 D.1 Holstein-Primakoff representation of the electronic and nuclear spins . . . . 172 D.2 Determination of the classical reference state . . . . . . . . . . . . . . . . . 174 D.3 Excitation spectrum of the coupled nuclear-electronic model . . . . . . . . . 175 D.4 Magnetization, susceptibility, and heat capacity . . . . . . . . . . . . . . . . 177 E Part II: Solution of the coupled-dimer model with nuclear spins . . . . . . . . . . . 181 E.1 Bond-operator description of the electronic spins . . . . . . . . . . . . . . . 181 E.2 Determination to the electronic ground state . . . . . . . . . . . . . . . . . 185 E.3 Holstein-Primakoff representation of the nuclear spins . . . . . . . . . . . . 188 E.4 Excitation spectrum of the coupled nuclear-electronic model . . . . . . . . . 189 E.5 Staggered magnetization and susceptibility . . . . . . . . . . . . . . . . . . 192 F Part III: Calculation of domain-induced effective interactions . . . . . . . . . . . . . 198 Bibliography . . . . . . . . . . . . . . . . . . . . 203

Orientador: Eduardo Miranda / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-23T18:51:04Z (GMT). No. of bitstreams: 1 SuarezVillagran_MarthaYolima_D.pdf: 7321255 bytes, checksum: d76479a0e0c1143207cb4ee380a8034d (MD5) Previous issue date: 2013 / Resumo: Estudamos nesta tese alguns aspectos da transição metal-isolante de Mott no caso desordenado. O modelo no qual baseamos nosso estudo é o modelo de Hubbard desordenado, que é o modelo mais simples a apresentar a transição metal-isolante de Mott. Analisamos esse modelo através da Teoria Dinâmica de Campo Médio Estatística (StatDMFT). Essa teoria é uma extensão natural da Teoria Dinâmica de Campo Médio (DMFT), que foi usada com relativo sucesso nos últimos anos para analisar a transição de Mott no caso limpo. Como no caso dessa última, a StatDMFT incorpora os efeitos de correlação eletrônica apenas nos seus aspetos locais. A desordem é tratada de maneira a incorporar todos os efeitos de localização de Anderson. Com essa técnica, analisamos a transição de Mott desordenada no caso bi-dimensional, usando o Monte Carlo quântico para resolver os problemas de impureza única de Anderson requeridos pela StatDMFT. Encontramos as linhas espinodais nas quais o metal e o isolante deixam de ser meta-estáveis. Também estudamos os padrões espaciais das flutuações de quantidades locais, como a auto-energia e a função de Green local, e mostramos como há o aparecimento de regiões metálicas dentro do isolante e viceversa. Analisamos efeitos de tamanho finito e mostramos que, em consonância com os teoremas de Imry e Ma, a transição de primeira ordem desaparece no limite termodinâmico. Analisamos as propriedades de transporte desse sistema através de um mapeamento a um sistema de resistores aleatórios clássicos e calculamos a corrente média e sua distribuição através da transição metal-isolante. Finalmente, estudamos o comportamento da parede de domínio que se forma entre o isolante e o metal no caso limpo. Isso foi feito através de um modelo de uma cadeia unidimensional conectada a reservatórios, um metálico e um isolante, cada um em uma de suas extremidades. Nesse caso, utilizamos o método da Teoria de Perturbação Iterada para a solução dos modelos de impureza única. Encontramos o comportamento da parede como função da temperatura e das interações / Abstract: In this thesis, we studied some aspects of the Mott metal-insulator transition in the disordered case. The model on which we based our analysis is the disordered Hubbard model, which is the simplest model capable of capturing the Mott metal-insulator transition. We investigated this model through the Statistical Dynamical Mean-Field Theory (statDMFT). This theory is a natural extension of the Dynamical Mean-Field Theory (DMFT), which has been used with relative success in the last several years with the purpose of describing the Mott transition in the clean case. As is the case for the latter theory, the statDMFT incorporates the electronic correlation effects only incorporate Anderson localization effects.. With this technique, we analyzed the disordered two-dimensional Mott transition, using Quantum Monte Carlo to solve the associated single-impurity problems. We found the spinodal lines at which metal and insulator cease to be meta-stable. We also studied the spatial fluctuations of local quantities, such as the self-energy and the local Green¿s function, and showed the appearance of metallic regions within the insulator and vice-versa. We carried out an analysis of finite-size effects and showed that, in agreement with the theorems of Imry and Ma, the first-order transition is smeared in the thermodynamic limit. We analyzed transport properties by means of a mapping to a random classical resistor network and calculated both the average current and its distribution across the metalinsulator transition. Finally, we studied the behavior of the domain wall which forms between the metal and the insulator in the clean case. This was done by means of a model of a one-dimensional chain connected to two reservoirs, one metallic and the other insulating, each attached to one of the chain¿s ends. In this case, we used the Iterated Perturbation Theory technique in order to solve the associated singleimpurity problems. We then established the behavior of the domain wall width as a function of temperature and interactions / Doutorado / Física / Doutora em Ciências

This thesis is concerned with the influence of nanoscale boundaries and interfaces upon the electronic processes that occur within the inorganic semiconductors. Inorganic semiconductor nanowires and their blends with semiconducting polymers have been investigated using state-of-the-art ultrafast optical techniques to provide information on the sub-picosecond to nanosecond photoexcitation dynamics in these systems. Chapters 1 and 2 introduce the theory and background behind the work and present a literature review of previous work utilising nanowires in hybrid organic photovoltaic devices, revealing the performances to date. The experimental methods used during the thesis are detailed in Chapter 3. Chapter 4 describes the crucial roles of surface passivation on the ultrafast dynamics of exciton formation in gallium arsenide (GaAs) nanowires. By passivating the surface states of nanowires, exciton formation via the bimolecular conversion of electron-hole plasma can observed over few hundred picoseconds, in-contrast to the fast carrier trapping in 10 ps observed in the uncoated nanowires. Chapter 5 presents a novel method to passivate the surface-states of GaAs nanowires using semiconducting polymer. The carrier lifetime in the nanowires can be strongly enhanced when the ionization potential of the overcoated semiconducting polymer is smaller than the work function of the nanowires and the surface native oxide layers of nanowires are removed. Finally, Chapter 6 shows that the carrier cooling in the type-II wurtzite-zincblend InP nanowires is reduced by order-of magnitude during the spatial charge-transfer across the type-II heterojunction. The works decribed in this thesis reveals the crucial role of surface-states and bulk defects on the carrier dynamics of semiconductor nanowires. In-addition, a novel approach to passivate the surface defect states of nanowires using semiconducting polymers was developed.