In this thesis, results of the investigation of a new low-dimensional cobaltates Ba2-xSrxCoO4 are presented. The synthesis of both polycrystalline and single crystalline compounds using the methods of conventional solid state chemical reaction and floating-zone optical furnace is first introduced. Besides making polycrystalline powders, we successfully, for the first time, synthesized large single crystals of Ba2CoO4. Single crystals were also obtained for Sr doped Ba2-xSrxCoO4. Powder and single crystal x-ray diffraction results indicate that pure Ba2CoO4 has a monoclinic structure at room temperature. With Sr doping, the lattice structure changes to orthorhombic when x ≥ 0.5 and to tetragonal when x = 2.0. In addition, Ba2CoO4 and Sr2CoO4, have completely different basic building blocks in the structure. One is CoO4 tetrahedron and the later is CoO6 octahedron, respectively. Electronic and magnetic properties were characterized and discussed. The magnetic susceptibility, specific heat and thermal conductivity show that Ba2CoO4 has an antiferromagnetic (AF) ground state with an AF ordering temperature TN = 25 K. However, the magnitude of the Néel temperature TN is significantly lower than the Curie-Weiss temperature (|θ| ~ 110 K), suggesting either reduced-dimensional magnetic interactions and/or the existence of magnetic frustration. The AF interaction persists in all the samples with different doping concentrations. The Néel temperature doesn’t vary much in the monoclinic structure regime but decreases when the system enters orthorhombic. Magnetically, Ba2CoO4 has an AF insulating ground state while Sr2CoO4 has a ferromagnetic (FM) metallic ground state. Neutron powder refinement results indicate a magnetic structure with the spin mostly aligned along the a-axis. The result from a μ-spin rotation/relaxation (μ+SR) experiment agrees with our refinement. It confirms the AF order in the ab-plane. We also studied the spin dynamics and its anisotropy in the AF phase. The results from inelastic neutron scattering show that spin waves have a clear dispersion along a-axis but not along c-axis, indicating spin anisotropy. This work finds the strong spin-lattice coupling in this novel complex material. The interplay between the two degrees of freedom results an interesting phase diagram. Further research is needed when large single crystal samples are available.

Thesis advisor: Joshua E. Greene / We construct taut foliations in every closed 3-manifold obtained by r-framed Dehn surgery along a positive 3-braid knot K in S^3, where r < 2g(K)-1 and g(K) denotes the Seifert genus of K. This confirms a prediction of the L--space conjecture. For instance, we produce taut foliations in every non-L-space obtained by surgery along the pretzel knot P(-2,3,7), and indeed along every pretzel knot P(-2,3,q), for q a positive odd integer. This is the first construction of taut foliations for every non-L-space obtained by surgery along an infinite family of hyperbolic L-space knots. We adapt our techniques to construct taut foliations in every closed 3-manifold obtained along r-framed Dehn surgery along a positive 1-bridge braid, and indeed, along any positive braid knot, in S^3, where r < g(K)-1. These are the only examples of theorems producing taut foliations in surgeries along hyperbolic knots where the interval of surgery slopes is in terms of g(K). / Thesis (PhD) — Boston College, 2020. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Mathematics.

京都大学 / 0048 / 新制・課程博士 / 博士(人間・環境学) / 甲第22546号 / 人博第949号 / 新制||人||226(附属図書館) / 2019||人博||949(吉田南総合図書館) / 京都大学大学院人間・環境学研究科相関環境学専攻 / (主査)准教授 木下 俊哉, 教授 吉田 鉄平, 教授 森成 隆夫 / 学位規則第4条第1項該当 / Doctor of Human and Environmental Studies / Kyoto University / DGAM

In this study, the thermal properties of low dimensional materials such as graphene and boron nitride nanotube were investigated. As one of important heat transfer characteristics, interfacial thermal resistance (ITR) between graphene and Cu film was estimated by both experiment and simulation. In order to characterize ITR, the micropipette sensing technique was utilized to measure the temperature profile of suspended and supported graphene on Cu substrate that is subjected to continuous wave laser as a point source heating. By measuring the temperature of suspended graphene, the intrinsic thermal conductivity of suspended graphene was measured and it was used for estimating interfacial thermal resistance between graphene and Cu film. For simulation, a finite element method and a multiparameter fitting technique were employed to find the best fitting parameters. A temperature profile on a supported graphene on Cu was extracted by a finite element method using COMSOL Multiphysics. Then, a multiparameter fitting method using MATLAB software was used to find the best fitting parameters and ITR by comparing experimentally measured temperature profile with simulation one. In order to understand thermal transport between graphene and Cu substrate with different interface distances, the phonon density of states at the interface between graphene and Cu substrate was calculated by MD simulation.As another low dimensional material for thermal management applications, the thermal conductivity of BNNT was measured by nanoscale thermometry. For this work, a noble technique combining a focused ion beam (FIB) and nanomanipulator was employed to pick and to place a single BNNT on the desired location. The FIB technology was used to make nanoheater patterns (so called nanothermometer) on a prefabricated microelectrode device by conventional photolithography processes. With this noble technique and the nanoheater thermometry, the thermal conductivity of BNNT was successfully characterized by temperature gradient and heat flow measurements through BNNT.

This thesis aims to provide a classification of low-dimensional Lie algebras. We make emphasis on several structural properties, such as nilpotency, solvability and (semi) simpli- city. The first two properties relate to two fundamental theorems by Lie and Engels which classification results will be presented in a table for ease of access. / <p>I presented my thesis on 1st of October 2021.</p>

No description available.

Over the past two decades, controlling thermal transport properties at the nanoscale has become more and more relevant. This is mostly motivated by the need of developing novel energy-harvesting techniques based on thermoelectricity and the necessity to control the heat dissipation in semiconductor devices. In this field, two major research lines can be identified: On one side 'phononics', which aims at developing devices such as thermal diodes, thermal transistors, and thermal logic gates, among others, and on the other side, phonon engineering aiming at controlling heat transport by producing or structurally modifying heterostructures made of novel nanomaterials (e.g., two-dimensional (2D) materials, nanotubes, organic systems). In order to gain insight into the factors controlling nanoscale heat flow and to be able to design highly-efficient thermal devices, the development of new computational approaches is crucial. The primary goal of the present thesis is the implementation of new methodologies addressing classical and quantum thermal transport at the nanoscale. We will focus on three major issues: (i) We will study thermal rectification effect in nanodevices made of novel 2D materials by means of nonequilibrium molecular dynamics simulations. The influence of structural asymmetry and substrate deposition on the thermal rectification will be investigated. (ii) To address quantum ballistic thermal transport in nanoscale systems, we will implement a nonequilibrium Green's functions (NEGF) treatment of transport combined with a density-functional based approach. Here, we will explore the dependence of the thermal transport properties of 2D materials and nanotubes on different intrinsic (structural anisotropy and grain boundaries) and external (molecular functionalization, strain engineering, and doping) factors. Finally, (iii) a time-dependent NEGF formalism will be developed and implemented to probe the transient and steady thermal transport in molecular junctions. In short, our results show that the mechanisms governing the thermal rectification effect in the 2D thermal rectifiers proposed in this work are shape asymmetries, interface material (planar stacking order), and changes in the degree of spatial localization of high-frequency modes (under nonequilibrium heat transport conditions). The rectification effect can be also controlled by substrate engineering. Moreover, we found that quantum ballistic thermal transport in 2D puckered materials displays an anisotropic behavior. The presence of structural disorder in the form of grain boundaries in graphene reduces overall its thermal transport efficiency. Dynamical disorder induced by coupling to a thermostat has however a weaker effect, suggesting that structural defects are playing a major role. External factors have a noticeable influence on the heat transport in new 2D materials and BNC heteronanotubes. On the other hand, we have also been able to characterize, from a quantum point of view, the phonon dynamics in carbon-based molecular junctions. We expect that the results obtained within this thesis will yield new insights into the thermal management of low-dimensional materials, and thus open new routes to the design of thermoelectric and phononic devices. / In den letzten zwei Jahrzehnten hat die Kontrolle der thermischen Transporteigenschaften im Nanobereich immer mehr an Bedeutung gewonnen. Dies ist vor allem auf die Notwendigkeit zurückzuführen, neue Energiegewinnungstechniken zu entwickeln, die auf Thermoelektrizität basieren, sowie auf die Problematik, die Wärmeabfuhr in Halbleiterbauelementen kontrollieren zu müssen. In diesem Bereich lassen sich zwei große Forschungslinien identifizieren: Auf der einen Seite 'Phononik', die unter anderem auf die Entwicklung von Bauelementen wie thermischen Dioden, Transistoren und Logikgattern abzielt, und auf der anderen Seite die Phononentechnik, die den Wärmetransport durch Herstellung oder strukturelle Modifikation von Heterostrukturen aus neuartigen Nanomaterialien (z.B. zweidimensionalen (2D) Materialien, Nanoröhren, organischen Systemen) steuert. Um einen Einblick in die Faktoren zu erhalten, die den Wärmefluss im Nanobereich steuern, und um hocheffiziente thermische Bauteile entwickeln zu können, ist die Entwicklung neuer Berechnungsansätze entscheidend. Das Hauptziel der vorliegenden Arbeit ist die Implementierung neuer Methoden, die sich mit dem klassischen und dem quantenthermischen Transport auf der Nanoskala befassen. Wir werden uns auf drei Hauptthemen konzentrieren: (i) Wir werden den thermischen Rektifikationseffekt in Nanobauteilen aus neuartigen 2D-Materialien mit Hilfe von Nichtgleichgewichts-Molekulardynamiksimulationen studieren. Der Einfluss von Strukturasymmetrie und Substratablagerung auf die thermische Rektifikation wird untersucht. (ii) Um den quantenballistischen Wärmetransport in nanoskaligen Systemen anzugehen, werden wir eine NEGF-Behandlung (Nichtgleichgewichts-Greensche Funktionen) des Transports in Kombination mit einem dichtefunktionalen Ansatz implementieren. Hier wird die Abhängigkeit der thermischen Transporteigenschaften von 2D-Materialien und Nanoröhrchen von verschiedenen intrinsischen (strukturelle Anisotropie und Korngrenzen) und externen (molekulare Funktionalisierung, Stammtechnik und Dotierung) Faktoren untersucht. Schließlich wird (iii) ein zeitabhängiger NEGF-Formalismus entwickelt und implementiert, um den transienten und stetigen Wärmetransport in molekularen Verbindungen zu untersuchen. Unsere Ergebnisse zeigen, dass die wesentlichen Mechanismen für die thermische Gleichrichtung in 2D thermischen Gleichrichtern durch Asymmetrien der Bauteilform, das Interface-Material (planare Stapelung Reihenfolge), und änderungen im Grad der räumlichen Lokalisierung von Hochfrequenz-Modi (unter Nicht-Gleichgewicht Wärmetransport-Bedingungen) gegeben sind. Der Gleichrichteffekt kann auch durch die Wahl des Substrats gesteuert werden. Darüber hinaus haben wir festgestellt, dass der quantenballistische Wärmetransport in 2D-Puckered-Materialien ein anisotropes Verhalten zeigt. Das Vorhandensein von strukturellen Störungen in Form von Korngrenzen in Graphen reduziert insgesamt die Effizienz des Wärmetransports. Dynamische Störungen, die durch die Ankopplung an einen Thermostaten hervorgerufen werden, haben jedoch eine schwächere Wirkung, was darauf hindeutet, dass strukturelle Defekte eine große Rolle spielen. Externe Faktoren haben einen nachweislichen Einfluss auf den Wärmetransport in neuen 2D-Materialien und BNC-Heteronanotubes. Weiterhin konnten wir auch die Phononendynamik in kohlenstoffbasierten molekularen Verbindungen quantitativ charakterisieren. Wir erwarten, dass die Ergebnisse dieser Arbeit neue Erkenntnisse über das Wärmemanagement von niedrigdimensionalen Materialien liefern und damit neue Wege für das Design von thermoelektrischen und phononischen Bauelementen eröffnen.

Dans cette thèse nous avons étudié des indicateurs visant à caractériser les propriétés métalliques ou isolantes de systèmes de basse dimensionnalité à partir de calculs théoriques basés sur la fonction d'onde. Ces systèmes sont intéressants car ils permettent une compréhension en profondeur des phénomènes physiques qui peuvent ensuite être extrapolés à des systèmes plus étendus. Afin de réaliser cette étude nous avons utilisé un nouvel outil basé sur la théorie de la conductivité de Kohn : le tenseur de délocalisation total ou total position spread-tensor (TPS). Ce tenseur est défini comme le second cumulant de l'opérateur position : ? = <?|X2|?> - <?|X|?>2. Divisé par le numéro des électrons, il diverge quand la fonction d'onde est fortement délocalisée (forte fluctuation de la position des électrons) et converge vers une valeur finie dans le cas contraire. Ainsi, la conductivité est relié à la délocalisation de la fonction d'onde. Dans ce travail, deux définitions du TPS ont été abordées : une quantité sommée sur le spin (spin-summed TPS, SS-TPS) d'une part, et une décomposition selon le spin (spin-partitioned TPS, SSP-TSP) d'autre part. Cette dernière s'est avérée être un outil très efficace pour l'étude de systèmes fortement corrélés. Au cours de la thèse, nous avons commencé par étudier plusieurs systèmes diatomiques présentant des liaisons de natures différentes à l'aide de calculs d'interaction de configurations totale (FCI). Le TPS présente alors un maximum dans une zone précédant la rupture de liaison avant de converger asymptotiquement vers les valeurs atomiques, comme la consistance de taille du tenseur le laissait présager. Dans le cas de systèmes pour lesquels l'état électronique présente un croisement évité, le TPS diverge, mettant ainsi en évidence la forte délocalisation de la fonction d'onde. Le SS-TPS est donc un indicateur de choix pour suivre la nature de la liaison chimique. Nous avons ensuite considéré des systèmes à valence mixte de type II pour lesquels l'état fondamental présente un double-puits de potentiel avec un croisement évité avec le premier état excité. Il est donc nécessaire ici d'utiliser un traitement multi-configurationnel. Deux systèmes modèles ont ainsi été étudiés : i) deux di- mères H2 en interaction faible au niveau FCI et ii) un composé du type spiro au niveau CAS-SCF (à l'aide d'un code que nous avons implémenté dans Molpro). Dans les deux cas, le TPS présentait un maximum très marqué dans la région du croisement évité, signature d'une forte mobilité électronique. Nous nous sommes également intéressés à trois types de chaines d'atomes d'hydrogène : i atomes équidistants ii) chaines dimérisées à longueur de liaison H2 fixée et iii) chaines dimérisées. Tant le SS-TPS que le SP-TPS montrent des comportements différents selon le type de chaine considérée. Les premières ont un caractère métallique et une délocalisation de spin prononcée dans le régime fortement corrélé. Les secondes sont de nature isolante avec une délocalisation limitée. Les chaines dimérisées, quant à elle, dissocient très rapidement vers un état isolant mais avec une forte délocalisation de spin. Ces chaines demi-remplies ont aussi été traitées à l'aide d'hamiltonien de Hubbard et de Heisenberg. Nous avons ainsi pu rationaliser le comportement des SS-TPS et SP-TPS en variant le rapport de l'intégrale de saut et de la répulsion électron- électron (-t/U) entre sites adjacents. Le caractère ferromagnétique/anti-ferromagnétique a également pu être suivi en modifiant la valeur de la constante de couplage J dans le cas fortement corrélé. Finalement, ces indicateurs ont été mis en oeuvre pour des polyacenes cycliques. Dans ce cas, le TPS a permis de comprendre la nature des fonctions d'onde de l'état fondamental obtenues au niveau CAS-SCF et NEVPT2. / I carried out a theoretical study to characterize metallic and insulating properties of low-dimensional systems using wave function methods. Low-dimensional systems are particularly important because they allow an understanding that can be extrapolated to higher dimensional systems. We have employed a new tool based on the theory of conductivity of Kohn that we have named: total position-spread tensor (TPS). The TPS is defined as the second moment cumulant of the total position operator: ? = <?|X2|?> - <?|X|?>2 . The tensor divided by the number of electrons diverges when the wave function is delocalized (high fluctuation of electrons' positions), and it takes finite values for localized ones. In this way, the electrical conductivity is related to the proper delocalization of the wave function. In addition, the tensor can be divided in spin-summed (SS-TPS) and spin-partitioned tensors (SP-TPS). The latter one becomes a powerful tool to the study of strongly correlated systems. In this dissertation, we started to investigate at full configuration interaction (FCI) level diatomic molecules showing different types of bond. The TPS presented a marked maximum before the bond was broken and in the asymptotic limit one recovers the TPS values of isolated atoms (size consistency). For the case of diatomic systems showing avoided-crossing electronic states, the TPS diverges evidencing the high delocalization of the wave function. Therefore, the SS-TPS is capable of monitoring and characterizing molecular wave functions. We considered mixed-valence systems that are often distinguished by a double-well potential energy surface presenting an avoided-crossing. Thus, such a configuration possesses a strongly multireference nature involving at least two states of the same symmetry. Two different systems were investigated: i) two weakly interacting hydrogen dimers that were investigated at Full CI level, and ii) a spiro like molecule where the TPS tensor was evaluated in a CAS-SCF state-averaged wave function using our implementation of the SS- TPS formalism in MOLPRO. We found that the tensor's component in the direction of the electron transfer (ET) shows a marked maximum in the avoided-crossing region, evidencing the presence of a high electron mobility. The formalisms of the SS- and SP-TPS was applied to one dimensional systems composed by three types of half-filled hydrogen chains: i) equally-spaced chains, ii) fixed-bond dimerized chains, and iii) homothetic dimerized chains. Both the SS- and SP-TPS showed different signatures associated to the three types of systems. Equally-spaced chains have metallic wave functions and a high spin delocalization in the strongly correlated regime. In contrast, fixed-bond dimerized chains have an insulating character and a restricted spin delocalization. Finally, homothetic dimerized chains dissociate very quickly which renders them in the insulating state but with a high spin delocalization. We also studied half-filled chains by using the Hubbard and the Heisenberg Hamiltonians. On the one hand, we were able to depict the response of the SS- and SP-TPS by varying the ratio between the hopping and electron-electron repulsion (-t/U parameter) of topological connected sites. On the other hand, the ferromagnetic and anti-ferromagnetic character of the wave functions were evaluated by varying the coupling constant (J) in the strongly correlated systems. A theoretical study of closed polyacenes (PAH) structures was performed at CAS-SCF and NEVPT2 level. Our methodology for choosing the active space using the Hückel Hamiltonian was able to characterize the ground state of the systems that indeed fulfilled the Ovchinnikov rule. Finally, we applied the SS-TPS to understand the nature of the wave functions of these PAHs.

This work is about the properties of several low dimensional, small systems of interacting particles. We demonstrate that interaction between particles in the low dimensional small systems can lead to many unexpected effects. We considered electrons in a Luttinger liquid, in a superconducting state, and atoms in a magneto-optical trap. Using bosonization techniques we calculated the thermopower of a Luttinger liquid wire with an impurity. We predicted the appearance of a phase dependent force and resonant phase dependent magnetization in the nanoscopic superconductor - normal metal superconductor (or superconductor - two dimensional electron gas - superconductor) junction. We also considered plasma oscillations inside thin superconducting tubes and rings and predicted that the velocities of the plasmons in these systems are periodic functions of the magnetic flux. By considering neutral atoms in a harmonic trap we discovered that strongly repelling atoms do not form Bose-Einstein condensate at zero temperature but tend to occupy different orbitals with small mutual overlap, forming crystallite structures similar to Wigner molecules of electrons inside a quantum dot.

Spatial confinement of electrons and their interactions as well as confinement of the spin dimensionality often yield drastic changes of the electronic and magnetic properties of solids. Novel quantum transport and optical phenomena, involving electronic spin degrees of freedom in semiconductor heterostructures, as well as a rich variety of exotic quantum ground states and magnetic excitations in complex transition metal oxides that arise upon such confinements, belong therefore to topical problems of contemporary condensed matter physics. In this work electron spin systems in reduced dimensions are studied with Electron Spin Resonance (ESR) spectroscopy, a method which can provide important information on the energy spectrum of the spin states, spin dynamics, and magnetic correlations. The studied systems include quasi onedimensional spin chain materials based on transition metals Cu and Ni. Another class of materials are semiconductor heterostructures made of Si and Ge. Part I deals with the theoretical background of ESR and the description of the experimental ESR setups used which have been optimized for the purposes of the present work. In particular, the development and implementation of axial and transverse cylindrical resonant cavities for high-field highfrequency ESR experiments is discussed. The high quality factors of these cavities allow for sensitive measurements on μm-sized samples. They are used for the investigations on the spin-chain materials. The implementation and characterization of a setup for electrical detected magnetic resonance is presented. In Part II ESR studies and complementary results of other experimental techniques on two spin chain materials are presented. The Cu-based material Linarite is investigated in the paramagnetic regime above T > 2.8 K. This natural crystal constitutes a highly frustrated spin 1/2 Heisenberg chain with ferromagnetic nearest-neighbor and antiferromagnetic next-nearestneighbor interactions. The ESR data reveals that the significant magnetic anisotropy is due to anisotropy of the g-factor. Quantitative analysis of the critical broadening of the linewidth suggest appreciable interchain and interlayer spin correlations well above the ordering temperature. The Ni-based system is an organic-anorganic hybrid material where the Ni2+ ions possessing the integer spin S = 1 are magnetically coupled along one spatial direction. Indeed, the ESR study reveals an isotropic spin-1 Heisenberg chain in this system which unlike the Cu half integer spin-1/2 chain is expected to possess a qualitatively different non-magnetic singlet ground state separated from an excited magnetic state by a so-called Haldane gap. Surprisingly, in contrast to the expected Haldane behavior a competition between a magnetically ordered ground state and a potentially gapped state is revealed. In Part III investigations on SiGe/Si quantum dot structures are presented. The ESR investigations reveal narrowlines close to the free electron g-factor associated with electrons on the quantum dots. Their dephasing and relaxation times are determined. Manipulations with sub-bandgap light allow to change the relative population between the observed states. On the basis of extensive characterizations, strain, electronic structure and confined states on the Si-based structures are modeled with the program nextnano3. A qualitative model, explaining the energy spectrum of the spin states is proposed.