Dans cette thèse, nous étudions expérimentalement la génération d'impulsions carrées très énergétiques et accordable à l’échelle nanosecondes et d'impulsions ultracourtes à haute puissance moyenne de sortie dans les lasers à fibre utilisant les nanomatériaux comme absorbant saturable. Tout d'abord, puisque la dynamique des impulsions est dominée par l'interaction de la non linéarité et de la dispersion chromatique cubique de la fibre avec un mécanisme de discrimination d'intensité appelé absorbant saturable, la stabilité d'une distribution harmonique en mode verrouillé est étudiée par injection externe d'une onde continue.Enfin, nous avons utilisés des absorbant saturable à base de nanomatériaux déposés sur des tapers optiques dans les lasers à fibre pour générer des impulsions ultracourtes avec une puissance de sortie moyenne élevée. / In this thesis, we investigate experimentally the generation of high energy nanosecond tunable square pulses and high output power ultrashort pulses in fiber lasers. First, since pulse dynamics are dominated by the interaction of the fiber's cubic Kerr nonlinearity and chromatic dispersion with an intensity-discriminating mechanism referred to as a saturable absorber, the stability of a harmonic mode-locked distribution is studied by external injection of a continuous wave. Finally, we implemented nanomaterial based saturable absorbers in fiber laser configuration to generate ultrashort pulses with high average output power. Different techniques of achieving such components are explicitly detailed: ultrashort pulse generation in ring cavities where graphene and topological insulators are deposited on optical tapers to form a saturable absorber.

L'étude des phases de la matière est d'un intérêt fondamental en physique. La théorie de Landau, qui est le "modèle standard" des transitions de phases, caractérise les phases de la matière en termes des brisures de symétrie, décrites par un paramètre d'ordre local. Cette théorie a permis la description de phénomènes remarquables tels que la condensation de Bose-Einstein, la supraconductivité et la superfluidité.<p><p>Il existe cependant des phases qui échappent à la description de Landau. Il s'agit des phases quantiques topologiques. Celles-ci constituent un nouveau paradigme et sont caractérisées par un ordre global défini par un invariant topologique. Ce dernier classe les objets ou systèmes de la manière suivante: deux objets appartiennent à la même classe topologique s'il est possible de déformer continument le premier objet en le second. Cette propriété globale rend le système robuste contre des perturbations locales telles que le désordre. <p><p>Les atomes froids constituent une plateforme idéale pour simuler les phases quantiques topologiques. Depuis l'invention du laser, les progrès en physique atomique et moléculaire ont permis un contrôle de la dynamique et des états internes des atomes. La réalisation de gaz quantiques,tels que les condensats de Bose-Einstein et les gaz dégénérés de Fermi, ainsi que la réalisation de réseaux optiques à l'aide de faisceaux lasers, permettent d'étudier ces nouvelles phases de la matière et de simuler aussi la physique du solide cristallin.<p><p>Dans cette thèse, nous nous concentrons sur l'etude d'isolants topologiques avec des atomes froids. Ces derniers sont isolants de volume mais possèdent des états de surface qui sont conducteurs, protégés par un invariant topologique. Nous traitons trois sujets principaux. Le premier sujet concerne la génération dynamique d'un isolant topologique de Mott. Ici, les interactions engendrent l'isolant topologique et ce, sans champ de jauge de fond. Le second sujet concerne la détection des isolants topologiques dans les expériences d'atomes froids. Nous proposons deux méthodes complémentaires pour caractériser celles-ci. Finalement, le troisième sujet aborde des thèmes au-delà de la définition standard d'isolant topologique. Nous avons d'une part proposé un algorithme efficace pour calculer la conductivité de Berry, la contribution topologique à la conductivité transverse lorsque l'énergie de Fermi se trouve dans une bande d'énergie. D'autre part, nous avons utilisé des méthodes pour caractériser les propriétés quantiques topologiques de systèmes non-périodiques.<p><p>L'étude des isolants topologiques dans les expériences d'atomes froids est un sujet de recherche récent et en pleine expansion. Dans ce contexte, cette thèse apporte plusieurs contributions théoriques pour la simulation de systèmes quantiques sur réseau avec des atomes froids. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

Cette thèse est consacrée à de nouveaux phénomènes en physique liées au spin et à la topologie des quasi-particules lumière-matière dans des hétérostructures. Elle est divisée en quatre parties. Chapitre 1 donne un fond nécessaire et introduit les propriétés fondamentales des polaritons et des excitons indirects dans des puits quantiques couplés. Chapitre 2 est concentré sur la dynamique de spin et sur formation de défauts topologiques dans des systèmes aux excitons indirects. Les 2 derniers chapitres considèrent les structures basées sur les microcavités. Chapitre 3 est consacré à la dynamique de spin des polaritons dans des oscillateurs paramétriques optiques. Finalement, chapitre 4 étudie les réseaux des microcavités en forme des piliers et introduit l’isolant topologique polaritonique. / The present thesis manuscript is devoted to new phenomena in physics of light-matter quasiparticles in heterostructures, related to spin and topology. It is divided into four parts. Chapter 1 gives a necessary background, introducing basic properties of microcavity polaritons and indirect excitons in coupled quantum wells. Chapter 2 is focused on spin dynamics and topological defects formation in indirect exciton many-body systems. The last 2 chapters are related to microcavity-based structures. Chapter 3 is devoted to polariton spin dynamics in optical parametric oscillators. Finally, Chapter 4 studies pillar microcavity lattices and introduces the polariton topological insulator.

Dans cette thèse je me suis intéressé au caractère relativiste de matériaux topologiques tridimensionnels : les semi-métaux de Weyl et les isolants topologiques. Après une introduction aux états de surfaces et aux matériaux topologiques, je discute leurs propriétés de covariance sous les rotations trigonométriques et hyperboliques. Ces transformations me permettent de traiter les équations du mouvement d'un électron dans un champ magnétique ou à la surface, sous l'influence d'un champ électrique ou d'une inclinaison de la relation de dispersion. En première partie, je l'illustre dans le cas de la réponse magnéto-optique des semi-métaux de Weyl, en présence d'une inclinaison. Ces calculs sont en lien avec ma collaboration avec les expérimentateurs du LNCMI à Grenoble pour la caractérisation de la structure de bande de Cd₃As₂ où l'on montre que ce matériau est un semi-métal de Kane et non un semi-métal de Dirac dans la gamme de potentiels chimiques expérimentalement accessible. L'autre partie de cette thèse porte sur les états de surface des isolants topologiques où l'on montre qu'il existe des états de surface massifs au-delà de l'état de surface chiral. Ces états semblent avoir été observés par des études en ARPES d'échantillons de Bi₂Se₃ et Bi₂Te₃ oxydés et par des mesures de transport sur HgTe déformé. J'ai ainsi eu l'occasion de travailler avec les expérimentateurs du LPA à Paris sur le comportement des états de surface de HgTe sous forts effets de champ. Je termine par une discussion des états à l'interface entre un semi-métal de Weyl et un isolant dans le cas où le gap de ce dernier est suffisamment petit pour observer l'effet d'un champ magnétique et d'une inclinaison de la relation de dispersion sur les états de surface. / During my PhD studies I focused on the relativistic properties of threedimensional topological materials, namely Weyl semimetals and topological insulators. After introducing surface states and topological materials I discuss their covariance in trigonometric and hyperbolic rotations. These transformations help to solve the equations of motion of an electron in a magnetic field or at the surface with an applied electric field or with a tilt in the band dispersion. In a first place, I illustrate these transformations for the magneto-optical response of tilted Weyl semimetals. This work is related to my collaboration with experimentalists at LNCMI, Grenoble for characterizing the band structure of Cd₃As₂ where we show that this material is a Kane semi-metal instead of a Dirac semi-metal in the experimentally accessible range of chemical doping. The other part of this thesis is concerned with the surface states of topological insulators. I show that massive surface states can also exist in addition to the chiral surface state due to band inversion. Such states may have already been observed in ARPES measurement of oxidized Bi₂Se₃ and Bi₂Te₃ and in transport measurement of strained bulk HgTe. I show the work we performed with experimentalists at LPA, Paris on the behavior of HgTe surface states for strong field effects. Finally, I discuss the states at the interface of a Weyl semimetal and a small gap insulator. In this situation, an applied magnetic field or the tilt of the band dispersion can strongly affect the observed surface states.

This thesis was inspired by the discovery of Bi14Rh3I9, the first so-called weak three-dimensional topological insulator (3D-TI) and has been concerned with the topic of TIs in general. Two aspects were tackled to gain a deeper understanding of this new state of matter. On one hand, the expansion of the material’s basis and on the other hand developing a simple model of the structure and analysing it via density-functional theory (DFT) based methods. To discover new materials, a systematic investigation of the metal-rich parts of the bismuth–platinum-metal–iodine phase systems was conducted. It led to six new phases among the bismuth subiodides. Some of which, e.g. Bi14Rh3I9, share a honeycomb network of platinum-metal-centred bismuth-cubes and are the seed of a family of materials with this structural motive. The others show strand-like structures or layered structures with platinum-platinum bonds. The latter were so far unknown amongst bismuth subiodides. The honeycomb network was separately analysed and shown to host the TI properties. Structurally and electronically it can be seen as a “heavy graphene analogue”, which refers to the fact that graphene with hypothetical strong spin-orbit coupling (“heavy graphene”) was the first TI put forward by theoreticians. Apart from DFT-calculations, physical experiments confirmed the TI properties. Angle-resolved photoelectron spectroscopy (ARPES) was used to verify the electronic structure and scanning tunnelling microscopy and spectroscopy (STM and STS) to reveal the protected 1D edge states present at the cleaving surface of this material. As the arrangement of the honeycomb layer varies between the different known and newly discovered materials within this family of structures, this influence was also investigated. All further materials were also characterised by DFT-calculations and physical experiments, e.g. magnetisation and transport measurements. This thesis might give an experimental and theoretical basis for a deeper understanding of the TI state of matter. The 1D edge states on the surface of Bi14Rh3I9 could be a chance to handle spins and therefore propel spintronic research, or they could host Majorana fermions, which could be used as qubits in quantum computing.

The term "topological insulator" (TI) represents a novel class of compounds which are insulating in the bulk, but simultaneously and unavoidably have a metallic surface. The reason for this is the non-trivial band topology, arising from particular band inversions and the spin-orbit interaction, of the bulk. These topologically protected metallic surface states are characterized by massless Dirac dispersion and locked helical spin polarization, leading to forbidden back-scattering with robustness against disorder. Based on the extraordinary features of the topological insulators an abundance of new phenomena and many exciting experiments have been proposed by theoreticians, but still await their experimental verification, not to mention their implementation into applications, e.g. the creation of Majorana fermions, advanced spintronics, or the realization of quantum computers. In this perspective, the 3D TIs Bi2Te3 and Bi2Se3 gained a lot of interest due to their relatively simple electronic band structure, having only a single Dirac cone at the surface. Furthermore, they exhibit an appreciable bulk band gap of up to ~ 0.3 eV, making room temperature applications feasible. Yet, the execution of these proposals remains an enormous experimental challenge. The main obstacle, which thus far hampered the electrical characterization of topological surface states via transport experiments, is the residual extrinsic conductivity arising from the presence of defects and impurities in their bulk, as well as the contamination of the surface due to exposure to air. This thesis is part of the actual effort in improving sample quality to achieve bulk-insulating Bi2Te3 films and study of their electrical properties under controlled conditions. Furthermore, appropriate capping materials preserving the electronic features under ambient atmosphere shall be identified to facilitate more sophisticated ex-situ experiments. Bi2Te3 thin films were fabricated by molecular beam epitaxy (MBE). It could be shown that, by optimizing the growth conditions, it is indeed possible to obtain consistently bulk-insulating and single-domain TI films. Hereby, the key factor is to supply the elements with a Te/Bi ratio of ~8, while achieving a full distillation of the Te, and the usage of substrates with negligible lattice mismatch. The optimal MBE conditions for Bi2Te3 were found in a two-step growth procedure at substrate temperatures of 220°C and 250°C, respectively, and a Bi flux rate of 1 Å/min. Subsequently, the structural characterization by high- and low-energy electron diffraction, photoelectron spectroscopy, and, in particular, the temperature-dependent conductivity measurements were entirely done inside the same ultra-high vacuum (UHV) system, ensuring a reliable record of the intrinsic properties of the topological surface states. Bi2Te3 films with thicknesses ranging from 10 to 50 quintuple layers (QL; 1QL~1 nm) were fabricated to examine, whether the conductivity is solely arising from the surface states. Angle resolved photoemission spectroscopy (ARPES) demonstrates that the chemical potential for all these samples is located well within the bulk band gap, and is only intersected by the topological surface states, displaying the characteristic linear dispersion. A metallic-like temperature dependency of the sheet resistance is observed from the in-situ transport experiments. Upon going from 10 to 50QL the sheet resistance displays a variation by a factor 1.3 at 14K and of 1.5 at room temperature, evidencing that the conductivity is indeed dominated by the surface. Low charge carrier concentrations in the range of 2–4*10^12 cm^−2 with high mobility values up to 4600 cm2/Vs could be achieved. Furthermore, the degradation effect of air exposure on the conductance of the Bi2Te3 films was quantified, emphasizing the necessity to protect the surface from ambient conditions. Since the films behave inert to pure oxygen, water/moisture is the most probable source of degeneration. Moreover, epitaxially grown elemental tellurium was identified as a suitable capping material preserving the properties of the intrinsically insulating Bi2Te3 films and protecting from alterations during air exposure, facilitating well-defined and reliable ex-situ experiments. These findings serve as an ideal platform for further investigations and open the way to prepare devices that can exploit the intrinsic features of the topological surface states.:Abstract Kurzfassung Acronyms List of Symbols Introduction 1 Topological insulators 1.1 Basic theory of topological insulators 1.2 3D topological insulator materials: bismuth chalcogenides 2 Experimental techniques 2.1 General layout of the UHV-system 2.2 Molecular beam epitaxy 2.3 Structural and spectroscopic characterization 2.3.1 RHEED and LEED 2.3.2 Photoelectron spectroscopy 2.3.3 Ex situ x-ray diffraction 2.4 In situ electrical resistance measurements 2.4.1 In situ transport setup 2.4.2 Measurement equipment and operation modes 2.5 Substrates and sample holders 3 MBE growth and structural characterization of Bi2Te3 thin films 3.1 Bi2Te3 growth optimization and in situ structural characterization 3.1.1 1-step growth on Al2O3 (0001) 3.1.2 2-step growth on Al2O3 (0001) 3.1.3 2-step growth on BaF2 (111) 3.2 Ex situ structural characterization 4 In situ spectroscopy and transport properties of Bi2Te3 thin films 4.1 In situ spectroscopy of Bi2Te3 thin films 4.1.1 XPS 4.1.2 ARPES 4.2 Combined ARPES and in situ electrical resistance measurements of bulk-insulating Bi2Te3 thin films 4.2.1 Quality of the in situ electrical sample contacts 4.2.2 Verification of the intrinsic conduction through topological surface states of bulk-insulating Bi2Te3 thin films 5 Effect of surface contaminants on the TI properties 5.1 Effect of air exposure on the electrical conductivity of Bi2Te3 surfaces 5.2 Determination of the contaminants causing degradation of the TI properties 5.3 Long-time resistance behavior of a Bi2Te3 film exposed to minimal traces of contaminants 6 Protective capping of bulk-insulating Bi2Te3 thin films 6.1 Capping with BaF2 6.1.1 MBE growth and structure of BaF2 on Bi2Te3 thin films 6.1.2 Electron spectroscopy and electrical transport properties of BaF2 capped Bi2Te3 6.2 Capping with tellurium 6.2.1 MBE growth and structure of Te on Bi2Te3 thin films 6.2.2 Photoelectron spectroscopy and electrical transport properties of Te capped Bi2Te3 6.2.3 De-capping of Te 6.2.4 Efficiency of Te capping against air exposure 7 Conclusion and outlook Bibliography Versicherung Curriculum vitae Veröffentlichungen / Der Begriff "Topologischer Isolator" (TI) beschreibt eine neuartige Klasse von Verbindungen deren Inneres (engl. Bulk) isolierend ist, dieses Innere aber gleichzeitig und zwangsläufig eine metallisch leitende Oberfläche aufweist. Dies ist begründet in der nicht-trivialen Topologie dieser Materialien, welche durch eine spezielle Invertierung einzelner Bänder in der Bandstruktur und der Spin-Bahn-Kopplung im Materialinneren hervorgerufen ist. Diese topologisch geschützten, metallischen Oberflächenzustände sind gekennzeichnet durch eine masselose Dirac Dispersionsrelation und gekoppelte Helizität der Spinpolarisation, welche die Rückstreuung der Ladungsträger verbietet und somit zur Stabilisierung der Zustände gegenüber Störungen beiträgt. Auf Grundlage dieser außergewöhnlichen Merkmale haben Theoretiker eine Fülle neuer Phänomene und spannender Experimente vorhergesagt. Deren experimentelle Überprüfung steht jedoch noch aus, geschweige denn deren Umsetzung in Anwendungen, wie zum Beispiel die Erzeugung von Majorana Teilchen, fortgeschrittene Spintronik, oder die Realisierung von Quantencomputern. Aufgrund ihrer relativ einfachen Bandstruktur, welche nur einen Dirac-Kegel an der Oberfläche aufweist, haben die 3D TI Bi2Te3 und Bi2Se3 in den letzten Jahren großes Interesse erlangt. Weiterhin besitzen diese Materialien eine merkliche Bandlücke von bis zu ~0,3 eV, welche sogar Anwendungen bei Raumtemperatur ermöglichen könnten. Dennoch ist deren experimentelle Umsetzung nachwievor eine enorme Herausforderung. Das Haupthindernis, welches bis jetzt insbesondere die elektrische Charakterisierung the topologischen Oberflächenzustände behindert hat, ist die zusätzliche Leitfähigkeit des Materialinneren, welche durch Kristalldefekte und Beimischungen, sowie die Verunreinigung der Probenoberfläche durch Luftexposition bedingt wird. Die vorliegende Arbeit liefert einen Beitrag zu aktuellen den Anstrengungen in der Verbesserung der Probenqualität der TI um die Leitfähigkeit des Materialinneren zu unterdrücken, sowie die anschließende Untersuchung der elektrischen Eigenschaften unter kontrollierten Bedingungen durchzuführen. Weiterhin sollen geeignete Deckschichten identifiziert werden, welche die besonderen elektronischen Merkmale der TI nicht beeinflussen sowie diese gegen äußere Einflüsse schützen, und somit die Durchführung anspruchsvoller ex situ Experimente ermöglichen können. Die untersuchten Bi2Te3 Schichten wurden mittels Molekularstrahlepitaxie (MBE) hergestellt. Es konnte gezeigt werden, dass es allein durch Optimierung der Wachstumsbedingungen möglich ist Proben herzustellen, die gleichbleibend isolierende Eigenschaften des TI Inneren aufweisen und Eindomänen-Ausrichtung besitzen. Die zentralen Faktoren sind hierbei die Aufrechterhaltung eines Flussratenverhältnisses von Te/Bi ~8 der einzelnen Elemente, sowie die Wahl einer ausreichend hohen Substrattemperatur, um ein vollständiges Abdampfen (Destillation) des überschüssigen Tellur zu erreichen. Weiterhin müssen Substrate mit gut angepassten Gitterparametern verwendet werden, welches bei BaF2 (111) gegeben ist. Optimales MBE Wachstum konnte durch ein Zwei-Stufen Prozess bei Substrattemperaturen von 220°C und 250°C und einer Bi-Verdampfungsrate von 1 Å/min erreicht werden. Die nachfolgende Charakterisierung der strukturellen Eigenschaften, Photoelektronenspektroskopie, sowie temperaturabhängige Leitfähigkeitsmessungen wurden alle in einem zusammenhängenden Ultrahochvakuum-System durchgeführt. Auf diese Weise wird eine zuverlässige Erfassung der intrinsischen Eigenschaften der TI sichergestellt. Zur Überprüfung, ob die Leitfähigkeit der Proben tatsächlich nur durch die Oberflächenzustände hervorgerufen wird, wurden Filme mit Schichtdicken im Bereich von 10 bis 50 Quintupel-Lagen (QL; 1QL~ 1 nm) hergestellt und charakterisiert. Winkelaufgelöste Photoelektronenspektroskopie (ARPES) belegt, dass das chemische Potential (Fermi-Niveau) in allen Proben innerhalb der Bandlücke der Bandstruktur des Materialinneren liegt und nur von den topologisch geschützten Oberflächenzuständen gekreuzt wird, welche die charakteristische lineare Dirac Dispersionsrelation aufweisen. Die temperaturabhängigen Widerstandsmessungen zeigen ein metallisches Verhalten aller Proben. Bei der Variation der Schichtdicke von 10 zu 50QL wird eine Streuung des Flächenwiderstandes vom Faktor 1,3 bei 14K und 1,5 bei Raumtemperatur beobachtet. Dies beweist, dass die gemessene Leitfähigkeit vorrangig durch die topologisch geschützten Oberflächenzustände hervorgerufen wird. Eine geringe Oberflächenladungsträgerkonzentration im Bereich von 2–4*10^12 cm^−2 und hohe Mobilitätswerte von bis zu 4600 cm2/Vs wurden erreicht. Weiterhin wurden die negativen Auswirkungen auf die Eigenschaften der TI durch Luftexposition quantifiziert, welches die Notwendigkeit belegt, die Oberfläche der TI vor Umgebungseinflüssen zu schützen. Die Proben verhalten sich inert gegenüber reinem Sauerstoff, daher ist Wasser aus der Luftfeuchte höchstwahrscheinlich der Hauptgrund für die beobachtbare Verschlechterung. Darüber hinaus konnte epitaktisch gewachsenes Tellur als geeignete Deckschicht ausfindig gemacht werden, welches die Eigenschaften der Bi2Te3 Filme nicht beeinflusst, sowie gegen Veränderungen durch Luftexposition schützt. Die gewonnenen Erkenntnisse stellen eine ideale Grundlage für weiterführende Untersuchungen dar und ebnen den Weg zur Entwicklung von Bauelementen welche die spezifischen Besonderheiten der topologischen Oberflächenzustände.:Abstract Kurzfassung Acronyms List of Symbols Introduction 1 Topological insulators 1.1 Basic theory of topological insulators 1.2 3D topological insulator materials: bismuth chalcogenides 2 Experimental techniques 2.1 General layout of the UHV-system 2.2 Molecular beam epitaxy 2.3 Structural and spectroscopic characterization 2.3.1 RHEED and LEED 2.3.2 Photoelectron spectroscopy 2.3.3 Ex situ x-ray diffraction 2.4 In situ electrical resistance measurements 2.4.1 In situ transport setup 2.4.2 Measurement equipment and operation modes 2.5 Substrates and sample holders 3 MBE growth and structural characterization of Bi2Te3 thin films 3.1 Bi2Te3 growth optimization and in situ structural characterization 3.1.1 1-step growth on Al2O3 (0001) 3.1.2 2-step growth on Al2O3 (0001) 3.1.3 2-step growth on BaF2 (111) 3.2 Ex situ structural characterization 4 In situ spectroscopy and transport properties of Bi2Te3 thin films 4.1 In situ spectroscopy of Bi2Te3 thin films 4.1.1 XPS 4.1.2 ARPES 4.2 Combined ARPES and in situ electrical resistance measurements of bulk-insulating Bi2Te3 thin films 4.2.1 Quality of the in situ electrical sample contacts 4.2.2 Verification of the intrinsic conduction through topological surface states of bulk-insulating Bi2Te3 thin films 5 Effect of surface contaminants on the TI properties 5.1 Effect of air exposure on the electrical conductivity of Bi2Te3 surfaces 5.2 Determination of the contaminants causing degradation of the TI properties 5.3 Long-time resistance behavior of a Bi2Te3 film exposed to minimal traces of contaminants 6 Protective capping of bulk-insulating Bi2Te3 thin films 6.1 Capping with BaF2 6.1.1 MBE growth and structure of BaF2 on Bi2Te3 thin films 6.1.2 Electron spectroscopy and electrical transport properties of BaF2 capped Bi2Te3 6.2 Capping with tellurium 6.2.1 MBE growth and structure of Te on Bi2Te3 thin films 6.2.2 Photoelectron spectroscopy and electrical transport properties of Te capped Bi2Te3 6.2.3 De-capping of Te 6.2.4 Efficiency of Te capping against air exposure 7 Conclusion and outlook Bibliography Versicherung Curriculum vitae Veröffentlichungen

Indiana University-Purdue University Indianapolis (IUPUI) / The prevalent applications of energy storage devices have incited wide-spread efforts on production of thin, flexible, and light-weight lithium-ion batteries. In this work, lithium-ion batteries using novel flexible paper-based current collectors have been developed. The paper-based current collectors were fabricated from carbon nanotube (CNT)-coated wood microfibers (CNT-microfiber paper). This thesis presents the fabrication of the CNT-microfiber paper using wood microfibers, coating electrode materials, design and assemblies of battery, testing methodologies, and experimental results and analyses. Wood microfibers were coated with carbon nanotubes and poly(3,4-ethylenedioxythiophene) (PEDOT) through an electrostatic layer-by-layer nanoassembely process and formed into a sheet, CNT-microfiber paper. The CNT loading of the fabricated paper was measured 10.1 μg/cm2 subsequently considered. Electrode material solutions were spray-coated on the CNT-microfiber paper to produce electrodes for the half and full-cell devices. The CNT current collector consists of a network structure of cellulose microfibers at the micro-scale, with micro-pores filled with the applied conductive electrode materials reducing the overall internal resistance for the cell. A bending test revealed that the paper-based electrodes, compared to metal ones, incurred fewer damages after 20 bends at an angle of 300o. The surface fractures on the paper-based electrodes were shallow and contained than metallic-based electrodes. The micro-pores in CNT-microfiber paper structure provides better adherence to the active material layer to the substrate and inhibits detachment while bending. Half-cells and full-cells using lithium cobalt oxide (LCO), lithium titanium oxide (LTO), and lithium magnesium oxide (LMO) were fabricated and tested. Coin cell assembly and liquid electrolyte was used. The capacities of half-cells were measured 150 mAh/g with LCO, 158 mAh/g with LTO, and 130 mAh/g with LMO. The capacity of the LTO/LCO full-cell also was measured 126 mAh/g at C/5 rate. The columbic efficiency of the LTO/LCO full-cell was measured 84% for the first charging cycle that increased to 96% after second cycle. The self-discharge test of the full-cell after charging to 2.7 V at C/5 current rate is showed a stable 2 V after 90 hours. The capacities of the developed batteries at lower currents are comparable to the metallic electrode-based devices, however, the capacities were observed to drop at higher currents. This makes the developed paper-based batteries more suitable for low current applications, such as, RFID tags, flexible electronics, bioassays, and displays. The capacities of the batteries at higher current can be improved by enhancing the conductivity of the fibers, which is identified as the future work. Furthermore, fabrication of an all solid state battery using solid electrolyte is also identified as the future work of this project.

This report discusses higher differential forms with applications in the study of topological phenomena. The integer quantum Hall effect is first discussed, demonstrating a connection between models on a lattice and quantum field theories bridged by a topological invariant, namely the Chern number. Next, for parametrized models on a lattice, the higher Berry curvature is described. This is a rank-(d + 2) differential form on a (d + 2)-dimensional parameter manifold which provides a relation between models in a bulk and on a lower-dimensional interface. Finally, a family of quantum field theories connected to a (d + 1)-dimensional manifold, termed a target space, is constructed. This connection is realized through the incorporation of a set of classical fields, and the effective action of the full field theories all contain a Wess-Zumino-Witten term given by the pullback of a rank-(d + 1) differential form from the target space to spacetime. By performing an extension of spacetime, a (d + 2)-form on a (d + 2)-dimensional target space is constructed in a similar way. Extending a theory in d dimensions thus yields a form on a target space of the same dimension as that of a (d + 1)-dimensional theory without extension, defining a dimensional hierarchy. The dimensional relations inherent in the two higher forms studied indicate the possibility of a relation between them. / Denna rapport beskriver högre ordningens differentialformer med tillämpningar inom topologiska fenomen. Den heltaliga kvantmekaniska Halleffekten beskrivs först, som ett exempel på ett samband mellan modeller på ett gitter och kvantfältteorier som förbindas av topologiska invarianter, specifikt Chern-talet. För parametriserade modeller på ett gitter beskrivs därefter den högre Berrykrökningen. Detta är en differentialform av ordning (d + 2) definierad på en (d + 2)-dimensionell parametermångfald som ger en koppling mellan modeller i en kropps inre och på dens gränsskikt, som är i en lägre dimension. Slutligen konstrueras en familj av kvantfältteorier som är kopplade till en (d + 1)-dimensionell mångfald kallad modellens målrum. Denna koppling realiseras genom introduktionen av ett antal klassiska fält, och den effektiva verkan för den fullständiga teorin innehåller en Wess-Zumino-Witten-term som ges av en tillbakadragen (d + 1)-form från målrummet till rumtiden. Genom att utvidga rumtiden kan även en (d + 2)-form på en (d + 2)-dimensionellt målrum konstrueras på ett motsvarande sätt. Utvidgningen av en teori i d dimensioner ger därmed en differentialform på ett målrum med samma dimension som målrummet för en (d + 1)-dimensionell teori utan utvidning, vilket definierar en dimensionell hierarki. Dimensionsrelationerna inbyggda i dessa två differentialformer indikerar den möjliga existensen av en relation mellan dem.

[pt] Nesta tese estudamos dois importantes sistemas de Isoladores Topológicos (TIs), onde nos concentramos particularmente no papel das interações e percolação nos estados de borda topológicos. Primeiro, analisamos o papel das interações vizinhas mais próximas em um protótipo de TI unidimensional, o modelo Su-Schrieffer-Heeger (SSH). Com base em um formalismo de função de Green, aplicamos a equação de Dyson em combinação com a aproximação da matriz-T para verificar a correspondência bulk-edge na presença de interações. Os expoentes críticos próximos às transições de fase topológicas são os mesmos do modelo SSH não interagente, indicando que o sistema permanece na mesma classe de universalidade, apesar da presença de interações. O segundo sistema é um TI bidimensional simétrico na inversão de tempo, ou seja, o modelo de Bernevig-Hughes-Zhang (BHZ) em conjunto com um metal ferromagnético com quebra de reversão do tempo (FMM), onde investigamos a percolação do estado Hall de spin quântico do modelo BHZ para o FMM por meio de um modelo de ligações fortes (tight-binding). Demonstramos que dependendo de se o estado de borda do cone de Dirac submerge nas sub-bandas do FMM e da direção da magnetização do FMM, a percolação do estado de borda e seu spin-momentum-locking são afetados de maneiras diferentes. Surpreendentemente, descobrimos que a corrente de spin de borda de equilíbrio no modelo BHZ, naturalmente esperada dos estados de borda de propagação do spin polarizado, está de fato ausente devido ao cancelamento das bandas de valência. No entanto, fluxos laminares de correntes de carga e spin persistente à temperatura ambiente são produzidos perto da interface da junção BHZ / FMM. Usando teoria de resposta linear, investigamos a polarização de spin induzida pela corrente causada pela percolação do estado de borda, que serve como um torque de rotação que é encontrado ser predominantemente field-like. Além disso, a polarização do spin é dramaticamente aumentada perto das impurezas na borda do modelo BHZ. / [en] In this thesis we studied two important Topological Insulators (TIs), where we focused particularly on the role of interactions and percolation on the topological edge states. First, we analyzed the role of nearest-neighbor interactions in a prototype one-dimensional TI, namely the Su-Schrieffer-Heeger (SSH) model. Based on a Green s function formalism, we applied Dyson s equation in combination with T-matrix approximation to verify the bulk-edge correspondence in the presence of interactions. The critical exponents near topological phase transitions are found to be the same as the noninteracting SSH model, indicating that the system stays in the same universality class despite the presence of interactions. The second system is a two-dimensional timereversal symmetric TI, namely the Bernevig-Hughes-Zhang (BHZ) model in conjunction with a time-reversal breaking ferromagnetic metal (FMM), where we investigated the percolation of the quantum spin Hall state from the TI layer to the FMM by means of a tight-binding model. We demonstrated that depending on whether the edge state Dirac cone submerges into the FMM subbands and the direction of the magnetization of the FMM, the percolation of the edge state and its spin-momentum locking are affected in different ways. Surprisingly, we uncover that the equilibrium edge spin current in the BHZ model, naturally expected from the spin polarized propagating edge states, is in fact absent due to the cancellation from the valence bands. Nevertheless, laminar flows of room temperature persistent charge and spin currents are produced near the interface of the BHZ/FMM junction. Using a linear response theory, we investigate the current-induced spin polarization caused by the percolation of the edge state, which serves as a spin torque that is found to be predominantly field-like. Moreover, the spin polarization is dramatically enhanced near the impurities at the edge of the BHZ model.

[pt] A investigação da geometria quântica em semicondutores e isoladores tornou-se significativa devido às suas implicações nas características dos materiais. A noção de geometria quântica surge considerando a métrica quântica do estado de Bloch da banda de valência, que é definido a partir da sobreposição dos estados de Bloch em momentos ligeiramente diferentes. Ao integrar a métrica quântica em toda a zona de Brillouin, introduzimos uma quantidade que chamamos de número de fidelidade, que significa a distância média entre estados de Bloch adjacentes. Além disso, apresentamos um formalismo para expressar o número de fidelidade como um marcador de fidelidade local no espaço real que pode ser definido em qualquer sítio da rede. O marcador pode ser calculado diretamente diagonalizando o hamiltoniano da rede que descreve o comportamento das partículas na rede. Posteriormente, o conceito de número e marcador de fidelidade é estendido para temperatura finita utilizando a teoria de resposta linear, conectando-os a medições experimentais que envolvem analisar o poder de absorção óptica global e local quando o material é exposto à luz linearmente polarizada. Particularmente para materiais bidimensionais, a opacidade do material permite a determinação direta do número de fidelidade espectral, permitindo a detecção experimental do número de fidelidade. Finalmente, um marcador de fidelidade não local é introduzido considerando a divergência da métrica quântica. Este marcador é postulado como um indicador universal de transições de fase quântica, assumindo que o momento cristalino permanece um número quântico válido. Este marcador não local pode ser interpretado como uma função de correlação dos estados de Wannier, que são funções de onda localizadas que descrevem estados eletrônicos em um cristal. A generalidade e aplicabilidade destes conceitos são demonstradas através da investigação de vários isoladores topológicos e transições de fase topológicas em diferentes dimensões. Essas descobertas elaboram o significado dessas quantidades e sua conexão com vários fenômenos fundamentais na física da matéria condensada. / [en] The investigation of quantum geometry in semiconductors and insulators has become significant due to its implications for material characteristics. The notion of quantum geometry arises by considering the quantum metric of the valence-band Bloch state, which is defined from the overlap of the Bloch states at slightly different momenta. By integrating the quantum metric through-out the Brillouin zone, we introduce a quantity that we call fidelity number, which signifies the average distance between adjacent Bloch states. Furthermore, we present a formalism to express the fidelity number as a local fidelity marker in real space that can be defined on every lattice site. The marker can be calculated directly by diagonalizing the lattice Hamiltonian that describes particle behavior on the lattice. Subsequently, the concept of the fidelity number and marker is extended to finite temperature using linear-response theory, connecting them to experimental measurements which involves analyze the global and local optical absorption power when the material is exposed to linearly polarized light. Particularly for two-dimensional materials, the material s opacity enables straightforward determination of the fidelity number spectral, allowing for experimental detection of the fidelity number. Finally, a nonlocal fidelity marker is introduced by considering the divergence of the quantum metric. This marker is postulated as a universal indicator of quantum phase transitions, assuming the crystalline momentum remains a valid quantum number. This nonlocal marker can be interpreted as a correlation function of Wannier states, which are localized wave functions describing electronic states in a crystal. The generality and applicability of these concepts are demonstrated through the investigation of various topological insulators and topological phase transitions across different dimensions. These findings elaborate the significance of these quantities and their connection to various fundamental phenomena in condensed matter physics.