Proefschrift Universiteit van Amsterdam. / Met lit. opg. - Met samenvatting in het Roemeens en Nederlands.

Thesis (Ph. D.)--Rijksuniversiteit te Leiden, 1988. / Includes bibliographical references.

Thesis (Revise). / Includes bibliographical references.

Universiẗat, Diss., 2002--Münster (Westfalen).

Techn. University, Diss., 2005--Berlin.

Adding interactions to topological (non-)trivial free fermion systems can in general have four different effects: (i) In symmetry protected topological band insulators, the correlations may lead to the spontaneous breaking of some protecting symmetries by long-range order that gaps the topological boundary modes. (ii) In free fermion (semi-)metal, the interaction could vice versa also generate long-range order that in turn induces a topological mass term and thus generates non-trivial phases dynamically. (iii) Correlation might reduce the topological classification of free fermion systems by allowing adiabatic deformations between states of formerly distinct phases. (iv) Interaction can generate long-range entangled topological order in states such as quantum spin liquids or fractional quantum Hall states that cannot be represented by non-interacting systems. During the course of this thesis, we use numerically exact quantum Monte Carlo algorithms to study various model systems that (potentially) represent one of the four scenarios, respectively. First, we investigate a two-dimensional $d_{xy}$-wave, spin-singlet superconductor, which is relevant for high-$T_c$ materials such as the cuprates. This model represents nodal topological superconductors and exhibits chiral flat-band edge states that are protected by time-reversal and translational invariance. We introduce the conventional Hubbard interaction along the edge in order to study their stability with respect to correlations and find ferromagnetic order in case of repulsive interaction as well as charge-density-wave order and/or additional $i$s-wave pairing for attractive couplings. A mean-field analysis that, for the first time, is formulated in terms of the Majorana edge modes suggests that any order has normal and superconducting contributions. For example, the ferromagnetic order appears in linear superposition with triplet pairing. This finding is well confirmed by the numerically exact quantum Monte Carlo investigation. Second, we consider spinless electrons on a two-dimensional Lieb lattice that are subject to nearest-neighbor Coulomb repulsion. The low energy modes of the free fermion part constitute a spin-$1$ Dirac cone that might be gapped by several mass terms. One option breaks time-reversal symmetry and generates a topological Chern insulator, which mainly motivated this study. We employ two flavors of quantum Monte Carlo methods and find instead the formation of charge-density-wave order that breaks particle-hole symmetry. Additionally, due to sublattices of unequal size in Lieb lattices, this induces a finite chemical potential that drives the system away from half-filling. We argue that this mechanism potentially extends the range of solvable models with finite doping by coupling the Lieb lattice to the target system of interest. Third, we construct a system with four layers of a topological insulators and interlayer correlation that respects one independent time-reversal and a unitary $\mathbb{Z}_2$ symmetry. Previous studies claim a reduced topological classification from $\mathbb{Z}$ to $\mathbb{Z}_4$, for example by gapping out degenerate zero modes in topological defects once the correlation term is designed properly. Our interaction is chosen according to this analysis such that there should exist an adiabatic deformation between states whose topological invariant differs by $\Delta w=\pm4$ in the free fermion classification. We use a projective quantum Monte Carlo algorithm to determine the ground-state phase diagram and find a symmetry breaking regime, in addition to the non-interacting semi-metal, that separates the free fermion insulators. Frustration reduces the size of the long-range ordered region until it is replaced by a first order phase transition. Within the investigated range of parameters, there is no adiabatic path deforming the formerly distinct free fermion states into each other. We conclude that the prescribed reduction rules, which often use the bulk-boundary correspondence, are necessary but not sufficient and require a more careful investigation. Fourth, we study conduction electron on a honeycomb lattice that form a Dirac semi-metal Kondo coupled to spin-1/2 degrees of freedom on a Kagome lattice. The local moments are described by a variant of the Balents-Fisher-Girvin model that has been shown to host a ferromagnetic phase and a $\mathbb{Z}_2$ spin liquid at strong frustration. Here, we report the first numerical exact quantum Monte Carlo simulation of the Kondo-coupled system that does not exhibit the negative-sign problem. When the local moments form a ferromagnet, the Kondo coupling induces an anti-ferromagnetic mass term in the conduction-electron system. At large frustration, the Dirac cone remains massless and the spin system forms a $\mathbb{Z}_2$ spin liquid. Owing to the odd number of spins per unit cell, this constitutes a non-Fermi liquid that violates Luttinger's theorem which relates the Fermi volume to the particle density in a Fermi liquid. This phase is a specific realization of the so called 'fractional Fermi liquid` as it has been first introduced in the context of heavy fermion models. / Durch Hinzufügen von Wechselwirkungen zu topologisch (nicht-)trivialen, freien Fermion-systemen können im Allgemeinen vier verschiedene Effekte entstehen: (i) Im Fall von symmetriegeschützen topologischen Bandisolatoren können Korrelationen durch langreichweitige Ordnung einige der schützenden Symmetrien spontan brechen, sodass die topologischen Randzustände eine Bandlücken aufweisen. (ii) In (Halb-)metallen mit freien Elektronen können Wechselwirkungen im Gegenzug langreichweitige Ordnung erzeugen, welche wiederum einen topologischen Massenterm induzieren und so eine nicht-triviale Phase dynamisch erzeugen. (iii) Korrelationen können außerdem zur Reduktion der topologischen Klassifikation freier Fermionsystemen führen, indem sie adiabatische Manipulationen zwischen zuvor verschiedenen Zuständen ermöglichen. (iv) Wechselwirkungen können langreichweitig verschränkte topologische Ordnung in Zuständen wie Quanten-Spin-Flüssigkeiten oder fraktionellen Quanten-Hall-Zuständen erzeugen, die nicht durch wechselwirkungsfreie Systeme dargestellt werden können. Im Laufe dieser Dissertation benutzen wir numerisch-exakte Quanten-Monte-Carlo Algorithmen um verschiedene Modelsysteme zu untersuchen, die (potentiell) eines der vier Szenarien darstellen. Als Erstes untersuchen wir zwei-dimensionale, $d_{xy}$-Wellen, spin-singlet Supraleiter, die relevant für Hochtemperatur-Supraleiter wie den Cupraten sind. Dieses Model repräsentiert lückenlose Supraleiter und weist chirale dispersionslose Randzustände auf, die durch Zeitumkehr- und Translationssymmetrie geschützt sind. Wir führen die übliche Hubbard-Wechselwirkung entlang des Randes ein um die Stabilität in Bezug auf Korrelationen zu untersuchen und beobachten ferromagnetische Ordnung im Fall von repulsiven Wechselwirkungen sowie Ladungsdichtewellen und/oder zusätzliche $i$s-Wellen-Paarung bei attraktiven Kopplungen. Eine Molekularfeldanalyse, die zum ersten Mal bezüglich der Majorana Randzuständen formuliert wird, deutet an, dass jede Ordnung normale und supraleitende Beiträge enthält. Diese Erkenntnis wird durch die numerisch-exakte Quanten-Monte-Carlo Untersuchung gut bestätigt. Als Zweites betrachten wir spinlose Elektronen auf einem zwei-dimensionalen Lieb-Gitter die der nächsten-Nachbar Coulombwechselwirkung ausgesetzt sind. Die Niedrigenergiemoden des freien Teilsystems bilden Spin-$1$ Dirac-Fermionen mit verschiedenen möglichen Massentermen. Bei einem davon wird die Zeitumkehrsymmetrie gebrochen und ein topologischer Chern-Isolator erzeugt, was die Hauptmotivation dieser Untersuchen darstellt. Wir verwenden zwei verschiedene Arten der Quanten-Monte-Carlo Methoden und finden stattdessen die Bildung von Ladungsdichtewellenordnung, welche die Teilchen-Loch-Symmetrie bricht. Zusätzlich führt dies, durch die verschieden großen Untergitter die Lieb-Gitters, zu einem endlichen chemischen Potential und treibt das System weg von Halbfüllung. Wir argumentieren, dass dieser Mechanismus möglicherweise die Breite von lösbaren Modellen mit endlicher Dotierung erweitert, indem das Lieb-Gitter an das Zielmodel von Interesse angekoppelt wird. Als Drittes konstruieren wir ein System, bestehend aus vier Schichten eines topologischen Isolators, mit Wechselwirkungen zwischen den Schichten, das eine unabhängige Zeitumkehr- und eine unitäre $\mathbb{Z}_2$ Symmetrie respektiert. Vorangegangene Untersuchungen legen nahe eine von $\mathbb{Z}$ auf $\mathbb{Z}_4$ reduzierte topologische Klassifikation, zum Beispiel durch das Aufspalten entarteter Nullmoden in topologischen Defekten, sofern die Korrelationen entsprechend entworfen wurden. Unsere Wechselwirkungen sind den Regeln dieser Analysis folgend gewählt, sodass ein adiabatischer Pfad zwischen Zuständen, deren topologische Quantenzahl sich um $\Delta q=\pm4$ unterscheiden, existieren sollte. Wir benutzen einen projektiven Quanten-Monte-Carlo Algorithmus um das Phasendiagramm des Grundzustandes zu bestimmen und erhalten, zusätzlich zum nicht-wechselwirkenden Halbleiter, einen symmetriegebrochenen Bereich der die nicht-wechselwirkenden Isolatoren voneinander trennt. Frustration reduziert die Größe dieser Region mit langreichweitiger Ordnung bis sie durch einen Phasenübergang erster Ordnung ersetzt wird. Im betrachteten Parameterbereich gibt es keinen adiabatischen Pfad, der zuvor verschiedene nicht-wechselwirkende Zustände ineinander überführt. Wir schließen daraus, dass die beschriebenen Regel zur Reduktion, die oft die Korrespondenz zwischen dem Probeninneren und dem Rand verwenden, notwendig aber nicht hinreichend sind und dass es hierzu weiterer Studien bedarf. Als Viertes betrachten wir Leitungselektronen auf einem Honigwabengitter, die einen Dirac Halbleiter verkörpern, und Kondo-gekoppeln diese mit Spin-$1/2$ Freiheitsgraden auf einem Kagomegitter. Die lokalen Momente werden durch eine Variante des Balents-Fisher-Girvin Models beschrieben, welches nachweislich eine ferromagnetische Phase und eine $\mathbb{Z}_2$ Spinflüssigkeit bei starker Frustration beherbergt. Wir berichten hier über die erste numerisch-exakte Quanten-Monte-Carlo Simulation des Kondo-gekoppelten Systems, die kein negatives Vorzeichenproblem aufweist. Wenn die lokalen Momente einen Ferromagneten bilden, überträgt dies einen antiferromagnetischen Massenterm auf das System der Leitungselektronen. Bei starker Frustration bleiben die Dirac-Fermionen masselos und das Spinsystem bildet eine $\mathbb{Z}_2$ Spinflüssigkeit. Aufgrund der ungeraden Anzahl von Spin-Freiheitsgraden pro Einheitszelle stellt dies keine Fermiflüssigkeit dar und verletzt das Theorem von Luttinger, dass das Fermivolumen mit der Teilchendichte der Fermiflüssigkeit verbindet. Diese Phase ist eine spezielle Realisation der sogenannten `fraktionellen Fermiflüssigkeit' die zuerst im Zusammenhang mit Schwerfermion-Systeme eingeführt worden ist.

This thesis aims to investigate the form-phase diagram of aqueous solutions of the triblock copolymer Pluronic P123 focusing on its high-temperature phases. P123 is based on polyethylene as well as polypropylene oxide blocks and shows a variety of di erent temperaturedependent micelle morphologies or even lyotropic liquid crystal phases in aqueous solutions. Besides the already well-studied spherical aggregates at intermediate temperatures, the size and internal structure of both worm-like and lamellar micelles, which appear near the cloud point, is determined using light, neutron and X-ray scattering. By combining the results of time-resolved dynamic light as well as small-angle neutron and X-ray scattering experiments, the underlying structural changes and kinetics of the sphere-to-worm transition were studied supporting the random fusion process, which is proposed in literature. For temperatures near the cloud point, it was observed that aqueous P123 solutions below the critical crystallization concentration gelate after several hours, which is linked to the presence and structure of polymeric surface layers on the sample container walls as shown by neutron re ectometry measurements. Using a hierarchical model for the lamellar micelles including their periodicity as well as domain and overall size, it is possible to unify the existing results in literature and propose a direct connection between the near-surface and bulk properties of P123 solutions at temperatures near the cloud point. / Ziel dieser Dissertation ist die Untersuchung des Form-Phasendiagrams des Dreiblock-Co- polymers Pluronic P123 mit dem besonderen Fokus auf dessen Phasenverhalten bei hohen Temperaturen. P123 besteht aus Polyethylen- und Polypropylenoxid-Blöcken und zeigt in wässriger Lösung vielfältige, temperaturabhängige Mizellformen oder sogar Flüssigkristallphasen. Neben den bereits intensiv untersuchten sphärischen Aggregaten bei mittleren Temperaturen, werden die Größen und inneren Strukturen der wurmartigen und lamellearen Aggregate mittels Licht-, Neutronen- und Röntgenstreumethoden untersucht, welche nahe des Trübungspunktes der Lösungen auftreten. Durch die Kombination von zeitaufgelösten dynamischen Licht- und Kleinwinkelstreuung-Experimenten wurden die strukturellen Änderungen und kinetischen Prozesse während des Kugel-Wurm-Übergangs untersucht, welche den bereits in der Literatur vorgeschlagenen zufälligen Fusionsprozess weiter bestätigen. Es wurde beobachtet, dass wässrige P123-Lösungen unterhalb der kritischen Kristallisationskonzentration nach mehreren Stunden gelieren, was durch Neutronenreflektometrie mit dem Auftreten und der Struktur von oberflächennahen Monolagen auf den Messzellwänden in Verbindung gebracht wurde. Wenn ein hierarchisches Model für die lamellaren Mizellen verwendet wird, das deren Periodizität, Domänen- und Gesamtgröße berücksichtigt, ist es außerdem möglich, die bisherigen Ergebnisse in der Literatur zu vereinigen und eine direkte Verbindung zwischen dem Aggregationsverhalten von P123 auf Oberflächen und in Lösung bei Temperaturen nahe des Trübungspunktes zu ziehen.

The innovative flash-sintering technique has been considered to investigate the effect of DC electric field on sintering and electrical conductivity of two oxide ceramics MnCo2O4 and La0.6Sr0.4Co0.2 Fe0.8O3 (LSCF). These oxides are renowned for their high electrical conductivity and oxygen reduction properties, and therefore find application in solid oxide fuel cell as interconnect coating and cathode respectively. Flash-sintering of LSCF composite with 10 mol% Gd doped ceria (GDC), which is considered more promising than pure LSCF for cathodic application, is also reported. In flash-sintering-effect, when an adequately high DC electric field is applied on a green specimen, which is subjected to heating at a constant rate, the field drives rapid increase in the conductivity at a suitable furnace temperature. This event drives sintering, and the rate of shrinkage is so rapid that the material, generally, sinters in a couple of seconds without requiring elevated temperature. The aim of the present work is to better understand such electric field effect on sintering as it may affect the material properties (microstructure, conductivity etc.). Till now, the technique has been mostly reported for weakly conducting or insulating materials. The present work deals with the conducting-edge materials to point out the versatility of flash-sintering technique. The present work demonstrates the flash-sintering of conductive oxides, MnCo2O4 and LSCF. These oxides are sintered under electric field ranging from 7.5 to 12.5 V/cm at furnace temperatures 100-200°C, which are 1000°C lower than traditional heat treatments. LSCF, being highly conductive, surprisingly sinters at 25°C under 12.5 V/cm. On the other hand, the composite phases (LSCF/GDC: 60/40, 50/50 and 40/60 weight ratios) flash sinters at higher temperatures and electric fields which is systematic with GDC additions. The role of electric field and temperature in sintering is realized from specimen temperature which helps to understand the observed outstanding event. The flash-sintering occurs at conventional sintering temperatures and therefore, enhanced sintering at a particular temperature at this stage is expected to result from increased defect concentrations. Rapid increase in the conductivity possibly provides diffusion-able sites at rapid rate and the high sintering rate can be explained to occur using these sites. At drastic conductivity increase, the thermal effect is so dominant that ions diffuse for sintering more with the support of local temperature and less by the electric field. The extent of sintering is confirmed through scanning electron microscopy. The microstructural analysis carried on flash-sintered samples suggests that the surface morphology and grain growth homogeneity resemble that of traditionally-sintered samples. With the proper choice of processing parameters (electric field and current density), dense and pore-free microstructure for MnCo2O4 coating and porous microstructure of LSCF for cathodic application are obtained in very short sintering time. From the case of composites, current is clearly pointed to be a determining parameter in controlling the density. An enhanced electric field effect is recorded on the microstructure of MnCo2O4 starting at 1100°C. No such temperature discrimination is observed for LSCF, the sintering effects being regular with the temperature. From XRD analysis, MnCo2O4 undergoes to a significant phase reduction for the specimen temperature in excess of 1100°C. The LSCF and its composite phase’ are stable and compatible with GDC10 against flash-sintering. These observations are in agreement with conventional sintering. The flash-effect is investigated by analyzing electrical conductivity property of dense specimen. Consistent changes in current-voltage characteristics with temperature suggest that the electric field controls the conductivity in the same way as temperature does. At sufficient temperature, the electric field enhances the conductivity by increasing thermal excitation of charge carrier. At low temperature, the field enhances the conductivity by direct energy transfer; these temperature and field has a fundamental role in flash-sintering. On the basis of conductivity analysis, flash-sintering is proposed to be accelerated by utilizing defect complexes formed during the “polaron-hopping” which is the usual conduction mechanism of these materials, MnCo2O4 and LSCF. On the basis of correlation between the microstructure and phase stability, a constraint about the utilization of defect complex is realized. Sintering is enhanced when there is stabilization of reduction reaction in hopping process. This condition assures the availability of defect complexes for sintering; under equal probability of hopping transitions, the reduction is more under the tendency of oxidation. It was realized in the sintering of MnCo2O4 is enhanced over conventional for temperatures higher than 1080°C which corresponds to the reduction temperature. Such implication was verified on LSCF where sintering is found to be enhanced for all the considered temperatures as it undergoes reduction as sintering starts. Therefore, sintering is proposed to occur by the movement of reduced transition metal cations during usual hopping mechanism. Sintering at unusually low temperatures, in very short times and involving quite usual ionic transitions shows its potentials for ceramics manufacturing especially in multilayer production and temperature sensitive application.

The remarkable discovery of flash sintering came across during the early work of Cologna et al. and emerged as an attractive technique in the field of ceramic processing. In this technique the applied electric field initiates the “flash” event, while the densification is controlled by the current density set. Sintering occurs in less than 5 s at a threshold temperature for a given applied field. The objective of this thesis is to analyse the phenomena of flash sintering with different ceramic oxides; such as alumina-zirconia composite, hydroxyapatite and doped-alumina. The technique involved the application of constant electric field to a dog bone shaped specimen by means of two platinum electrodes while heating. Experiments were performed either in constant heating rate or in Isothermal condition. For the two-phase 3YSZ-alumina ceramic flash sintering was studied by constant heating rate (CHR) and isothermal sintering experiments. In CHR experiment the 50 vol% 3YSZ-alumina composite was shown to flash sinter at a furnace temperature of 1060°C under an electrical field of 150 V cm−1. Conversely, undoped single-phase alumina remains immune to sintering under fields up to 1000 V cm−1, although single-phase 3YSZ flash sinters at 750°C (furnace temperature). The mechanisms of field assisted sintering are divided into two regimes. At low fields the sintering rate increases gradually (FAST), while at high fields sintering occurs abruptly (FLASH). Interestingly, alumina/zirconia composites show a hybrid behaviour such that early sintering occurs in FAST mode, which is then followed by flash-sintering. The specimens held in the flashed state, after they had sintered to nearly full density, show much higher rate of grain growth than in conventional experiments. These results are in contrast to earlier work where the rate of grain growth had been shown to be slower under weak electrical fields. In the case of isothermal field-assisted sintering of two-phase, 50 vol% 3YSZ-alumina, the composites exhibit an incubation time for the onset of the flash event. Weaker applied fields and lower temperatures lengthen the incubation period. The effect is highly non-linear. For example at 1300°C and 150 V cm–1 the flash occurs nearly instanteously (in 10 s), but extends to two hours at 1275°C and 65 V cm–1. This behaviour is reminiscent of nucleation and growth phenomena in chemically driven experiments involving phase transformations in the solid state. Here, a model for nucleation under electrical driving forces, based upon the growth of embryos of colossal permittivity is presented. The flash sintering was also studied for composites with in-creasing volume faction of alumina in zirconia (10-50 vol%). The flash onset temperature or the incubation time for the 3YSZ-alumina composites increases with increasing the alumina volume fraction. In case of CHR experiments of hydroxyapatite, flash effect was shown at 840°C for an applied field of 2000 V cm-1. All the flash sintered samples show stable hydroxyapatite phase. However the sample sintered at 500 V cm-1 requires higher sintering temperature and shows enhanced preferred orientation due to higher diffusivity along c-axis. In case of alumina, field in excess to 1000 V cm-1 are re-quired to induce flash effect, whereas doped alumina shows flash sintering at 1000 V cm-1.

Controlled drug delivery systems, which are intended to deliver drugs at predetermined rates for predefined periods of time, have been used to overcome the shortcomings of conventional drug formulations. Injectable drug-loaded matrices and controlled release technology offer numerous advantages compared to conventional dosage. However, one of the greatest challenges in applying this system to the clinical phase is the relatively large initial burst release. To reduce this effect of large initial burst release, a new drug delivery system was fabricated in this thesis. Both alginate and gelatin are biocompatible nature polymers and have been largely used as biomaterials for long time. By cross-linking alginate solution carrying drug-loaded uncross-linked gelatin microbeads, the initial burst release was reduced significantly, compared with drug directly releasing from gelatin or cross-linked alginate matrix. Firstly, a series of gelatin microbeads were prepared in a water-in-oil (W/O) emulsion by a traditional emulsification method. The effects of the concentration of gelatin solution, volumetric ratio of water-to-oil phase, stirring speed and emulsifying time on the particle size and dispersity of gelatin microbeads were studied. Secondly, drug-loaded gelatin microbeads were encapsulated into the cross-linked sodium alginate macro-beads. The release behavior of drug-loaded gelatin microbeads encapsulated within cross-linked alginate gel was characterized both at room temperature and 37°C and compared with the release from gelatin microbeads and cross-linked alginate gel alone. This system represents a promise for the development of novel and versatile injectable drug delivery systems. Thirdly, a dual-drug delivery system was fabricated by encapsulating drug-loaded gelatin microbeads into the mixture of cross-linkable sodium alginate and another drug. The effects of preparation methods of drug-loaded gelatin microbeads and ratio between gelatin microbeads and alginate on drug release behaviors of both drugs were studied. This system shows a significant potential in dual drug delivery field due to the synergistic effect between gelatin and alginate. Additionally, combination of multi-drugs in one system has been revealed as a promising application in the drug delivery systems. Therefore, in the fifth chapter of this thesis, an idea for the multi-drug delivery system was simply demonstrated. Rods of gelatin gels loaded with different drugs were separated by the agarose gel in a polycarbonate tube. The effects of the length of agarose gel and temperature on the drug release profiles were investigated. The results suggested the feasibility to employ this idea to the practical applications.