Thesis (M.S.)--Mississippi State University. Department of Electrical and Computer Engineering. / Title from title screen. Includes bibliographical references.

- / In the present diplomatic project is realised a process of measurements of the leakage current by the system of measurement that was manufactured by gentleman Sideraki, in the frames of his doctoral thesis. The measurements were realised in the substation 150 kV of Crete‟s system of transport and in the substation 150 kV of A.I.S. Linoperamaton. In the first chapter, is presented the phenomenon of the insulators‟ pollution, while it constitutes the prime cause of the leakage current. Here are presented the main causes of pollution, its unfavourable results as well as her ways of confrontation. There is an extensive report, in the use of multilateral insulators and multilateral coatings for the confrontation of the phenomenon of pollution. Particularly is stressed the hydrophobic characteristic of these materials which leads to the reduction of the quantity of pollution on the surface of the insulators. The second chapter, is a presentation of the work of various researchers over the world, in the effort of studying the leakage current and its connection with the phenomena of ageing and flashover. Also there are mentioned the experimental provisions that they used in the frames of their studies and are reported the mainer conclusions to which they were led. Common point of their conclusions constitutes the make of ascertainment that the biggest price of the leakage current, constitutes an unreliable indicator of description of the distressed insulator‟s surface, since important information on the situation of the surface we draw also from the waveform of the leakage current. In the third chapter there is a concise presentation of Fourier„s theory and transforming, while an extensive report in the distinguishable Fourier transforming (DFT) is also mentioned. Finally, is presented the fast Fourier transforming (FFT), which constitutes an algorithm of fast calculation of distinguishable transformation Fourier and is used among others for the spectrum analysis of signals of distinguishable time. In the fourth chapter, is realised the treatment of measurements, with the use of Labview for the study of the leakage current in the field of frequency. Leakage current‟s waveforms are categorized, with criteria, the lack of linearity and the presence of discharges or not and conclusions are exported on these waveforms, from their spectrum analysis.

Thesis (M.Ing.)--University of Stellenbosch, 2000. / ENGLISH ABSTRACT: The application of cycloaliphatic epoxide (CE) insulation in the Republic of South Africa is investigated within this thesis. There was a request from industry to evaluate the product and indicate its suitability for application within the various geographic and climatic zones typical of the RSA. An extensive survey was conducted into the historic origins of the material, and the experiences of international utilities applying the insulation medium in respect of polluted conditions. The properties of the Automatic Pressure Gelation (APG) CE insulator manufacturing process are discussed with reference to the manufacture of glass and porcelain insulation, and typical areas for concern are discussed with reference to insulators found to deviate from specification. Typical insulators were obtained from the manufacturers and utilities associated with the product, and were subjected to electrical, material and visual examination tests. The electrical tests included AC wet and dry, lightning impulse, clean fog, salt fog, mould release resiliency and the IEC 1109 voltage test. The material tests included the identification of the epoxide systems in use in the RSA, ultraviolet radiation aging simulation, water hydrolysis and salt deposit density tests. The main findings are: • CE insulation is sensitive to marine pollution and continuous-wetting pollution types. • The use of CE insulation is promoted in respect of inland and medium industrial pollution types. • Class B pin-type CE insulation is prone to partial discharge related failures. • Surface roughening on the insulator surfaces leads to reduced AC wet flashover voltages and increased pollution catch. Additionally: • A comprehensive aging hypothesis was developed detailing three independent aging stages/modes applying to CE insulation. • A hypothesis was developed for a new evaluation method for documenting changes on insulator surfaces due to the action of aging mechanisms: The Surface Area Index. / AFRIKAANSE OPSOMMING: Die aanwending van sikloalifatiese epoksied (SE) isolasie in die Republiek Van Suid Afrika word in hierdie skripsie ondersoek. Hierdie ondersoek is geloods op versoek van die elektrisiteitsbedryf om die toepaslike aanwending van die produk onder die verskeie heersende streeksweersomstandighede binne die RSA te evalueer. Breedvoerige navorsing is gedoen om die geskiedkundige oorsprong van die materiaal vas te stel, sowel as om die prestasie daarvan as insulasiemiddel te boekstaaf. Daar is veral gelet op die prestasie van die materiaal onder besoedelende omstandighede en ondervinding wat opgedoen is deur intemasionale ondememings. Die eienskappe van die automatiese drukjelvormings-vervaardigingsproses (APG) word behandel met verwysing na die maak van glas en porselein insulators. Tipiese probleemareas word bespreek van insulators wat afwyk van spesifikasie af. Verteenwoordigende isolators is vanaf vervaardigers en ondememings verkry wat met die produk bemoei is. Hulle is blootgestel aan elektriese, materiaal en visuele toetse. Die elektriese toetse het die volgende behels: nat en droog wisselstroom, skoon waterdamp, sout waterdamp en die IEe 1109 spanningstoets. Die effek van die verlies van die anti-kleefmiddel (gebruik tydens die gietproses) as gevolg van veroudering is ook in detail behandel. Die materiaaltoetse het ingesluit: die uitkenning van die epoksied stelsels in gebruik in die RSA, gesimuleerde veroudering deur ultravioletligbestraling, water hidroliese en soutlaag digtheids toetse. Die hoofbevindings is: • SE isolasie word bemvloed deur seelug besoedeling sowel as volgehoue benatting. Die gebruik van SE isolasie word voorgestel vir binnelandse gebruik sowel as in gebiede met mediumvlak nywerheidsbesoedeling. • Klas B pen-tipe SE isolasie is geneig tot deelontladings wat dan tot faling lei. • Oppervlakvergroffing lei tot In verminderde wisselstroom orvonksspanning onder nat toestande sowel as verhoogde vangs van besoedeling. Bykomend hiertoe is: • 'n breedvoerige SE verouderingshipotese ontwikkel wat drie onafhanklike stadia en modusse van die verouderingsproses uitgewys het. • 'n hipotese ontwikkel vir In nuwe evaluasiemetode om die verandering in die isolatoroppervlak as gevolg van veroudering te dokumenteer: Oppervlakte- Area Indeks (SAl).

Thesis (MScEng)--University of Stellenbosch, 2003. / ENGLISH ABSTRACT: This project relates to the unexplained failure of 33kV porcelain line post insulators in ESKOM's Southern Region. An initial investigation suggested that the failures could probably be due to a combination of internal manufacturing flaws and the effects of lightning. The failures all occurred in insulators based on a new design that uses a metal spindle for mechanical attachment to a power line structure embedded in the insulator base. This thesis investigates the non-destructive detection of internal flaws in porcelain line post insulators. The research was structured as follows: • The examination of the manufacturing process and materials used to determine the cause, location and nature of internal flaws. • An electrical field simulation study to verify whether a void in the sulphur cement will experience discharge activity when exposed to systeni nominal voltage or lightning potential. • The identification of non-destructive techniques (NDT) that are potentially viable for determining the presence of insulator internal flaws. • The design of NDT experiments for X-ray, partial discharge (PD) detection and ultrasonic testing. These experiments were evaluated for their effectiveness in determining the presence of internal flaws and their usefulness as a quality control measure in the insulator manufacturing process. The main findings are: The major cause of insulator internal flaws is the fast setting sulphur cement used for cementing the metal spindle (mechanical attachment) to the porcelain body of the insulator. The field simulation study shows that a discharge in a 3mm diameter spherical void on the insulator's axis of symmetry will occur if the insulator is exposed to lightning potential. High energy X-raying is an effective technique for exposing the location, nature, size and number of flaws in the insulator, but is impractical due to the high Xraying cost and over-utilisation of the only high energy X-ray facility in the RSA. The PD experiment was effective in revealing the presence of internal flaws, but the location, nature, size and number of flaws cannot be determined. The experiment is time consuming and is therefore not suitable for quality control in the insulator manufacturing process. A preliminary investigation into the suitability of ultrasonic testing techniques encountered major technical difficulties. Further investigation into the use of ultrasonic 3D imaging techniques is recommended. / AFRIKAANSE OPSOMMING: Hierdie projek hou verband met die onverklaarbare faling van 33kV porselein staaftipe isolators in ESKOM se Suidelike Streek. 'n Aanvanklike ondersoek het daarop gedui dat die falings veroorsaak is deur 'n kombinasie van interne vervaardigingsfoute en die effek van weerlig. Die falings het almal plaasgeving op isolators waarvan die vashegtingsbout direk in die porselein versink is. Die doel van hierdie navorsingsprojek is om nie-vernietigende toetsmetodes (NVT) te ondersoek, teneinde interne foute in die tipe isolators op te spoor. Die tesis is soos volg gestruktureer: • Die ondersoek van die vervaardigingsproses en die materiale wat gebruik word, ten einde die oorsaak, posisie en aard van hierdie foute vas te stel. • 'n Simulasie van die elektriese veld om vas te stelof 'n holte in die swaelsement ontladings salondervind onder die invloed van nominale spanning en weerlig. • Die indentifisering van nie-vernietignde toetsmetodes wat gebruik kan word om die teenwoordigheid van interne foute te bepaal. • Die ontwerp van NVT eksperimente vir X-straal, gedeeltelike ontlading ("PD") deteksie en ultrasoniese toetsing. Hierdie eksperimente is geëvalueer om hul effektiwiteit om die teenwoordigheid van interne foute vas te stel, asook hul nuttigheid as 'n kwaliteitsbeheermaatreël in die iso latorvervaardigingsproses. Die hoofbevindinge is: Die hoofoorsaak van die interne foute is die vinnig-stollende swael-sement wat gebruik word om die metaalinsetsel aan die porselein te heg. Die veldsimulasies het getoon dat 'n ontlading in 'n 3mm sferiese holte op die isolator se simmetrie-as sal plaasvind as die isolator aan weerligpotensiaal onderwerp word. Hoë-energie-X-strale is 'n effektiewe tegniek om die posisie, aard, grootte en aantal foute in die isolator vas te stel. Dit is egter onprakties as gevolg van die hoë koste en oorbenutting van die enigste hoë-energie-X-straal-fasiliteit in die RSA. Die ontladingsdeteksie eksperiment was effektief om die teenwoordigheid van interne foute aan te dui, maar die posisie, aard; grootte en getal foute kan nie bepaal word nie. Die eksperiment is tydrowend en is daarom nie geskik vir kwaliteitsbeheer van die isolatorvervaardigingsproses nie. 'n Voorlopige ondersoek na die geskiktheid van ultrasoniese toetsmetodes het groot tegniese stuikelblokke opgelewer. Verdere ondersoek van die gebruik van ultrasoniese 3D-beeldtegnieke word aanbeveel.

Fractional Chern insulators (FCIs) are strongly correlated, topological phases of matter that may exist on a lattice in the presence of broken time-reversal symmetry. This thesis explores the link between FCI states and the quantum Hall effect of the continuum in the context of the Hofstadter model, using a combination of nonperturbative, perturbative and numerical methods. We draw links to experimental realisations of topological phases, and go on to consider a novel way of generating general FCI states using strong interactions on a lattice. We begin by considering the Hofstadter model at weak field, where we use a semiclassical analysis to obtain nonperturbative expressions for the band structure and Berry curvature of the single-particle eigenstates. We use this calculation to justify a perturbative approximation, an approach that we extend to the case when the amount of flux per plaquette is close to a rational fraction with a small denominator. We find that eigenstates of the system are single- or multicomponent wavefunctions that connect smoothly to the Landau levels of the continuum. The perturbative corrections to these are higher Landau level contributions that break rotational invariance and allow the perturbed states to adopt the symmetry of the lattice. In the presence of interactions, this approach allows for the calculation of generalised Haldane pseudopotentials, and in turn, the many-body properties of the system. The method is sufficiently general that it can apply to a wide variety of lattices, interactions, and magnetic field strengths. We present numerical simulations of the Hofstadter model relevant to its recent experimental realisation using optical lattices, noting the additional complications that arise in the presence of an external trap. Finally, we show that even if a noninteracting system is topologically trivial, it is possible to stabilise an FCI state by introducing strong interactions that break time-reversal symmetry. We show that this method may also be used to create a (time-reversal symmetric) fractional topological insulator, and provide numerical evidence to support our argument.

La découverte de l'effet Hall quantique par von Klitzing en 1980 a ouvert la voie à ce qui sera connu plus tard comme la théorie topologique des bandes. Dans le cadre de cette théorie, on ne s'intéresse plus uniquement à la relation de dispersion énergétique des électrons dans les cristaux, mais aussi à l'organisation topologique de la structure de bande. Cette théorie a permis la découverte d'une nouvelle phase de la matière, représentée par les isolants topologiques. Ces isolants topologiques ont de particulier qu'ils se comportent comme des isolants normaux dans le bulk, mais présentent des états de surface conducteurs. Dans cette thèse, on s'intéresse particu- lièrement aux isolants topologiques dits Z2, pour lesquels les états de surface sont protégés par la symétrie de renversement du temps : ils ne peuvent disparaître en présence d'une perturbation qui préserve cette symétrie sans que le système ne traverse une transition de phase quantique. Pour les isolants topologiques à trois dimensions, nous proposons dans cette thèse, un critère expérimental utilisant les oscillations quantiques magnétiques, permettant d'identifier un type particulier d'isolants topologiques : les isolants topologiques forts. Pour les systèmes à deux dimensions, nous nous sommes intéressés aux phénomènes liés à la rupture de la symétrie par renversement du temps à cause de la présence d'un ordre antiferro- magnétique. Dans ce cas, la symétrie d'importance devient le renversement du temps fois une translation. Dans ce contexte, nous avons tout d'abord établi analytiquement l'expression d'un invariant topologique pour les systèmes présentant aussi la symétrie d'inversion. Nous avons ensuite adapté trois méthodes numériques normalement utilisées dans le cadre des isolants topo- logiques invariants par renversement du temps : la méthode de la phase de jonction, la méthode des centres de charge des fonctions de Wannier et la construction explicite des états de bord. Nous avons montré qu'elles permettaient de tester la nature triviale ou topologique de plusieurs modèles théoriques pour lesquelles aucune méthode n'existait, par exemple les systèmes sans symétrie d'inversion. / The discovery of the quantum Hall effect by von Klitzing in 1980 paved the way for what is now known as topological band theory. In this theory, we are interested not only in the energy spectra of the electrons in crystals, but also in the topological structure of the bands. A new phase of matter was discovered thanks to this theory : the topological insulators. Topological insulators are unique in the sense that they behave like trivial insulators in the bulk, but possess metallic edge states. In this thesis, we are particularly interested in so-called Z2 topological insulators, whose edge states are protected by time reversal symmetry : they cannot disappear in the presence of a perturbation that respects this symmetry, without the system undergoing a quantum phase transition. For three-dimensional topological insulators, we propose an experimental criterion based on magnetic quantum oscillations to identify a special kind of topological insulators : the strong topological insulator. In two dimensions, we study the consequences of time reversal symmetry breaking due to anti-ferromagnetic order. In this case, the important symmetry is time reversal times a trans- lation. In this context, we first establish an analytical expression for systems that also have inversion symmetry. We then adapt three numerical methods usually employed for time reversal symmetric systems : the reconnection phase method, the Wannier charge center method and the explicit construction of edge states. We show that they are useful to probe the topology of models for which no methods were available ; such as non-centrosymmetric systems.

The aim of this thesis was to identify topologically protected states in the materials SnTe and Fe3Sn2. Such states are currently receiving a large amount of interest due to their applications for spintronic devices. Recently SnTe was discovered to be a crystalline topological insulator, a state of matter where its surface is highly conducting while the bulk remains insulating. However detection of these surface states is difficult using transport measurements, since the bulk is not totally insulating but still contains a large number of free carriers. SnTe undergoes a rhombohedral structural distortion on cooling caused by a soft transverse optic phonon, with the exact Tc strongly dependent on the carrier concentration. The distortion acts to lower crystal symmetry removing some of the symmetries that protect the surface state. Single crystal samples displaying the structural transition were grown and investigated using inelastic X-ray scattering to measure the phonon softening previously reported by other authors. The soft phonon was seen to recover again after distortion indicative of a 2nd order ferroelectric transition. This is the first reported discovery of the recovery showing the distortion is ferroelectric in nature. Shubnikov de Haas quantum oscillations were measured to study the Fermi surface under ambient and high hydrostatic pressure conditions. A distortion of the Fermi surface caused by the structural transition was evident, resulting in 4 distinct oscillation frequencies. However at applied pressures above 6 kbar, the transition was suppressed and only 1 oscillation measured. A two component Hall response also becomes apparent under high pressure. The possible origin of this and its relation to possible surface states is discussed. The anomalous Hall effect was also measured in the ferromagnet Fe3Sn2 which has a bilayer Kagome structure. Previous measurements on polycrystalline Fe3Sn2 suggested a non-collinear spin rotation from the spins pointing along the c-axis at high temperature to lying in the a-b plane below 80 K. A spin glass phase is then expected below 80 K. Single crystal magnetisation measurements carried out in this thesis show the spins are in the a-b plane at high temperatures and begin to display a ferromagnetic component along the c-axis approaching 80 K. The difference is accounted for by considering the demagnetising factor in the plate shaped single crystals. For this temperature range an applied field along the c-direction however rotates the moments towards c. At intermediate fields there are strong features evident in both the anomalous Hall effect and magnetoresistance. These features may be due to a topological Hall effect caused by a non-collinear spin structure. The possible existence of Skyrmion excitations was also recently discussed theoretically in Fe3Sn2. Our data is more suggestive of static Skyrmions known to cause topological Hall effects in MnSi.

abstract: Topological insulators with conducting surface states yet insulating bulk states have generated a lot of interest amongst the physics community due to their varied characteristics and possible applications. Doped topological insulators have presented newer physical states of matter where topological order co&ndashexists; with other physical properties (like magnetic order). The electronic states of these materials are very intriguing and pose problems and the possible solutions to understanding their unique behaviors. In this work, we use Electron Energy Loss Spectroscopy (EELS) – an analytical TEM tool to study both core&ndashlevel; and valence&ndashlevel; excitations in Bi2Se3 and Cu(doped)Bi2Se3 topological insulators. We use this technique to retrieve information on the valence, bonding nature, co-ordination and lattice site occupancy of the undoped and the doped systems. Using the reference materials Cu(I)Se and Cu(II)Se we try to compare and understand the nature of doping that copper assumes in the lattice. And lastly we utilize the state of the art monochromated Nion UltraSTEM 100 to study electronic/vibrational excitations at a record energy resolution from sub-nm regions in the sample. / Dissertation/Thesis / M.S. Materials Science and Engineering 2013

Neste trabalho estudamos uma rede hexagonal com uma cadeia de impurezas nas bordas e com supercondutividade induzida, de forma a mostrar a existência de fases com férmions de Majorana. Para tal, começamos introduzindo invariantes topológicos, número de Chern e Z2 e mostramos dois modelos para rede hexagonal. O primeiro, modelo de Haldane, fazemos como motivação histórica. O segundo, modelo de Kane-Mele, é usado como base para todo o trabalho. Seguimos introduzindo supercondutividade e como ela ocorre quando aplicada junto do Modelo de Kane-Mele, o método auto-consistente e quais as condições necessárias para termos supercondutividade apenas nas bordas. Continuamos com efeitos de impurezas magnéticas nas bordas e introduzimos férmions de Majorana que são os alvos principais dos resultados. Mostramos então, que existe fases topológicas em cadeias de impureza magnética, com momentos em espiral, contudo o diagrama de fase depende de várias condições. Por fim, mostramos que a variação da fase topológica se deve a oscilações nos níveis de energia em que o invariante topológico também varia, contrariando resultados obtidos para a rede quadrada. Concluímos esse trabalho com implicações experimentais desse resultado e possíveis caminhos que podem ser seguidos. / In this work, we study a honeycomb lattice with induced superconductivity and edge impurity in order to show the existence of a phase that host Majorana bound state. To do so, we start introducing topological invariants, Chern number and Z2, and we show two models for honeycomb lattice. The first, Haldane\'s Model, due its historical importance. The second, Kane-Mele model, because it will be used during all this work. Then we review superconductivity, showing the self-consistent method, and we apply it to Kane-Mele model, in which we find some necessary conditions to induce superconductivity only at the edges. From this point, we study the effect of magnetic impurities at the edges, and we introduce Majorana bound state, that will be the main objective of our results. In our results, we show the existence of topological non-trivial phases for spiral magnetic chain in the zigzag edge. With this we make a phase diagram. We also find oscillation in the energy spectrum and the topological phase changes with the oscillation, this is different from square lattice in which we should not have a change in the topological phase. We conclude this work with experimental implications of our result and possible developments.

Nessa tese de doutorado apresentamos um estudo da estrutura eletronica de materiais isolantes topologicos. A teoria fundamental dos isolantes topologicos foi abordada atraves de invariantes topologicos Z2, assim como os seus metodos para o calculo desses invariantes topologicos e as consequencias da topologia de bandas nao-trivial. Assim como as propriedades atomisticas e energeticas, as propriedades eletronicas de alguns isolantes topologicos foram calculadas atraves de metodos de primeiros principios baseados na Teoria do Funcional da Densidade. Apresentamos nessa tese o estudo de quatro sistemas de interesse fisico: (1) Em isolantes topologicos do tipo Bi2Se3 e Bi2Te3 com falhas de empilhamentos, encontramos que o Bi2Te3 com falhas de empilhamentos apresentam estados metalicos na regiao do defeito; (2) Na interface Bi2Se3/GaAs com tratamento de Se na regiao do GaAs, encontramos que a interacao entre o cone de Dirac do Bi2Se3 com a banda de valencia do GaAs abre um gap de energia no ponto ; (3) Em nanoestradas de germaneno imersas em germanano com interfaces zigzag, encontramos que a partir de uma largura critica podemos observar o efeito Hall quantico de spin; e (4) nas ligas desordenadas hexagonais de SixGe1-x em duas dimensoes, o sistema desordenado compartilha a mesma topologia de bandas do siliceno e do germaneno, enquanto que a liga ordenada Si0.5Ge0.5 e um isolante trivial. As estruturas eletronicas desses sistemas foram investigadas no intuito de entender as consequencias fisicas da topologia de bandas nao-trivial nos estados de Bloch de bulk e de superficies/interfaces. / In this doctoral thesis we present a study of the electronic structure of topological insulators materials. The fundamental theory of topological insulators was addressed through the Z2 topological invariants, as well as their methods to calculate these topological invariants and the consequences of non-trivial band topology. Just as atomistic and energetic properties, the electronic properties of some topological insulators were calculated using first-principles methods based upon Density Functional Theory. We present in this thesis the study of four systems of physical interest: (1) In topological insulators like Bi2Se3 and Bi2Te3 with stacking faults, we found that the Bi2Te3 with stacking faults presents metallic states in the region of the defect; (2) For Bi2Se3/GaAs interface with Se-treatment in the GaAs region, we found that the interaction between the Dirac cone of the Bi2Se3 and the valence band of the GaAs opens a bandgap at the -point; (3) In germanene nanoroads embedded on germanane with zigzag interfaces/edge, we found that from a critical width we can observe the quantum spin Hall effect; and (4) For SixGe1x two-dimensional hexagonal disordered alloy, the system shares the same non-trivial band topology of the silicene and germanene, while the ordered alloy Si0.5Ge0.5 is a trivial insulator. The electronic structures of these systems were investigated in order to understand the physical consequences of non-trivial band topology in the bulk and surfaces/interfaces Bloch states.