Over the past twenty-five years, condensed matter physics has been developing materials with novel electronic characteristics for a wide range of future applications. Two research directions have shown particular promise: topological insulators, and high temperature copper based superconductors (cuprates). Topological insulators are a newly discovered class of materials that can be manipulated for spintronic or quantum computing devices. However there is a poor spectroscopic understanding of the current topological insulators and emerging topological insulator candidates. In cuprate superconductors, the challenge lies in raising the superconducting transition temperature to temperatures accessible in non-laboratory settings. This effort has been hampered by a poor understanding of the superconducting mechanism and its relationship with a mysterious pseudogap phase. In this thesis, I will describe experiments conducted on topological insulators and cuprate superconductors using scanning tunneling microscopy and spectroscopy, which provide nanoscale spectroscopic information in these materials. / Physics

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.

In Topologischen Isolatoren (TI) werden metallische Zustände an der Oberfläche beobachtet, während die entsprechenden Volumenzustände eine Bandlücke aufweisen. Der Volumenbeitrag zur Leitfähigkeit von TI-Materialien macht eine Synthese von Nanokristallen bzw. eine Dotierung nötig. Der Fokus der Untersuchungen dieser Arbeit liegt dabei auf der Erzeugung von Nanokristallen der TI-Materialien Bi2Te3- und Bi2Te2Se sowie dotierter Bi2Se3-Nanokristallen. Die Synthese der Nanokristalle erfolgte durch den Gasphasentransport im geschlossenen System über den Mechanismus einer Zersetzungssublimation bzw. unter dem Einsatz eines Transportmittels. Für eine erfolgreiche Erzeugung der Nanokristalle sind im Vorfeld thermodynamische Modellierungen des Gasphasentransports sowie Versuche zum chemischen Transport für die quasibinären Systeme Bi2Se3-Bi2Te3, Bi2Se3-Sb2Se3 und Bi2Se3-FeSe sowie für das ternäre System Mn-Bi-Se durchgeführt worden. Durch Versuche zum chemischen Transport konnten die Aussagen der Modellierung bestätigt und im Weiteren der Dotandengehalt in den abgeschiedenen Kristallen sowie der Einlagerungsmechanismus durch Ergebnisse aus XRD- und ICP-OES-Untersuchungen beschrieben werden. Die Synthese bzw. Dotierung der Nanokristalle wurde hauptsächlich durch die Transportrate und den Dampfdruck des Dotanden bestimmt. In den Systemen Bi2Se3-Bi2Te3 und Bi2Se3-Sb2Se3 ist ein Gasphasentransport über eine Zersetzungssublimation durchführbar und resultierte in einer erfolgreichen Darstellung von Bi2Te3- und Bi2Te2Se-Nanokristallen sowie von dotierten (SbxBi1-x)2Se3-Nanokristallen. Entgegen dessen erfolgte der Gasphasentransport in den Systemen Bi2Se3-FeSe und Mn-Bi-Se unter Verwendung eines Transportmittels. Hierbei verringerten die gesteigerten Transportraten das Wachtum von Nanokristallen. Im Weiteren gelang es dotierte (Fe,Mn)xBi2-xSe3-Volumenkristalle sowie MnBi2Se4-Einkristalle darzustellen und mittels XRD, ICP-OES, magnetischer Messungen sowie elektrischem Transport zu charakterisieren.

La thèse porte sur l'étude théorique des propriétés électroniques à la surface de l’oxyde de métal de transition SrTiO3. Ce matériau est la pierre angulaire de l'électronique des oxydes, un nouveau domaine de recherche qui a pour but d'enquêter sur les oxydes de métaux de transition en tant que candidats post-silicium pour une émergence future de nouveaux composants électroniques. Le SrTiO3 est en soi un système étonnant : dans sa plus pure composition chimique, c’est un bon isolant avec une large bande interdite. Cependant, en le dopant avec de petites quantités d'autres éléments, il se transforme en un métal à haute mobilité d'électrons. Le SrTiO3 a également saisi l'attention en raison de sa capacité à accueillir des gaz d'électrons bidimensionnels (2DEGs) quand il est interfacé avec certains oxydes polaires. Ces 2DEGs présentent des propriétés fascinantes, la plus visible étant la coexistence du magnétisme et de la supraconductivité.La surface du SrTiO3 peut également accueillir des 2DEGs, sans avoir besoin de s'interfacer avec d'autres matériaux ; dans ce cas, les électrons participant aux transports sont générés par des lacunes d'oxygène créées à la surface. Cette observation est remarquable, car le SrTiO3 offre une structure simple où les propriétés des 2DEGs peuvent être étudiées.Cette thèse s’articule autour des deux axes. Tout d'abord, elle étudie la bicouche STO orientée 111, formée de seulement deux cellules unitaires. Deuxièmement, elle analyse les puits quantiques générés par les postes vacants de l'oxygène à la surface 111 du STO. Les deux sujets sont abordés en utilisant des modèles de liaison forte, dans lesquels le Hamiltonien incorpore différents termes liés aux énergies sur place, aux interactions de saut et au couplage spin-orbite. A partir de ces calculs, j’ai réalisé une analyse exhaustive des propriétés, du caractère et de la parité des orbitaux des bandes de valence et de conduction, ainsi que des états de bord dans la bicouche 111. / The thesis is focused on the theoretical study of the electronic properties at the surface of the transition metal oxide STO. This material is the cornerstone of oxide electronics, an emerging research area that has the goal of investigating transition metal oxides as post-silicon candidates for a future emerging new electronics. STO is in itself an astounding system; in its purest chemical composition is a good ban-insulator with a wide bandgap. Nevertheless, upon doing it with tiny amounts of other elements it transforms itself in a metal with high electron mobility. Even more remarkably, at the lowest temperatures, typically below 300mK, it goes superconductor. And adding to these properties, strain induces also ferroelectricity in this material. Over the last years, STO has also grabbed attention because of its ability of hosting two-dimensional electron gas (2DEGs) when it is interfaced with some polar oxides. Such 2DEGs exhibit fascinating properties, the most conspicuous is the coexistence of magnetism and superconductivity.The surface of STO can host 2DEGs too, without need of interfacing it to other materials; in this case the electrons participating in transport are generated by oxygen vacancies created at the surface. This is remarkable observation, as it affords a simpler structure where the 2DEGs properties can be studied. In spite of the accumulated knowledge, still a better fundamental comprehension is required of the electronic structure of the quantum wells at the surfaces oriented along the 111 direction, for which the perovskite structure is reminiscent of the celebrated honeycomb-like structure of graphene. Contrary to the latter, in which electrons are in s- and p- states, 111 quantum wells in STO would host electrons in d-bands. Higher electronic correlations are then expected, that may bring new fascinating physics.The outline of this Thesis has two main branches: first, it studies the 111-oriented STO bilayer, formed by just two unit cells; secondly it analyzes the quantum wells generated by Oxygen vacancies at the 111-surface of STO. Both subjects are approached using tight-binding models in which the Hamiltonian incorporates different terms related to on-site energies, hopping interactions or spin-orbit coupling. From these calculations, I have carried out an exhaustive analysis of the orbital character and parity properties of valence and conduction bands, as well as edge states in the 111 bilayer. Tight-binding calculations have also shed light on the orbital character, space location and extension and energy of electronic states generated by oxygen vacancies at the 001 surface of STO.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第18062号 / 理博第3940号 / 新制||理||1568(附属図書館) / 30920 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 川上 則雄, 教授 石田 憲二, 准教授 藤本 聡 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第18779号 / 理博第4037号 / 新制||理||1581(附属図書館) / 31730 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 川上 則雄, 教授 佐々 真一, 教授 前野 悦輝 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM