Orientador: Prof. Dr. Gustavo Martini Dalpian / Tese (doutorado) - Universidade Federal do ABC, Programa de Pós-Graduação em Nanociências e Materiais Avançados, 2015. / Em 2004, foi descoberto que a interface formada entre as superf'ýcies (001) do SrTiO3 e LaAlO3 apresenta um g'as de el'etrons bidimensional (2DEG), apesar de o bulk desses materiais ser isolante. Em 2011, foi reportado um 2DEG similar na superf'ýcie (001) do SrTiO3. Apesar de haver muitos trabalhos acerca desse assunto, n¿ao h'a um consenso sobre a origem do 2DEG nesses sistemas. Inclu'ýda nesse contexto, esta tese reporta os resultados de c'alculos de primeiros princ'ýpios baseados na Teoria do Funcional da Densidade (DFT) da superf'ýcie (001) dos filmes finos de SrTiO3 e LaAlO3 e da interface (001) formada entre esses dois 'oxidos. Filmes finos de LaAlO3 e SrTiO3 tendem a ter vac¿ancias com menores energias de forma¸c¿ao da superf'ýcie, e quando com vac¿ancias apresentaram comportamento condutor. Filmes finos de SrTiO3 sem defeitos demonstraram comportamento isolante. A vac¿ancia de oxig¿enio na superf'ýcie com termina¸c¿ao TiO2 'e a menos custosa energeticamente, e nesse caso 'e detectado um 2DEG da superf'ýcie do SrTiO3. O mesmo ocorre em filmes finos de LaAlO3, com vac¿ancias de oxig¿enio e termina¸c¿ao AlO2 e vac¿ancias de La e termina¸c¿ao LaO, podendo haver forma¸c¿ao espont¿anea nesses casos. Em ambos os casos, as simula¸c¿oes sugerem que 'e formado um 2DEG na superf'ýcie. As simula¸c¿oes da interface mostraram que para a hete2 roestrutura sem defeitos 'e necess'aria a deposi¸c¿ao de quatro ou mais camadas de LaAlO3 sobre o substrato de SrTiO3 para que ocorra o comportamento met'alico. Vac¿ancias de oxig¿enio se formam preferencialmente na interface quando a espessura do LaAlO3 'e de tr¿es camadas ou menos. Para quatro ou mais camadas de LaAlO3, as vac¿ancias de oxig¿enio tendem a se localizar na superf'ýcie. Para todas as simula¸c¿oes da interface com defeitos, as heteroestruturas apresentaram comportamento met'alico, por'em n¿ao foi detectado um 2DEG na interface, j'a que as cargas n¿ao se apresentaram confinadas na regi¿ao da interface. Vac¿ancias justificam o 2DEG na superf'ýcie (001) de filmes finos de LaAlO3 e SrTiO3, por'em n¿ao explicam o 2DEG na interface entre os mesmos. / In 2004 it was discovered that the interface between the (001) SrTiO3 and LaAlO3 surfaces presents a two dimensional electron gas (2DEG), although the bulk of these materials are insulators. In 2011 it was reported a similar 2DEG at (001) SrTiO3 surface. Despite many studies on this subject, there is no consensus about the origin of the 2DEG in these systems. Included in this context, this thesis reports results of first principles calculations based on Density Functional Theory (DFT) about (001) SrTiO3 and LaAlO3 thin films surfaces and the (001) interface formed between these two oxides. For LaAlO3 and SrTiO3 thin films, vacancies tend to have lower formation energies at the surface. Non-defective SrTiO3 thin films have demonstrated an insulator behavior. The oxygen vacancy at the TiO2 terminated surface is the most stable and in this case is observed a 2DEG at the SrTiO3 surface. The same occurs for LaAlO3 thin films with oxygen vacancies and for the AlO2 termination and with La vacancies with LaO termination. These vacancies may be formed spontaneously. In both cases, the simulations suggest a 2DEG at the surface. The interface simulations showed that in the non-defective heterostructure it is necessary the deposition of four or more layers of LaAlO3 over SrTiO3 substrate to occur a metallic behavior. Oxygen 4 vacancies are preferably formed at the interface when the LaAlO3 thickness is three layers or less. For four LaAlO3 layers or more, the oxygen vacancies tend to be located at the surface. For all simulations of the defective interface, the heterostructures showed metallic behavior. However it was not detected a 2DEG at the interface, owing the fact that the charges are not confined at the interface region. Vacancies can justify the 2DEG at the SrTiO3 and LaAlO3 thin films surfaces, however does not explain the 2DEG at the interface between them.

De nombreuses propriétés étonnantes ont été récemment découvertes à l’interface de deux perovskites isolantes l’une polaire l’autre non polaire. La discontinuité de charge à l’interface LaAlO3/SrTiO3 engendre un gas d’électron quasi-bidimensionnel qui confère un caractère métallique à cette interface. Les mécanismes locaux et la quantification des propriétés ne font pas consensus car l’interdépendance de facteurs structuraux, chimiques et électroniques complexifie la résolution du problème posé. Une catastrophe polaire, des distorsions structurales, des lacunes d’oxygène, une interdiffusion cationique et une non stœchiométrie du film ont été séparément avancées pour expliquer cette conduction. Dans le cadre d’un programme international, nous avons reçu des héterointerfaces conductrices et isolantes élaborées par ablation laser pulsé (PLD). L’origine des porteurs de charge a été recherchée par une approche globale liant procédé, structure et propriétés électriques (mesurées dans le consortium). Nous avons systématiquement analysé les interfaces en combinant imagerie à haute résolution (STEM-HAADF) et spectroscopies électroniques (EELS) et ioniques (MEIS). Une non planéité des couches atomiques, une interdiffusion cationique et un transfert d’électrons permettent de réduire la divergence de potentiel, la catastrophe polaire n’a donc pas lieu. La formation de défauts donneurs à la surface du film devient favorable au-delà d’une épaisseur critique. Les électrons sont transférés à l’interface dans la bande de conduction du STO. Nous avons mis en évidence un mécanisme de compensation concurrentiel de la charge interfaciale par des lacunes de strontium chargées négativement, qui mettent le substrat en compression plane et s’opposent au confinement 2D électrons. La variation des paramètres procédés, tels que la durée du dépôt, la pression partielle en oxygène, la température et la stœchiométrie de la plume déplace l’équilibre des différents mécanismes mis en évidence. Ce travail démontre la relation complexe liant procédé, propriétés électriques et distribution des défauts autour de ces interfaces singulières. / Novel behavior at the interface between two insulating polar/non polar perovskites has been recently discovered. The polarization discontinuity at LaAlO3/SrTiO3 drives the formation of quasi two dimensional electron gas. Both the local mechanism and quantification of such behavior remain unclear due to interplay of structural, chemical and electronic factors. Several mechanisms have been proposed, such as the polar catastrophe, structural distortions, oxygen vacancies, cationic intermixing at the interface and film non-stoichiometry. In the frame of an international project conductive and insulating heterostrucutres have been synthetized by Pulsed-Laser Deposition. In this thesis, we have developed a comprehensive approach to investigate the origin of the charge carriers. The interfaces have been systematically analyzed by combining high resolution imaging (STEM-HAADF) to atomic resolved electron (EELS) and ion (MEIS) spectroscopies. The observed and quantified parameters have been related to the electrical properties of the interfaces measured in the consortium. Buckling of the atomic layers, intermixing and electron transfer reduce the polar divergence. This rules out the polar catastrophe scenario. The formation of donor defects at the film surface is favored above a critical film thickness. Electrons are transferred to interface in the STO conduction band. A competing compensation mechanism of the positive interfacial charge by negatively charged strontium vacancies has been demonstrated that generates an in plane compression of the STO, unfavorable for a strict 2D confinement of the charges. Varying the process parameters such as growth duration, oxygen partial pressure, temperature, and plume stoichiometry shift the equilibrium of the different mechanisms highlighted. This thesis emphasizes the complex relations between the process and the properties through the defects distribution around these singular interfaces.

Neste trabalho, apresentamos estudos de magnetotransporte em um sistema quase tridimensional de elétrons produzido em amostras contendo poços quânticos parabólicos (PQW, Parabolic Quantum Well ) formados em heteroestruturas de AlGaAs crescidos sobre substratos de GaAs pela técnica de epitaxia por feixe molecular (MBE). Na primeira parte do nosso trabalho realizamos medidas de magnetoresistência, efeito Hall e efeito Shubnikov-de Haas em PQWs com larguras de 1000 Å a fim de investigar as propriedades eletronicas tais como a concentração e a mobilidade dos elétrons nas amostras. Através de cálculos autoconsistentes determinou-se os perfis de potencial, os níveis de energia e as concentrações de cada uma das sub-bandas ocupadas no poço. Uma análise através da transformada de Fourier também permitiu determinar as concentrações eletrônicas nas sub-bandas. Em uma segunda parte estudou-se a influência da aplicação de potenciais externos através de uma porta metálica com barreira em uma amostra contendo um PQW de largura 3000 Å na presença de campos magnéticos perpendicular e paralelo à superfície da amostra. Encontrou-se que para uma tensão de porta de Vg = 0, 55V forma-se uma barreira de potencial ainda sem ter depleção de cargas no poço. Apresenta-se a idealização do dispositivo transistor válvula de spin, a partir do fato que aplicando uma tensão de porta é possível deslocar espacialmente os elétrons e mudar a sua orientaçãp de spin. / Results from magnetic transport studies made on quasi-three-dimensional electron systems are presented in this work. AlGaAs heterostructures grown on GaAs subtrates through molecular beam epitaxy (MBE) enable the existence of this type of systems by means of parabolic quantum wells (PQW) formation. This work was developed in two main parts. First, we studied magnetoresistence phenomena, such as Hall effect and Shubnikov-de Haas, on 1000 Å width PQWs. This permits to know the electronic concentration and mobility values of this type of samples, among other electrical properties. Then, self-consistent calculations gave an outline of the size and shape of the potentials, and gave the values for the energy levels and the electronic concentration on each occupied sub-band of the quantum well. Through Fourier transform analysis was also possible to obtain and confirm the electronic concentrations of the occupied sub-bands. In the second part of the work, we studied the effects of applying an external potential through a barrier gate to a 3000 Å width PQW sample in the presence of magnetic fields parallel and perpendicular to the sample surface. For a V g = 0, 55 V gate voltage, it was found that a potential barrier was formed even without charge depletion in the well. An idealization for the spin valve transistor device, based on the fact that applying a gate potential spatially dislocates the electrons and changes their spin orientation, is presented.

Neste trabalho, apresentamos estudos de magnetotransporte em um sistema quase tridimensional de elétrons produzido em amostras contendo poços quânticos parabólicos (PQW, Parabolic Quantum Well ) formados em heteroestruturas de AlGaAs crescidos sobre substratos de GaAs pela técnica de epitaxia por feixe molecular (MBE). Na primeira parte do nosso trabalho realizamos medidas de magnetoresistência, efeito Hall e efeito Shubnikov-de Haas em PQWs com larguras de 1000 Å a fim de investigar as propriedades eletronicas tais como a concentração e a mobilidade dos elétrons nas amostras. Através de cálculos autoconsistentes determinou-se os perfis de potencial, os níveis de energia e as concentrações de cada uma das sub-bandas ocupadas no poço. Uma análise através da transformada de Fourier também permitiu determinar as concentrações eletrônicas nas sub-bandas. Em uma segunda parte estudou-se a influência da aplicação de potenciais externos através de uma porta metálica com barreira em uma amostra contendo um PQW de largura 3000 Å na presença de campos magnéticos perpendicular e paralelo à superfície da amostra. Encontrou-se que para uma tensão de porta de Vg = 0, 55V forma-se uma barreira de potencial ainda sem ter depleção de cargas no poço. Apresenta-se a idealização do dispositivo transistor válvula de spin, a partir do fato que aplicando uma tensão de porta é possível deslocar espacialmente os elétrons e mudar a sua orientaçãp de spin. / Results from magnetic transport studies made on quasi-three-dimensional electron systems are presented in this work. AlGaAs heterostructures grown on GaAs subtrates through molecular beam epitaxy (MBE) enable the existence of this type of systems by means of parabolic quantum wells (PQW) formation. This work was developed in two main parts. First, we studied magnetoresistence phenomena, such as Hall effect and Shubnikov-de Haas, on 1000 Å width PQWs. This permits to know the electronic concentration and mobility values of this type of samples, among other electrical properties. Then, self-consistent calculations gave an outline of the size and shape of the potentials, and gave the values for the energy levels and the electronic concentration on each occupied sub-band of the quantum well. Through Fourier transform analysis was also possible to obtain and confirm the electronic concentrations of the occupied sub-bands. In the second part of the work, we studied the effects of applying an external potential through a barrier gate to a 3000 Å width PQW sample in the presence of magnetic fields parallel and perpendicular to the sample surface. For a V g = 0, 55 V gate voltage, it was found that a potential barrier was formed even without charge depletion in the well. An idealization for the spin valve transistor device, based on the fact that applying a gate potential spatially dislocates the electrons and changes their spin orientation, is presented.

An equilibrium multielectron bubble (MEB) in liquid helium is a fascinating object with a spherical two-dimensional electron gas on its surface. After it was first observed a few decades ago, a plethora of physical properties of MEBs, for example, a tunable surface electron density, have been predicted. In this thesis, we will discuss two new methods to create MEBs in liquid helium. Before the discussion, the way to generate a large number of electrons in a low temperature system will be discussed, including thermionic emission and field emission in helium. In the first new method to make MEBs, we used a dome-shaped cell filled with superfluid helium in which an MEB was created and confined at the dome. The lifetime of the MEB was substantially longer than the previously reported observations of MEBs. In the second method, MEBs were extracted from the vapor sheath around an electrically heated tungsten filament submerged in liquid helium, either by a high electric field (up to 15 kV/cm) or by a sudden increase of a negative pressure in liquid helium. High-speed photography was used to capture the MEB's motion. A method to determine the number of electrons was developed by monitoring the oscillations of the MEBs. Finally, an electromagnetic trap was designed to localize the MEBs created using the second method, which was important for future studies of the properties of MEBs. / Physics

High-mobility two-dimensional electron gas (2DEG) which resides at the interface between GaAs and AlGaAs layered semiconductors has been used experimentally and theoretically to study ballistic electron transport. The present project is motivated by recent experiments in magnetic electron focusing. The proposed device consists of two quantum point contacts (QPCs) serving as electron injector and detector which are placed in the same semiconductor GaAs/AlGaAs heterostructure. This thesis is focused on the theoretical study of electron flow coming from the injector QPC (a short quantum wire) and going into an open two-dimensional (2D) reservoir. The transport is considered for non-interacting electrons at different transmission regimes using the mode-matching technique. The proposed mode-matching technique has been implemented numerically using Matlab software. Electron flow through the quantum wire with rectangular, conical and rounded openings has been studied with and without an applied electric bias. We have found that the geometry of the opening does not play a crucial role for the electron flow propagation while the conical opening allows the electrons to travel longer distances into the 2D reservoir. When electric bias is applied, the electron flow also penetrates farther into the 2D region. The results of this study can be applied in designing magnetic focusing devices.

Multielectron bubbles (MEBs) are micron sized cavities in liquid helium that contain electrons confined within a nanometer thick layer on the inner surface of a bubble. These objects present a rich platform to study the behavior of a two dimensional electron gas (2DES) on a curved surface. Most crucially, the surface electron densities in MEBs can vary over a wide range, making it a suitable candidate for studying classical Wigner crystallization and quantum melting in a single system. So far, there has been only limited experimental study of MEBs, with most of the previous investigation transient in nature. As we discuss in our presentation, we have built a cryogenic system for performing transport and optical measurements of MEBs down to 1.3 K. We have developed a new technique of generating MEBs, and trapping them using two different methods. In the first method, we trapped MEBs using a Paul trap for more than hundreds of milliseconds. This allows the MEBs to be further manipulated with buoyant and electric forces, such as to obtain reliable measurements of their physical properties. As we observe experimentally, the surface charge density of a single MEB can vary by orders of magnitude during the course of one measurement, thereby covering a previously unexplored section of the 2DES phase diagram. In the second method, we trapped MEBs using a dielectric coated metal electrode over many seconds. This also allowed the properties of MEBs to be measured in a non-destructive manner. Since MEBs are charged bubbles, their motion can be controlled by electric fields, which allowed us to measure the drag of MEBs as a function of Reynolds number by analysing the trajectories. Due to the low viscosity and surface tension of helium compared to other liquids, these measurements could be performed at Morton Numbers that have never been explored. We also show that how the shape of a single MEB evolves from spherical to ellipsoidal as their speeds vary. During the course of experiments, we observed number of interesting phenomena, such as coalescence of similarly charged bubbles, as well as their splitting into secondary bubbles at high speeds. Most interestingly, we have imaged their dynamics in the presence of static, as well as oscillating electric fields, which may provide insight into the phase of the electronic system present inside the bubbles.

Les propriétés d'un gaz électronique bidimensionnel soumis à champs magnétiques intenses et à bas champs magnétiques sont étudiés par la spectroscopie optique: l'effet Hall quantique fractionnaire (FQHE) par photoluminescence et diffusion inélastique de la lumière, puis un nouvel effet oscillatoire de la résistance induit par micro-ondes (MIROs) par transport et absorption des micro-ondes. Les effets des interactions entre électrons du 2DEG sont à l'origine de FQHE. Jusqu'à maintenant, les expériences d'optiques n'ont pas permis les études des interactions entre électrons sur toute la gamme de fractions. Les fractions 1/3, 2/5, 3/7, 3/5, 2/3 et 1 sont clairement observées dans les spectres non traités et montrent une symétrie autour du facteur de remplissage 1/2. La symétrie des fermions composites ets observée dans les spectres. A bas champ magnétique, sous irradiation micro-onde, les propriétés de transport s'écartent nettement des oscillations bien connues de Shubnikov - de Haas pour évoluer vers une série d'états de résistance zéro. Les résultats des mesures d'absorption des micro-ondes sont présentés pour deux échantillons. L'échantillon de basse mobilité montre seulement une absorption autour de la résonance cyclotron (CR). L' échantillon de haute mobilité montre aussi des signaux d'absorption aux harmoniques de la CR. Les mesures ont permis d'inférer l'existence de deux processus d'absorption différents et séparés. L'absorption non résonante est mieux visible en transport et observée comme MIROs, et l'absorption résonante, mieux observée dans les mesures d'absorption, suit probablement les règles de polarisation de résonance cyclotron.

This work is concerned with the theoretical description of the Scanning Gate Microscopy (SGM) in general and with solving particular models of the quantum point contact (QPC) nanostructure, analytically and numerically. SGM is an experimental technique, which measures the conductance of a nanostructure, while a charged AFM tip is scanned above its surface. It gives many interesting results, such as lobed and branched images, interference fringes and a chequerboard pattern. A generally applicable theory, allowing for unambiguous interpretation of the results, is still missing. Using the Lippman-Schwinger scattering theory, we have developed a perturbative description of non-invasive SGM signal. First and second order expressions are given, pertaining to the ramp- and plateau-regions of the conductance curve. The maps of time-reversal invariant (TRI) systems, tuned to the lowest conductance plateau, are related to the Fermi-energy charge density. In a TRI system with a four-fold spatial symmetry and very wide leads, the map is also related to the current density, on any plateau. We present and discuss the maps calculated for two analytically solvable models of the QPC and maps obtained numerically, with Recursive Green Function method, pointing to the experimental features they reproduce and to the fundamental difficulties in obtaining good plateau tuning which they reveal.

Ce travail porte sur la description théorique de la microscopie à grille locale (SGM) et sur la résolution de modèles particuliers de contacts quantiques (QPC), analytiquement et numériquement. SGM est une technique expérimentale, qui mesure la conductance d'une nanostructure, lorsqu'une pointe de microscope a force atomique chargée balaye la surface, sans contacter cette dernière. Les images de SGM révèlent de nombreuses traits intéressants, tels que des lobes, des branches, des franges d'interférence et des motifs de damier. Aucune théorie généralement applicable, donnant une interprétation univoque, n’est disponible à ce jour. En utilisant la théorie de la diffusion de Lippman–Schwinger, nous avons développé une description perturbative de signal de SGM non invasive. Les expressions du premier et du second ordre ont été données, se rapportant aux régions de marche et de plateau de la courbe de conductance. Dans les systèmes invariants par renversement du temps (TRI), adaptés au premier plateau de conductance, les images SGM sont liées à la densité de charge à l`énergie de Fermi. Dans un système TRI, avec une symétrie spatiale centrale et de très larges contacts, les images sont aussi liées à la densité de courant, quelque soit le plateau. Nous présentons et discutons les images calculées pour deux modèles analytiques de QPC et les images obtenues numériquement avec la méthode des fonctions de Green récursives, reproduisant certains motifs observés expérimentalement, et pointant les difficultés fondamentales a se bien positionner sur le plateau de conductance. / This work is concerned with the theoretical description of the Scanning Gate Microscopy (SGM) in general and with solving particular models of the quantum point contact (QPC) nanostructure, analytically and numerically. SGM is an experimental technique, which measures the conductance of a nanostructure, while a charged AFM tip is scanned above its surface. It gives many interesting results, such as lobed and branched images, interference fringes and a chequerboard pattern. A generally applicable theory, allowing for unambiguous interpretation of the results, is still missing. Using the Lippman-Schwinger scattering theory, we have developed a perturbative description of non-invasive SGM signal. First and second order expressions are given, pertaining to the ramp- and plateau-regions of the conductance curve. The maps of time-reversal invariant (TRI) systems, tuned to the lowest conductance plateau, are related to the Fermi-energy charge density. In a TRI system with a four-fold spatial symmetry and very wide leads, the map is also related to the current density, on any plateau. We present and discuss the maps calculated for two analytically solvable models of the QPC and maps obtained numerically, with Recursive Green Function method, pointing to the experimental features they reproduce and to the fundamental difficulties in obtaining good plateau tuning which they reveal.