Propostas de construção de dispositivos que unem a eletrônica com a spintrônica utilizando compostos semicondutores magnéticos diluídos (DMS) tem se tornado cada mais frequentes junto à comunidade científica em geral. Em particular, por suas propriedades magnéticas e de transporte hoje conhecidas, camadas de GaAs/GaMnAs pertencem a um grupo de DMS com grandes possibilidades de utilização prática. Nesse sentido, entender suas propriedades de transporte é essencial para o desenvolvimento dessa nova área. Investigamos o transporte spin polarizado em nanocamadas de GaAs/GaMnAs que exibem uma fase ferromagnética abaixo de certa temperatura de transição de fase. Como procedimento de pesquisa, nosso cálculo da resistividade considerou a existência de uma banda de impureza que determina a natureza do estado no nível de Fermi e dos estados próximos a ele como estendidos (condução "metálica") ou localizados (condução por excitação térmica). A ordem magnética e a resistividade são interligados devido à influência da polarização de spin da banda de impurezas e um efeito tipo separação Zeeman sobre a mobility edge (1). Obtivemos para um dado intervalo de concentração de manganês e de portadores, um comportamento metálico em que o transporte por estados estendidos domina em baixas temperaturas e é dominado por um processo de excitação térmica dos estados localizados para temperaturas próximas e acima da temperatura de transição. O resultado dessa combinação de canais de condução foi o aparecimento de uma lombada na resistividade, a qual tem sido observada experimentalmente, e traz esclarecimentos sobre a relação entre as propriedades de transporte e magnéticas desse material. (1) Embora a expressão possa ter uma tradução, é comumente usada na área em inglês. / Construction proposals of the contrivances that put together electronic with spintronic using diluted magnetic semiconducting compounds (DMS) are more and more frequent to the scientific community in general. In particular, because of its magnetic and transporting rightnesses that has been known today, GaMnAs stratums belongs to a DMS group with great possibilities of the practical utilization. In this sense, to understand its transporting rightnesses is essential to the development in this new area. We investigate the polarized spin transport in GaMnAs nanolayers that display an ferromagnetic stage below of the specific phase transition temperature. As a procedure research, our resistivity estimate has consider the existence of an impurity band that determine the state nature in the Fermi level and the states near to it like extended (metallicconduction) or located (thermic excitation conduction). The magnetic order and resistivity are interconnected due to the influence of the spin polarization of the band of the impurities and another efect as a Zeeman separation over the moblility edge. We aquire, for a certain interval of bearings and manganese concentration, a metallic behavior in which the transport to the extended states rules in low temperatures and is ruled by an process of thermic excitation of the states located to near and over temperatures of the transition temperature. The result of this transport channels combination was the appearance of an acclivity in the resistivity that has been observed experimentally and brings elucidations about the relation between the magnetic and transporting rightnesses of this material.

Propostas de construção de dispositivos que unem a eletrônica com a spintrônica utilizando compostos semicondutores magnéticos diluídos (DMS) tem se tornado cada mais frequentes junto à comunidade científica em geral. Em particular, por suas propriedades magnéticas e de transporte hoje conhecidas, camadas de GaAs/GaMnAs pertencem a um grupo de DMS com grandes possibilidades de utilização prática. Nesse sentido, entender suas propriedades de transporte é essencial para o desenvolvimento dessa nova área. Investigamos o transporte spin polarizado em nanocamadas de GaAs/GaMnAs que exibem uma fase ferromagnética abaixo de certa temperatura de transição de fase. Como procedimento de pesquisa, nosso cálculo da resistividade considerou a existência de uma banda de impureza que determina a natureza do estado no nível de Fermi e dos estados próximos a ele como estendidos (condução "metálica") ou localizados (condução por excitação térmica). A ordem magnética e a resistividade são interligados devido à influência da polarização de spin da banda de impurezas e um efeito tipo separação Zeeman sobre a mobility edge (1). Obtivemos para um dado intervalo de concentração de manganês e de portadores, um comportamento metálico em que o transporte por estados estendidos domina em baixas temperaturas e é dominado por um processo de excitação térmica dos estados localizados para temperaturas próximas e acima da temperatura de transição. O resultado dessa combinação de canais de condução foi o aparecimento de uma lombada na resistividade, a qual tem sido observada experimentalmente, e traz esclarecimentos sobre a relação entre as propriedades de transporte e magnéticas desse material. (1) Embora a expressão possa ter uma tradução, é comumente usada na área em inglês. / Construction proposals of the contrivances that put together electronic with spintronic using diluted magnetic semiconducting compounds (DMS) are more and more frequent to the scientific community in general. In particular, because of its magnetic and transporting rightnesses that has been known today, GaMnAs stratums belongs to a DMS group with great possibilities of the practical utilization. In this sense, to understand its transporting rightnesses is essential to the development in this new area. We investigate the polarized spin transport in GaMnAs nanolayers that display an ferromagnetic stage below of the specific phase transition temperature. As a procedure research, our resistivity estimate has consider the existence of an impurity band that determine the state nature in the Fermi level and the states near to it like extended (metallicconduction) or located (thermic excitation conduction). The magnetic order and resistivity are interconnected due to the influence of the spin polarization of the band of the impurities and another efect as a Zeeman separation over the moblility edge. We aquire, for a certain interval of bearings and manganese concentration, a metallic behavior in which the transport to the extended states rules in low temperatures and is ruled by an process of thermic excitation of the states located to near and over temperatures of the transition temperature. The result of this transport channels combination was the appearance of an acclivity in the resistivity that has been observed experimentally and brings elucidations about the relation between the magnetic and transporting rightnesses of this material.

Esta tese apresenta um estudo experimental em sistemas eletrônicos multicamadas formados em diversas heteroestruturas semicondutoras de alta qualidade crescidas por epitaxia de feixes moleculares. Especificamente, poços quânticos isolados baseados em InGaAs/InP e super-redes baseadas em GaAs/AlGaAs foram caraterizados por meio de medidas de fotoluminescência (PL) em função da temperatura, potência de excitação e do campo magnético. O estudo de efeitos na dinâmica de processos de recombinação destes sistemas eletrônicos é a base principal deste trabalho. Além disso, exploramos os efeitos da desordem sobre os processos de recombinação e demonstramos que o espalhamento por rugosidade interfacial é responsável pela resposta óptica destes sistemas. Nas amostras de InGaAs/InP com maior largura do espaçador observamos um novo efeito, o tempo de recombinação Auger aumenta notavelmente com a potência de excitação. Atribuímos este novo efeito à distribuição de elétrons fotoexcitados em diferentes vales da banda de condução. E em amostras de menor largura do espaçador, o relaxamento da regra de seleção do momento induzido pela desordem faz que o tempo de recombinação Auger diminua com o aumento da potência. Por outro lado, nas amostras de GaAs/AlGaAs, evidenciamos que a desordem gerada pela rugosidade interfacial afeta consideravelmente o transporte dos elétrons da banda de condução, e em poços quânticos de largura apropriada resulta em uma transição metal-isolante. A borda de mobilidade Ec, energia crítica que separa os estados estendidos dos estados localizados, foi determinada a partir das medidas do tempo de recombinação em função da energia de emissão de PL. Para uma desordem crítica, a Ec mostra uma interseção com a energia do nível de Fermi, a qual corresponde à transição metal-isolante. Além disso, realizamos medidas de PL resolvida no tempo em função do campo magnético. Observamos que a redistribuição espacial de elétrons causada pelo campo magnético afeta os tempos de recombinação. Nas amostras metálicas, os resultados mostraram deslocamento da Ec para altas energias, devido à quantização da energia dos elétrons provocada pelo campo magnético. No entanto, nas amostras isolantes, o campo magnético foi responsável pelo relaxamento significativo da regra de seleção do momento, que aumenta a probabilidade de recombinação dos elétrons localizados com os buracos fotoexcitados da banda de valência e, por consequência, diminui o tempo de recombinação. / This thesis presents an experimental study in multilayer electronic systems formed in several high quality semiconductor heterostructures grown by molecular beam epitaxy. Specifically, GaAs/AlGaAs based superlattices and isolated quantum wells based on InGaAs/InP were characterized by photoluminescence (PL) measurements as a function of temperature, pump power and magnetic field. The study of effects on the dynamics of the recombination processes of these electronic systems is the principal goal of this work. In addition, we explore the effects of the disorder on the recombination processes and show that the interfacial roughness scattering is responsible for the optical response in these systems. In the small spacer InGaAs/InP samples, we observed a new effect, the Auger recombination time becomes larger with the increasing the pump power. We propose that the distribution of photoexcited electrons over different conduction band valleys might account for this effect. In large spacer quantum wells, the non-radiative recombination time is reduced with the increasing pump power, as a consequence the disorder-induced relaxation of the momentum rule. On the other hand, in GaAs/AlGaAs samples, we showed that the disorder generated by interfacial roughness considerably affects transport of the conduction band electrons and at appropriate quantum wells width results in a metal-to-insulator transition. The mobility edge energy Ec was determined from the measurements of the recombination time as a function of energy allowed. At a critical disorder, the mobility edge energy demonstrates intersection with the Fermi level energy which correspond to the metal-insulator transition. In addition, we perform time-resolved PL measurements as a function of the magnetic field. We observed that the spatial distribution of electrons caused by the magnetic field influence on the recombination time. In the metallic samples was observed a shift of the mobility edge to higher energy due to the magnetic field quantization of conduction band electron energy. However, in the insulating samples, the magnetic field was responsible to cause a significant relaxation of the momentum selection rule which enhances the probability of recombination of the localized electrons with the photoexcited holes of the valence band, and consequently the recombination time is reduced.

In this thesis, we have explored the commonalities and connections between different classes of quantum systems that do not thermalize. Specifically, we have (1) shown that localized systems possess conservation laws like integrable systems, which can be constructed in a systematic way and used to detect localization-delocalization transitions , (2) studied the phenomenon of many-body localization in a model with a single particle mobility edge, (3) shown that interesting finite-size scaling emerges, with universal exponents, when athermal quantum systems are forced to thermalize through the application of perturbations and (4) shown that these scaling laws also arise when a perturbation causes a crossover between quantum systems described by different random matrix ensembles. We conclude with a brief summary of each chapter. In Chapter 2, we have investigated the effects of finite size on the crossover between quantum integrable systems and non-integrable systems. Using exact diagonalization of finite-sized systems, we have studied this crossover by obtaining the energy level statistics and Drude weight associated with transport. Our results reinforce the idea that for system size L → ∞, non-integrability sets in for an arbitrarily small integrabilitybreaking perturbation. The crossover value of the perturbation scales as a power law ∼ L−3 when the integrable system is gapless and the scaling appears to be robust to microscopic details and the precise form of the perturbation. In Chapter 3, we have studied the crossover among different random matrix ensembles CHAPTER 6. CONCLUSION 127 [Poissonian, Gaussian Orthogonal Ensemble (GOE), Gaussian Unitary Ensemble (GUE) and Gaussian Symplectic Ensemble (GSE)] realized in different microscopic models. We have found that the perturbation causing the crossover among the different ensembles scales to zero with system size as a power law with an exponent that depends on the ensembles between which the crossover takes place. This exponent is independent of microscopic details of the perturbation. We have also found that the crossover from the Poissonian ensemble to the other three is dominated by the Poissonian to GOE crossover which introduces level repulsion while the crossover from GOE to GUE or GOE to GSE associated with symmetry breaking introduces a subdominant contribution. Finally,we have conjectured that the exponent is dependent on whether the system contains interactions among the elementary degrees of freedom or not and is independent of the dimensionality of the system. In Chapter 4, we have outlined a procedure to construct conservation laws for Anderson localized systems. These conservation laws are found as power series in the hopping parameters. We have also obtained the conservation laws for the disorder free Aubry-Andre model, where the states are either localized or extended depending on the strength of a coupling constant. We have formulated a specific procedure for averaging over disorder, in order to examine the convergence of the power series. Using this procedure for the Aubry-Andre model, we show that integrals of motion given by our construction are well-defined in the localized phase but not so in the extended phase. Finally, we also obtain the integrals of motion for a model with interactions to lowest order in the interaction. In Chapter 5, we have studied many body localization and investigated its nature in the presence of a single particle mobility edge. Employing the technique of exact diagonalization for finite-sized systems, we have calculated the level spacing distribution, time evolution of entanglement entropy, optical conductivity and return probability to characterize the nature of localization. The localization that develops in the presence of interactions in these systems appears to be different from regular Many-Body Localization (MBL) in that the growth of entanglement entropy with time is linear (like in CHAPTER 6. CONCLUSION 128 a thermal phase) instead of logarithmic but saturates to a value much smaller than the thermal value (like for MBL). All other diagnostics seem consistent with regular MBL

Dans ce manuscrit, nous présentons notre avancement pour réaliser une méthode spectroscopique pour étudier la transition d’Anderson avec des atomes froids. Cela repose sur la réalisation d'un potentiel désordonné sélectif en état de spin, le désordre n'étant significatif que pour l'un des deux états de spin impliqués. En combinant cela avec la technique de transfert par radiofréquence d’un état insensible au désordre à un état exclusivement sensible au désordre, il devient possible de charger une onde de matière dans le désordre dans des états d’énergie bien définies. Pour prouver le concept, nous avons effectué des mesures des fonctions spectrales d’atomes ultra-froids dans des potentiels désordonnés, qui sont directement proportionnels au taux de transfert des atomes. Nous présentons les résultats en montrant un excellent accord avec les calculs numériques. Cela a ouvert des perspectives pour d’autres études sur la transition d’Anderson. En particulier, nous cherchons à observer la transition entre les états diffusifs et les états localisés séparés par une énergie critique, appelée le seuil de mobilité. Une telle étude nécessite la réalisation d’un désordre sélectif en état de spin qui permet un long temps de propagation dans le désordre afin de distinguer les deux phases. À cette fin, nous présentons un nouveau schéma du désordre sélectif en état de spin avec deux lasers du speckle (speckle bichromatique). Cela ouvre la voie à une approche spectroscopique de la transition d’Anderson avec des atomes froids avec une résolution en énergie bien supérieure à celles des expériences précédentes. / In this manuscript, we present our progress towards realizing a spectroscopic method to study of Anderson transition with ultracold atoms. This relies on the realization of state-dependent disordered potential whereby the disorder is significant only for one of two involved spin-states. Combined with technique of radio-frequency transfer from the disorder-free state to the state with controlled disorder, it becomes possible to load a matter wave in the disorder in a well-defined energy states. As a proof of principle, we have performed measurements of the spectral functions of ultracold atoms in disordered potentials, which are directly proportional to the transfer rate of the atoms. We present the results showing excellent agreement with numerical calculations. This has opened up prospects for further studies of the Anderson transition. In particular we seek to observe transition between the diffusive and the localized states separated by a critical energy, the so-called mobility edge. Such study requires realization of state-dependent disorder which allows long propagation time in the disorder in order to distinguish the two phases. For this purpose, we present a new scheme of the state-dependent disorder with two laser speckles (bichromatic laser speckle). This paves the way towards spectroscopic approach of Anderson transition with ultracold atoms with energy resolution much higher than those in the previous experiments.

Anderson localization occurs when an otherwise conductive solid becomes insulatingdue to a sufficiently large degree of disorder in the medium. The electron band energy(as a function of disorder) at which this transition between extended and localizedelectron states occur is called the mobility edge (ME) and is energy-dependent only in3-dimensional systems. In lower dimensional systems, energy-independent ME (allstates localized or all extended) has been demonstrated by replacing disorder withquasi-periodic potential. However, recent theoretical findings indicate that neitherdisorder nor quasi-periodic potential is necessary for a material to exhibit electronlocalization and existence of energy-dependent pseudo ME at finite system size.In this thesis work, we use light in coupled silicon nitride waveguides to simulatesingle-particle transport of a solid-state medium and investigate the coexistence ofdelocalized and localized states in disorder-free photonic lattices of finite systemsize. This was achieved by implementing a simulated linearly increasing electricpotential on even-numbered sites by varying the refractive index of the wave guide(ch. 3). Through our experimental setup, we successfully achieved a coexistence oflocalized and delocalized states, where the degree of localization varies depending onthe strength of the applied electric field.The findings have implications for the field of quantum technology, whereunderstanding and controlling quantum states is crucial. The ability to achievelocalization in the absence of disorder opens new possibilities for designing andengineering photonic devices for quantum information processing tasks. / Anderson-lokalisering uppstår när ett annars ledande fast material blir isolerande pågrund av en tillräckligt stor grad av oordning i mediet. Elektronbandsenergin (som enfunktion av oordning) vid vilken denna övergång mellan förlängda och lokaliseradeelektrontillstånd sker kallas mobilitetskanten (ME) och är energiberoende endasti 3-dimensionella system. I lägre dimensionella system har energioberoende ME(alla tillstånd lokaliserade eller alla förlängda) påvisats genom att ersätta oordningmed kvasi-periodisk spänning. Nya teoretiska fynd indikerar dock att varkenoordning eller kvasi-periodisk spänning är nödvändig för att ett material ska uppvisaelektronlokalisering och förekomsten av energiberoende pseudo-ME för system avfinita storlekar.I detta examensarbete använder vi ljus i kopplade vågledare av kiselnitrid föratt simulera transport av en partikel i ett fast tillståndsmedium och undersökersamexistensen av icke-lokaliserade och lokaliserade tillstånd i finita system utanoordning med fotoniska gitter. Detta uppnåddes genom att implementera ensimulerad linjärt ökande elektrisk potential på varje jämnt numrerat gitterläge platsgenom att öka vågledarbredderna och noll elektrisk spänning på varje udda. Genomvårt experimentella upplägg lyckades vi uppnå lokaliserade och förlängda tillstånd, därgraden av lokaliseringen varierade beroende på styrkan av det tillämpade elektriskafältet.Fynden har implikationer för kvantteknologi, där förståelse och kontroll avkvanttillstånd är avgörande. Förmågan att uppnå lokalisering i frånvaro avoordning öppnar nya möjligheter för att designa och konstruera fotoniska enheter förkvantinformationsprocesser.

Ce mémoire présente une étude théorique des propriétés de localisation collective dans les superfluides de Bose désordonnés ou quasipériodiques. S'il est connu depuis Anderson que le désordre peut localiser les particules libres, comprendre ses effets dans les systèmes quantiques en interaction, où il est à l'origine de transitions de phase et d'effets de localisation non-Triviaux, représente aujourd'hui un défi majeur. En nous focalisant sur le cas d'un gaz de Bose dans le régime de faibles interactions, bien décrit par la théorie de Bogoliubov, nous étudions les transitions de localisation de ses excitations collectives dans différents contextes. Dans le cas d'un vrai désordre dans l'espace continu tout d'abord, nous développons un formalisme de désordre fort allant au-Delà des études antérieures, aboutissant à une description complète des propriétés de localisation des excitations en dimension arbitraire. Nous présentons un diagramme de localisation générique, et une interprétation microscopique de la propagation des excitations dans le désordre. Dans un second temps, nous considérons le cas d'un potentiel quasipériodique unidimensionel, aux propriétés intermédiaires entre un vrai désordre et un potentiel périodique. Notre traitement analytique et numérique du problème révèle une transition de localisation collective, que nous caractérisons et interprétons en termes de localisation dans un potentiel effectif multiharmonique. Pour finir, nous considérons le cas d'un gaz de Bose à deux composants. Nous développons le formalisme général pour étudier ces questions et décrivons la physique de base de ces systèmes qui présentent leurs propres spécificités. / In this thesis, we theoretically investigate the collective localization properties of weakly-Interacting Bose superfluids subjected to disordered or quasiperiodic potentials. While disorder has been recognized since Anderson to induce single-Particle localization, the interplay between disorder and interactions in quantum systems is today among the most challenging questions in the field, and underlies fascinating phase transitions and non-Trivial localization effetcs. Focusing on Bose gases in the weakly-Interacting regime for which the Bogoliubov theory proves a successful tool, we study the localization transitions of collective excitations in several contexts. First, in the case of a continuous true disorder, we develop a strong-Disorder formalism going beyond previous studies, providing us with a complete description of the localization behaviour of collective excitations in arbitrary dimension. A generic localization diagram is obtained and the transport of excitations in the disorder is microscopically interpreted. Secondly, we consider the case of one-Dimensional quasiperiodic potentials, which are known to display intermediate properties between periodic and disordered ones. We perform a numerical and analytical treatment of the localization problem of collective excitations, allowing us to quantitatively characterize and interpret the localization transition in terms of an effective multiharmonic problem. Finally, we set up the general inhomogeneous formalism to address such issues in multicomponent Bose gases, and enlighten the basic physic of such systems, which are known to exhibit their own specific features.