Made available in DSpace on 2016-06-02T20:15:31Z (GMT). No. of bitstreams: 1 5844.pdf: 11430873 bytes, checksum: b80a5790a9ebf6ae63ff48e52968ae60 (MD5) Previous issue date: 2014-02-21 / Universidade Federal de Sao Carlos / O crescimento e caracterização de sistemas de heteroestruturas semicondutoras quasi-unidimensionais têm atraído grande interesse devido à sua potencial de aplicação tecnológica, como foto-detectores, dispositivos opto-eletrônicos assim como seu para o processamento de informação quântica e aplicações em fotônica. O objetivo desta tese é o estudo das propriedades de transporte eletrônico e de spin em sistemas semicondutores quasi-unidimensionais, especificamente trataremos de nanofios (NWs) homogêneos, NWs acoplados, NWs do tipo plano-geminado (TP), diodos de tunelamento ressonante (ETD) e cadeias de pontos quânticos (QDCS). Escolhemos o método k-p, particularmente o Hamiltoniano de Luttinger, para descrever os efeitos de confinamento e tensão biaxial. Este sugeriu uma modulação do caráter do estado fundamental que, complementada com a dinâmica fônons fornecidas pelas simulações da Dinâmica Molecular (MD), permitiu a descrição da modulação da mobilidade de buracos por emissão ou absorção de fônons. Em relação ao sistema de NWs acoplado,estudamos, através do método da matriz de transferência (TMM), as propriedades de transporte de elétrons e spin sob a interação de spin-órbita (SOI) de Eashba, localizada na região de acoplamento entre fios. Foram consideradas várias configurações de tensões de gate (Vg) aplicadas nos fios. Desse modo, compreendemos a modulação do transporte de spin quando esse é projetado no direção-z através da combinação do SOI e das dimensionalidades do sistema. Da mesma forma, a combinação de SOI e da Vg aplicada deu origem a modulação da polarização, quando o spin medido é projetado na mesma direção em que o SOI de Eashba atua, a direção y. Usando o TMM, exploramos as propriedades de transporte de um DBS e o efeito de uma resistência em série com o intuito de provar a natureza da biestabilidade das curvas características I V bem como o aumento de sua área com temperatura, resultados fornecidos por experimentos. O modelo indicou que aumentando da resistência pela diminuição sa temperatura aumenta a área biestável. A presença de uma hetero-junção adicional ao sistema induz uma densidade de carga nas suas interfaces. De acordo com esta configuração, a queda de tensão total do ETDS muda, podendo ser confirmada experimentalmente. A formação dos peculiares campos de deformação e sua influência sobre a estrutura eletrônicas e propriedades de transporte em superredes de TP foi estudada sistematicamente. Assim, as propriedades de transporte, de ambos os elétrons e buracos, pode ser sintonizada eficientemente, mesmo no caso de elétrons r em sistemas de blenda de zinco, contrastando com a prevista transparência de elétrons r em superredes de semicondutores III-V heteroestruturados. Além disso, constatamos que a probabilidade de transmissão para buracos da banda de valência também poderia ser efetivamente modificada através de uma tensão externa.Por fim, colaboradores sintetizaram com sucesso sistemas de QDCs de InGaAs através da epitaxia de feixe molecular e engenharia de tensão. Um comportamento anisotrópico da condutância com a temperatura foi observado em QDCs com diferentes concentrações de dopagem, medida realizada ao longo e entre os QDCs. O modelo teórico 1D de hoppíng desenvolvido mostrou que a presença de estados OD modela a resposta anisotrópica da condutância neste sistemas. / The growth and characterization of semiconductor quasi-one-dimensional heterostructure systems have attracted increasing interest due to their potential technological application, like photo-detectors, optoelectronic devices and their promising features for quantum information processing and photonic applications. The goal of this thesis is the study of electronic and spin transport properties on quasi-one-dimensional semiconductor systems; specifically, homogenous nanowires (NWs), coupled NW s, twin-plane (TP) NWs, resonant tunneling diodes (RTDs), and quantum dot chains (QDCs). The k-p method, in particular the Luttinger Hamiltonian, was chosen to describe the effects of biaxial confinement and strain. This suggested a modulation of the ground state character that, complemented with the phonon dynamics provided by Molecular Dynamics (MD) simulations, allowed the description of the hole mobility modulation by either phonon emission or absorption. Regarding the coupled NW s system, the electron and spin transport properties affected by a Rashba spin-orbit interaction (SOI) at the joined region were unveiled through the Transfer Matrix Method (TMM). Various configurations of gate voltages (Vg), applied on the wire structure, were considered. We were able to understand the modulation of the spin transport projected in the z-direction trough the combination of the SOI and the system dimensionalities. Likewise, the combination of SOI and applied Vg gave rise to a modulation of the polarization, when the measured spin is projected in the same direction where the Rashba SOI acts, the y-direction. The transport properties of a DBS and the effect of a resistance in series was explored within the TMM to prove the nature of a bistability of the I V characteristics and its enhanced area with temperature provided by the experiment. The model indicates that increasing the resistente by decreasing the temperature, the bistable area enhances. The presence of an additional heterojunction induces a sheet charge at its interfaces. Under this configuration, the total voltage drop of the RTD changes and can be confirmed experimentally.The formation of the peculiar strain fields and their influence on the electronic structure and transport properties of a TP superlattice was systematically studied. Hence, the transport properties of both electrons and holes could be effectively tuned even in the case of T-electrons of zincblende systems, contrasting to the predicted transparency of T-electrons in heterolayered III-V semiconductor superlattices. Also, the transmission probability for holes at valence band could also be effectively modified by applying an external stress. Finally, using molecular-beam-epitaxy and skillful strain engineering, systems of In-GaAs QDCs were successfully synthesized by collaborators. The QDCs with different doping concentrations showed an anisotropic behavior of the conductance, measured along and across the QDCs, with temperature. The theoretical ID hopping model developed found that the presence of OD states shapes the anisotropic response of the conductance in this system.

Em sistemas com acoplamento spin-órbita (SO) é possível manipular eletricamente o spin do elétron via a aplicação de um campo elétrico.1 Isso permite a potencial aplicação do grau de liberdade de spin (Spintronica) no desenvolvimento de novos dispositivos e tecnologias, como por exemplo na tecnologia da informação (computação quântica).2,3 No entanto, sabe-se que a interação SO causa efeitos indesejáveis, como por exemplo a relaxação e o defasamento de spin.4 Dessa maneira, do ponto de vista de aplicações, torna-se desejável maximizar o tempo de vida do spin. Neste trabalho, investigamos a relaxação de spin dos elétrons de condução em poços quânticos com duas sub-bandas5 crescidos ao longo das direções [001] e [110] via o mecanismo de D\'yakonov-Perel\'.6 Combinando teoria de grupos, o método k.p, a aproximação da função envelope e teoria de perturbação de Löwdin obtemos um Hamiltoniano efetivo para os elétrons da banda de condução na presença das interações SO de Rashba e Dresselhaus. Aqui, diferentemente de alguns trabalhos anteriores,7,8 além de incluir o termo cúbico de Dresselhaus, também levamos em conta as contribuições devido à influência da segunda sub-banda de mais baixa energia do poço. A partir deste Hamiltoniano derivamos expressões para os tempos de relaxação do spin e analisamos como estas novas contribuições (termos do acoplamento com a segunda sub-banda) afetam os tempos de vida dos spins. Comparamos os tempos de relaxação para as direções [001] com os calculados para a direção [110]. Nossos resultados mostram que as contribuições devido à segunda sub-banda são desprezíveis para ambas as direções. Mostramos também que o tempo de relaxação para a direção [110] é mais longo que o da [001], resultado consistente com experimentos9,10 e outros trabalhos teóricos anteriores.7 / In systems with spin-orbit (SO) coupling, it is possible to electrically manipulate the electron spin via applied gate voltages.1 This allows for the potential use of the spin degree of freedom (Spintronics) in the development of new devices and technologies, for instance information technology (quantum computing).2,3 It is known however, that the SO interaction leads to the undesired effect of causing spin relaxation and spin dephasing.4 Thus from the point of view of applications, it is desirable to maximize the spin lifetimes. Here, we investigate the spin relaxation of the conduction electrons in quantum wells with two sub-bands5 grown along the [001] and [110] directions via the D\'yakonov-Perel\' mechanism.6 By combining group theory, the k.p method, the envelope function approach and the Löwdin perturbation theory, we obtain an effective Hamiltonian for the conduction electrons in the presence of the Rashba and Dresselhaus SO interactions. Differently from some early works,7,8 in addition to the cubic Dresselhaus term, we also account for the contributions arising from the second lowest sub-band of the well. We derive expressions for the spin relaxation times and analyze how the new contributions (second sub-band terms) affect the spin lifetimes. We compare the relaxation times obtained in the [001] direction with those calculated for the [110] direction. Our results show that the contributions from the second sub-band are negligible for both directions. We also find that the relaxation time in the [110] direction is longer than the one in the [001], a result consistent with experiments9,10 and earlier theoretical works.7

In the present thesis, magnetization reversal in both out-of-plane and in-plane magnetized thin lms and in devices fabricated out of those lms are explored. Pt/Co/Pt stacks with ultrathin Co layer were in-estimated initially for understanding their magnetic properties in this thesis. These perpendicular magnetized systems are good candidates for magnetic hard disc drives due to their large anisotropy, which may allow miniaturization of magnetic data storage devices. The spin Hall e ect mediated current-induced magnetization reversal in patterned Pt/Co/Pt devices were extensively investigated. Investigation of the magnetization reversal by means of a current instead of a magnetic eld is necessary to explore the possibilities of solid state magnetic memory devices. This is the primary motivation behind the investigation of current-induced magnetization reversal in Pt/Co/Pt system, in this thesis. Another important proposal for magnetic data storage is the race track memory, where the domain walls separating magnetic domains (in in-plane or out-of-plane magnetized materials) are moved by using a current. This involves a great deal of understanding of the domain wall motion in Nano-conduits under applied magnetics ends, and currents and also its interaction with engineered geometrical features. In this thesis work, magnetic led-driven domain wall pinning and deepening experiments on in-plane magnetized nanowires of perm alloy were performed to un-distend this interaction and the e act of domain wall chirality. In chapter 1, a general introduction to di errant data storage technologies and the current progress in the leg of spintronic is presented. This will highlight a perspective of this thesis work with respect to the present day research in spintronic and magnetization reversal studies. In chapter 2, a basic background of magnetism using the micromag-netic framework is illustrated. A brief introduction to magnetic domain walls is also presented. The Landau-Lifshitz-Gilbert dynamical equation is discussed and some case studies applied to a single domain particle with uniaxial anisotropy under the effect of spin-orbit torque are illu trated. The basics of spin-orbit coupling leading to spin Hall e ect is also explain In chapter 3, most of the essential experimental tools along with their basic working principles are described. Extensive e orts have been in-vested in designing and building the experimental tools. These include custom designs of a sputter deposition system, an ultra-high vacuum chamber for pulsed laser ablation, a magneto-optic Kerr e ect magne-tometer, a Kerr imaging system and a magneto-transport setup. All of these experimental setups have been automated, details of which are brie y discussed in this chapter. The Kerr imaging system was designed to measure hysteresis loops, observe domain wall motion and to measure domain wall velocity under applied magnetic elds and electric current. The magneto-transport setup was used for studying the domain wall pinning and depinning experiments in permalloy nanowires. In chapter 4, the optimization process for obtaining perpendicular mag-netic anisotropy in Pt/Co/Pt lms is described. The spin reorientation transition with varying thickness of Co (from 1.5 nm down to 0.35 nm) was studied. The magnetization easy axis direction changes from in-plane to out-of-plane as the thickness of Co is reduced. The dependence of Curie temperatures of ultrathin Co lms, with thickness as low as 0.35 nm, on the underlayer Pt thickness and its crystallinity was studied in detail. The e act of Ta but err layer on the texture of the Pt lm, and on the Curie temperature of the Pt/Co/Pt system was evaluated. To gain further insight of the role of the bottom Pt/Co and the top Co/Pt interfaces, ultrathin Cu lbs were inserted at the respective interfaces, and the anisotropy and magnetization reversal behaviour of these lbs were investigated. In chapter 5, studies on current-induced magnetization reversal in mi-corn sized wires of Pt/Co/Pt trilete is presented. The spin Hall e act assisted spin-orbit torque was used to reversibly switch the magnetization of these devices with and without the help of an external magnetic led. Since both the top and bottom layers are Pt, any contribution from Rashia e act towards spin-orbit torque could be ignored. By preparing devices with unequal top and bottom Pt thicknesses, a net spin-orbit torque could be applied to the magnetization of the Co layer. The thickness gradient/induced anisotropy in the Co layer was utilized to experimentally investigate current-induced deterministic switching. Sin-gel domain simulations with spin-orbit torque were also carried out to understand the mechanism of deterministic switching of magnetization in Pt/Co/Pt devices. This study is expected to have made sign cant contributions and to open up the possibilities of further investigation in the studies of spin-orbit torque in Pt/Co/Pt systems for solid state magnetic memory devices. In chapter 6, magnetic led-induced reversal in systems with in-plane magnetic anisotropy is presented. Here the e act of the width of a Nanos-trip on the anisotropy of a soft magnetic material like perm alloy was in-estimated. By introducing a nucleation pad to one end of the perm alloy nanowire, a single domain wall was generated at the junction with apple-cation of a proper magnetic led sequence. This domain wall could be in-jested into the nanowire by a magnetic led and pinned at a geometrical constriction inside the nanowire. The statistics of domain wall pinning and deepening processes indicated two di errant types of domain walls involved in the reversal process. With the assistance of micro magnetic simulations the domain walls were ident end as vortex walls of di errant chirality’s. Thus the interaction of domain walls with a Nano constriction and its dependence on the chirality of domain walls are understood. In chapter 7, a brief summary of the results obtained during the course of investigations is presented. An outlook presented at the end will help the readers of this thesis to understand the important research problems in this area and their potential future aspects.

Ce travail est une contribution ab initio à la caractérisation d'halogénures diatomiques de métaux de transition. Nous avons choisi de caractériser la structure électronique des chlorures de métaux de transition du groupe Vb (NbCl et TaCl) et du fluorure de nickel car une série de spectres les concernant ont été enregistrés mais aucune donnée théorique fiable n'était disponible dans la littérature.<p><p>Pour étudier ces molécules, nous avons appliqué une procédure de calcul à deux étapes qui permet de tenir compte des effets de corrélation électronique et des effets relativistes. Dans la première étape, nous avons réalisé des calculs CASSCF/ICMRCI+Q de grande taille qui tiennent compte de l'énergie de corrélation et introduisent des effets relativistes scalaires. Dans la deuxième étape, le couplage spin-orbite est traité par la "state interacting method" implémentée dans le logiciel MOLPRO. Nous avons développé des stratégies de calcul basées sur ces méthodes de calcul et adaptées aux différentes molécules ciblées. Ainsi, pour les molécules NbCl et TaCl, nous avons utilisé des pseudopotentiels relativistes scalaires et spin-orbite, tandis que pour la molécule NiF, nous avons réalisé des calculs tous électrons.<p><p>Nous avons d'abord testé la stratégie de calcul sur les cations Nb+ et Ta+. Ensuite, nous avons calculé pour la première fois les structures électroniques relativiste scalaire et spin-orbite des molécules NbCl (de 0 à 17000 cm-1) et TaCl (de 0 à 23000 cm-1). A l'aide de ces données théoriques, nous avons interprété les spectres expérimentaux en collaboration avec Bernath et al. Nous avons proposé plusieurs attributions de transitions électroniques en accord avec l'expérience mais nos résultats théoriques ne nous ont pas permis de les attribuer toutes. Néanmoins, nous avons mis en évidence une série d'autres transitions électroniques probables qui pourraient, à l'avenir, servir à l'interprétation de nouveaux spectres mieux résolus. <p><p>Outre son intérêt expérimental, cette étude a permis de comparer les structures électroniques des molécules isovalencielles VCl, NbCl et TaCl, mettant en évidence des différences importantes.<p>L'élaboration d'une nouvelle stratégie de calcul pour décrire les systèmes contenant l'atome de nickel représentait un véritable défi en raison de la complexité des effets de corrélation électronique. Notre stratégie de calcul a consisté à introduire ces effets en veillant à réduire au maximum la taille des calculs qui devenait considérable.<p>Nous l'avons testée sur l'atome Ni et appliquée ensuite au calcul des structures électroniques relativiste scalaire et spin-orbite de la molécule NiF entre 0 à 2500 cm-1. Nous avons obtenus des résultats qui corroborent l'expérience. <p> / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

Un des objectifs du Femtomagnetisme est de contrôler l’aimantation des matériaux avec des impulsions laser femtoseconde. Il a été démontré qu’une réponse magnéto-optique (MO) cohérente a lieu avant la thermalisation des populations de spins dans une configuration pompe-sonde MOKE. Elle résulte du couplage cohérent spin-photon dû à l’interaction spin-orbite. Une description simplifiée de cet effet a été faite en tenant compte d’un système à huit niveaux couplés au champ laser. La cohérence MO est définie par le temps de déphasage dépendent du champ T2MO. Dans ce travail, il est montré que la réponse MO cohérente d’un grenat dopé au bismuth peut être mesurée directement avec différentes configurations de mélange à quatre ondes MO. L’importance de connaître la phase spectrale de l’impulsion pour obtenir T2MO a été étudié. Avec des impulsions de 10fs dans le proche infra-rouge, une mesure de T2MO donne (2.8+/-1)fs, c. à d., du même ordre de grandeur que le temps de déphasage des charges. / One of the goals of Femtomagnetism is to manipulate the magnetization of materials using femtosecond optical pulses. It has been shown in ferromagnetic films that a magneto-optical (MO) coherent response takes place before the thermalization of the spins populations in a pump and probe MOKE experiment. It results from the coherent spin-photon coupling mediated by the spin-orbit interaction. A simplified description of this effect has been made by considering an eight-level system coupled with the laser field. The MO coherence can be defined by the magnetic field dependent dephasing time T2MO. In the present work, it is shown that the coherent MO response of a bismuth-doped garnet can be directly measured in different degenerated MO four-wave mixing configurations. The importance of well-knowing the spectral phase of the pulse to measure T2MO was studied. Using 10fs near infra-red pulses, T2MO was shown to be (2.8+/-1)fs that is of the same order of the charges dephasing time.

The chemistry of actinides in solution is a very important aspect of the nuclear fuel cycle, especially as the energy needs of the world continue to increase. However, the radio-active nature of the actinides makes experimentation very difficult and dedicated expensive instruments are required. In addition, the disposal of radio-active waste materials requires a proper understanding of their chemistry at a molecular level. To tackle the problem, and to underpin the experimental studies, in this thesis we have studied the redox chemistry and disproportionation mechanism of actinyl complexes in solution using state-of-the art computational methods. Reduction potentials of actinyl complexes in solution have been estimated in solution using density functional theory (DFT) approaches. Solvation effects were included in the quantum chemistry calculations with the conductor like polarisable continuum model (CPCM) solvation method. First of all, we have validated our computational method by studying a variety of solute cavity definitions within the CPCM solvation model and assessed the performance of a range of DFT functionals to suitable to accurately describe the actinide chemistry in solution. Penta-valent uranyl(V) ions are unstable and readily disproportionate; in this study we have explored outer-sphere electron transfer and disproportionation mechanisms to determine the stability of these ions in solution. We have found that the process of outer-sphere disproportionation is unlikely to occur in non-aqueous solutions, such as DMSO, DMF, DCM, acetonitrile and pyridine, when the uranyl(V) ion is bound with a multi-dentate organic ligand. However, our computational results hypothesise that the presence of a trace of water in the experimental conditions can promote a disproportionation reaction by protonating the uranyl(V) ‘yl’ oxygen atoms and then the electron transfer process would proceed through either inner or outer sphere mechanism. In addition, the effect of alkali metal cations on the outer-sphere disproportionation mechanisms was also studied. Overall it has been shown that DFT can be used to accurately predict the redox properties of actinyl complexes in solution and thus contributing for an effective and efficient design of nuclear material separations, proper as well as safer radioactive waste disposal.

In our pursuit of ever smaller transistors, with greater computational throughput, many questions arise about how material properties change with size, and how these properties may be modelled more accurately. Metallic nanocontacts, especially those for which magnetic properties are important, are of great interest due to their potential spintronic applications. Yet, serious challenges remain from the standpoint of theoretical and computational modelling, particularly with respect to the coupling of the spin and lattice degrees of freedom in ferromagnetic nanocontacts in emerging spintronic technologies. In this thesis, an extended method is developed, and applied for the first time, to model the interplay between magnetism and atomic structure in transition metal nanocontacts. The dynamic evolution of the model contacts emulates the experimental approaches used in scanning tunnelling microscopy and mechanically controllable break junctions, and is realised in this work by classical molecular dynamics and, for the first time, spin-lattice dynamics. The electronic structure of the model contacts is calculated via plane-wave and local-atomic orbital density functional theory, at the scalar- and vector-relativistic level of sophistication. The effects of scalar-relativistic and/or spin-orbit coupling on a number of emergent properties exhibited by transition metal nanocontacts, in experimental measurements of conductance, are elucidated by non-equilibrium Green’s Function quantum transport calculations. The impact of relativistic effects during contact formation in non-magnetic gold is quantified, and it is found that scalar-relativistic effects enhance the force of attraction between gold atoms much more than between between atoms which do not have significant relativistic effects, such as silver atoms. The role of non-collinear magnetism in the electronic transport of iron and nickel nanocontacts is clarified, and it is found that the most-likely conductance values reported for these metals, at first- and lastcontact, are determined by geometrical factors, such as the degree of covalent bonding in iron, and the preference of a certain crystallographic orientation in nickel. / Physics / Ph. D. (Physics)

Ce mémoire présente les résultats sur l’étude de la supraconductivité et de la réponse à des impuretés locales électrique et magnétiques des semi-métaux de Luttinger. Ces semi-métaux correspondent à des matériaux tri-dimensionnels dont la relation de dispersion électronique est caractérisée par des bandes quadratiques qui se touchent, en présence d’un fort couplage spin-orbite caractérisé par une pseudo-spin-3/2. Expérimentalement, certains semi-métaux de Luttinger supraconducteurs possèdent une température critique ne pouvant être expliquée par les théories conventionnelles (BCS) se référant principalement au mécanisme des phonons. Le volet supraconductivité de notre travail s’intéresse à la résolution numérique de l’équation d’Eliashberg, une théorie microscopique de la supraconductivité, avec interactions Coulombiennes écrantées comme mécanisme d’appariement des paires de Cooper. Nos résultats concernant la température critique montrent une dépendance linéaire avec la température de Fermi du matériau et nous constatons un accord entre température critique expérimentale et de notre modèle pour divers semi-métaux de Luttinger à base de bismuth, comme YPtBi, YPdBi, LuPtBi et LuPdBi. La réponse en densité de charge et spin à des impuretés locales électriques et magnétiques est aussi étudiée à température nulle analytiquement et à température non-nulle numériquement et est comparée aux résultats connus du gaz d’électron libre et des semi-métaux de Dirac. Contrairement à ces dernier, une réponse magnétique anisotropique est observée pour les semi-métaux de Luttinger et la susceptibilité magnétique de spin résultante se trouve être diamagnétique. Un Hamiltonien d’interaction entre deux impuretés magnétiques médié par le mécanisme RKKY, l’interaction entre des impuretés magnétiques obtenue par l’intermédiaire des électrons libres du matériau, est aussi présenté et discuté pour différents semi-métaux. Cette interaction par couplage RKKY pourrait être à l’origine de phases magnétiques exotiques, comme dans le cas du pyrochlore Pr2Ir2O7. Nous terminons en soulignant les explorations possibles concernant nos résultats, en ajoutant ou modifiant des termes brisant une symétrie dans l’Hamiltonien initial. / In this master thesis, I review my work on the superconductivity and on the inhomogeneities induced by impurities in Luttinger semimetals. Luttinger semimetals are characterized by a quadratic band-touching between electron and hole bands, at a time-reversal-invariant point of the Brillouin zone, and that describes effectively pseudo-spin 3/2 fermions. The superconductivity in some Luttinger semimetals can be peculiar due to the increase of the optical dielectric constant through interband excitations. For example, in YPtBi, the superconducting critical temperature is at odds with theoretical expectations from the BCS theory where Cooper pairs are induced by lattice vibrations, the phonons. We thus explore another mechanism of superconductivity, through the microscopic theory of Eliashberg that we solve numerically and where Cooper pairs are induced by the screened Coulomb interaction. In particular we compute the critical temperature and show that it scales linearly with the Fermi temperature of electrons, and compare our results to experimental observations. The multiple bands in Luttinger semimetals also affect the inhomogeneities in charge and in spin due to a charged or a magnetic impurity. We mainly study this phenomenon at zero temperature through analytical calculations and explore the influence of temperature numerically. We compare our results with inhomogeneities in a normal and in a Dirac electron gas. In particular, our results indicate that Luttinger semimetals tend to be diamagnetic on the contrary to normal and Dirac electron gases. We also derive the effective Hamiltonian of two magnetic impurities, where their mutual interaction is mediated by conduction electrons, also known as the RKKY mechanism. This interaction by RKKY coupling could be at the origin of exotic magnetic phases, as in the case of the pyrochlore Pr2Ir2O7. We finish by highlighting possible explorations of our results, by adding or modifying terms in the initial Hamiltonian.

Les signatures de l’existence des phonons sont omniprésentes dans les propriétés des matériaux. En première approximation, on peut scinder l'effet des phonons sur la structure électronique en deux contributions. D’une part, l'interaction électron-phonon capture la réponse électronique aux vibrations des noyaux du cristal, et d’autre, l'énergie libre de la population de phonons modifie le volume cristallin à l’équilibre. En plus d'être responsables de la dépendance en température de la structure électronique, ces deux mécanismes affectent les niveaux d'énergie à température nulle, à travers le mouvement du point zéro et l'énergie du point zéro. Cette thèse analyse l’apport de ces deux mécanismes à la renormalisation du point zéro (ZPR) de l'énergie de la bande interdite des semi-conducteurs. Une généralisation du modèle de Fröhlich prenant en compte l'anisotropie et les dégénérescences présentes dans les matériaux réels révèle que l'interaction non adiabatique entre les électrons et les noyaux domine le ZPR dans les matériaux polaires. La prise en compte de ce mécanisme dans l'évaluation de l'interaction électron-phonon est déterminante pour reproduire adéquatement les données expérimentales. L'approche développée par Grüneisen, qui néglige communément les effets du point zéro, reproduit la dilatation du point zéro du réseau (ZPLE) et sa contribution au ZPR obtenues avec la méthode standard basée sur la minimisation de l'énergie libre à moindre coût numérique, y compris pour les matériaux anisotropes. La contribution du ZPLE au ZPR total, qui a reçu peu d'attention dans la littérature, peut atteindre de 20% à plus de 80% de la contribution de l'interaction électron-phonon, y compris dans des matériaux constitués de noyaux légers. Elle domine même le ZPR du GaAs dans le contexte de la DFT semi-locale. Il est donc essentiel de traiter les deux contributions sur le même pied d'égalité pour modéliser le ZPR avec précision. L'inclusion du couplage spin-orbite (SOC) diminue le ZPR d'un ensemble substantiel de matériaux cubiques de structure zinc-blende, diamant et rock-salt. L'essentiel de cette variation tire son origine de l'effet du SOC sur les énergies électroniques statiques, qui provient en grande partie de la variation des masses effectives des bandes de valence au point \(\Gamma\). La réduction du ZPR peut être estimée à partir d'un modèle de Fröhlich généralisé auquel on a introduit le SOC. Les subtilités numériques liées au traitement de la séparation de Dresselhaus dans les matériaux non centrosymétriques sont discutées. On démontre enfin comment l'effet combiné de l'interaction électron-phonon et de la dilatation thermique affecte le diagramme de phase topologique du BiTeI. L'augmentation de la température repousse l'apparition de la phase d'isolant topologique \(\mathbb{Z}_2\) vers des pressions plus élevées et élargit la plage de pressions correspondant à la phase intermédiaire de type semi-métal de Weyl. Le caractère orbital dominant des extrema de bande influence significativement leur sensibilité à la pression et au changement de topologie. Pour guider la recherche expérimentale de phases topologiquement non triviales dans les matériaux de façon adéquate, les études numériques doivent donc considérer l'effet de la température. / Phonon signatures are ubiquitous in material properties. At first order, the effect of phonons on the electronic structure can be split into two contributions. On the one hand, the electron-phonon interaction captures the electronic response to the vibrations of the nuclei. On the other hand, the free energy of the phonon population modifies the crystalline volume at equilibrium. In addition to driving the temperature dependence of the electronic structure, these two mechanisms affect the energy levels at zero temperature through zero-point motion and zero-point energy. This thesis investigates the contribution of these two mechanisms to the zero point renormalization (ZPR) of the band gap energy of semiconductors. A generalized Fröhlich model taking into account the anisotropy and degeneracies occurring in real materials reveals that the non-adiabatic interaction between electrons and nuclei dominates the ZPR in polar materials. Taking this mechanism into account when evaluating the electron-phonon interaction is crucial to reproduce experimental data adequately. The Grüneisen formalism, which commonly neglects zero-point effects, reproduces the zero-point lattice expansion (ZPLE) and its contribution to the ZPR obtained from the standard method based on free energy minimization at lower numerical cost, including for anisotropic materials. The ZPLE contribution to the total ZPR, which has received little attention in the literature, can reach from 20% to more than 80% of the contribution of the electron-phonon interaction, including in materials containing light atoms. It even dominates the ZPR of GaAs within semilocal DFT. Therefore, both contributions should be treated on an equal footing to model the ZPR accurately. The inclusion of spin-orbit coupling (SOC) decreases the ZPR of a substantial set of cubic materials of zincblende, diamond and rocksalt structure. This variation originates mostly from the effect of SOC on the static electronic eigenvalues, which comes largely from the variation of the effective masses of the valence bands at the \(\Gamma\) point. The reduction of the ZPR can be estimated from a generalized Fröhlich model in which SOC has been introduced. Numerical subtleties related to the treatment of Dresselhaus separation in non-centrosymmetric materials are discussed. We finally show how the combination of electron-phonon interaction and thermal expansion affects the topological phase diagram of BiTeI. An increase in temperature pushes the \(\mathbb{Z}_2\) topological insulator phase towards higher pressures and widens the pressure range corresponding to the Weyl semi-metal intermediate phase. The leading orbital character of the band extrema significantly influences their sensitivity to variations in pressure and topology. To adequately guide the experimental search for topologically non-trivial phases in materials, numerical studies must therefore consider the effect of temperature.

Cold-atom quantum simulators offer unique possibilities to prepare, manipulate, and probe quantum many-body systems. However, despite the high level of control in modern experiments, not all observables of interest are easily accessible. This thesis aims at establishing protocols to measure currently elusive static and dynamic properties of quantum systems. The experimental feasibility of these schemes is illustrated by means of numerical simulations for relevant applications in many-body physics and quantum simulation. In particular, we introduce a general method for measuring dynamical correlations based on non-Hermitian linear response. This enables unbiased tests of the famous fluctuation-dissipation relation as a probe of thermalization in isolated quantum systems. Furthermore, we develop ancilla-based techniques for the measurement of currents and current correlations, permitting the characterization of strongly correlated quantum matter. Another application is geared towards revealing signatures of supersolidity in spin-orbit-coupled Bose gases by exciting the relevant Goldstone modes. Finally, we explore a scenario for quantum-simulating post-inflationary reheating dynamics by parametrically driving a Bose gas into the regime of universal far-from-equilibrium dynamics. The presented protocols also apply to other analog quantum simulation platforms and thus open up promising applications in the field of quantum science and technology. / I simulatori quantistici ad atomi freddi offrono possibilità uniche per preparare, manipolare e sondare sistemi quantistici a molti corpi. Tuttavia, nonostante l'alto livello di controllo raggiunto negli esperimenti moderni, non tutte le osservabili di interesse sono facilmente accessibili. Lo scopo di questa tesi è quello di stabilire protocolli per misurare delle proprietà statiche e dinamiche dei sistemi quantistici attualmente inaccessibili. La fattibilità sperimentale di questi schemi è illustrata mediante simulazioni numeriche per applicazioni rilevanti nella fisica a molti corpi e nella simulazione quantistica. In particolare, introduciamo un metodo generale per misurare le correlazioni dinamiche basato su una risposta lineare non hermitiana. Ciò consente test imparziali della famosa relazione fluttuazione-dissipazione come sonda di termalizzazione in sistemi quantistici isolati. Inoltre, sviluppiamo tecniche basate su ancilla per la misura di correnti e correlazioni di corrente, consentendo la caratterizzazione della materia quantistica fortemente correlata. Un'altra applicazione è orientata a rivelare l'impronta della supersolidità nei gas Bose con accoppiamento spin-orbita eccitando il corrispondente modo di Goldstone. Infine, esploriamo uno scenario per la simulazione quantistica della dinamica di riscaldamento post-inflazione modulando parametricamente un gas Bose e portandolo nel regime della dinamica universale lontana dall'equilibrio. I protocolli presentati si applicano anche ad altre piattaforme di simulazione quantistica analogica e aprono quindi applicazioni promettenti nel campo della scienza e della tecnologia quantistica. / Quantensimulatoren auf Basis ultrakalter Atome eröffnen einzigartige Möglichkeiten zur Präparation, Manipulation und Untersuchung von Quanten-Vielteilchen-Systemen. Trotz des hohen Maßes an Kontrolle in modernen Experimenten sind jedoch nicht alle interessanten Observablen auf einfache Weise zugänglich. Ziel dieser Arbeit ist es, Protokolle zur Messung aktuell nur schwer erfassbarer statischer und dynamischer Eigenschaften von Quantensystemen zu etablieren. Die experimentelle Realisierbarkeit dieser Verfahren wird durch numerische Simulationen anhand relevanter Anwendungen in der Vielteilchenphysik und Quantensimulation veranschaulicht. Insbesondere wird eine allgemeine Methode zur Messung dynamischer Korrelationen basierend auf der linearen Antwort auf nicht-hermitesche Störungen vorgestellt. Diese ermöglicht unabhängige Tests des berühmten Fluktuations-Dissipations-Theorems als Indikator der Thermalisierung isolierter Quantensysteme. Darüber hinaus werden Verfahren zur Messung von Strömen und Strom-Korrelationen mittels Kopplung an einen Hilfszustand entwickelt, welche die Charakterisierung stark korrelierter Quantenmaterie erlauben. Eine weitere Anwendung zielt auf die Enthüllung spezifischer Merkmale von Supersolidität in Spin-Bahn-gekoppelten Bose-Einstein-Kondensaten ab, indem die relevanten Goldstone-Moden angeregt werden. Schließlich wird ein Szenario zur Quantensimulation post-inflationärer Thermalisierungsdynamik durch die parametrische Anregung eines Bose-Gases in das Regime universeller Dynamik fern des Gleichgewichts erschlossen. Die dargestellten Protokolle lassen sich auch auf andere Plattformen für analoge Quantensimulation übertragen und eröffnen damit vielversprechende Anwendungen auf dem Gebiet der Quantentechnologie.