Cette thèse porte principalement sur l'étude de modèles de fermions en interactions contenant un couplage spin-orbite. Ces modèles (i) peuvent décrire une classe de matériaux composés d'iridates sur le réseau en nid d'abeille ou (ii) pourraient être réalisés artificiellement dans des systèmes d’atomes froids. Nous avons étudié, dans un premier temps, le système à demi-remplissage avec l'interaction de Hubbard et un couplage spin-orbite anisotrope. Nous avons trouvé plusieurs phases: la phase isolant topologique pour de faibles corrélations, et deux phases avec des ordres magnétiques frustrés, l'ordre de Néel et l'ordre spiral, dans la limite de très fortes corrélations. La transition entre les régimes de faibles et de fortes corrélations est une transition de Mott dans laquelle les excitations électroniques se fractionnent en excitations de charge et de spin. Les charges sont localisées par l'interaction. Le secteur de spin présente de fortes fluctuations qui sont modélisées par un gaz d’instantons. Nous avons ensuite exploré la physique d'un système régi au demi-remplissage par le modèle de Kitaev-Heisenberg, qui présente une phase magnétique de type zig-zag. En dopant le système, autour du quart remplissage, la structure de bande présente de nouveaux centres de symétrie en plus de la symétrie d'inversion. Le couplage de spin de Kitaev-Heisenberg favorise alors la formation de paires de Cooper dans un état triplet autour de ces centres de symétrie. La condensation de ces paires de Cooper autour de ces vecteurs d'onde non triviaux se manifeste par une modulation spatiale du paramètre d'ordre supraconducteur, comme dans la supraconductivité de Fulde–Ferrell–Larkin–Ovchinnikov (FFLO). La dernière partie de la thèse propose et étudie une implémentation des phases topologiques dite de Haldane et de Kane-Mele dans un système avec deux espèces de fermions sur le réseau en nid d'abeille, stabilisée grâce à l’interaction RKKY médiée par l’espèce rapide et qui agit sur l’espèce lente. / This thesis is dedicated largely to the study of theoretical models describing interacting fermions with a spin-orbit coupling. These models (i) can describe a class of 2D iridate materials on the honeycomb lattice or (ii) could be realized artificially in ultra-cold gases in optical lattices. We have studied, in the first part, the half-filled honeycomb lattice model with on-site Hubbard interaction and anisotropic spin-orbit coupling. We find several different phases: the topological insulator phase at weak coupling, and two frustrated magnetic phases, the Néel order and spiral order, in the limit of strong correlations. The transition between the weak and strong correlation regimes is a Mott transition, through which electrons are fractionalized into spins and charges. Charges are localized by the interactions. The spin sector exhibits strong fluctuations which are modeled by an instanton gas. Then, we have explored a system described by the Kitaev-Heisenberg spin Hamiltonian at half-filling, which exhibits a zig-zag magnetic order. While doping the system around the quarter filling, the band structure presents novel symmetry centers apart from the inversion symmetry point. The Kitaev-Heisenberg coupling favors the formation of triplet Cooper pairs around these new symmetry centers. The condensation of these pairs around these non-trivial wave vectors is manifested by the spatial modulation of the superconducting order parameter, by analogy to the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) superconductivity. The last part of the thesis is dedicated to an implementation of the Haldane and Kane-Mele topological phases in a system composed of two fermionic species on the honeycomb lattice. The driving mechanism is the RKKY interaction induced by the fast fermion species on the slower one.

Dans cette thèse, on étudie la criticalité quantique ferromagnétique dans trois composés ternaires à base d'uranium, par des mesures thermodynamiques et de transport sur des échantillons monocristallins, à basse température et sous haute pression. URhSi et URhAl sont des systèmes ferromagnétiques itinérants, tandis que UCoAl est un système paramagnétique étant proche d'une instabilité ferromagnétique. Tous ont une phase ordonnée de type Ising. Dans le composé orthorhombique URhSi, on montre que la température de Curie diminue lorsqu'un champ magnétique est appliqué perpendiculairement à l'axe facile d'aimantation, et une transition de phase quantique est attendue autour de 40~T. Dans le système hexagonal URhAl, on établit le diagramme de phase pression--température pour la première fois, lequel indique une transition de phase quantique vers 5~GPa. Dans le composé isostructural UCoAl, on étudie la transition métamagnétique par des mesures d'aimantation, d'effet Hall, de résistivité et de dichroïsme circulaire magnétique des rayons X. On observe des phénomènes de relaxation magnétique intrigants, avec des sortes de marches. L'effet Hall et la résistivité ont été mesurés à des températures de réfrigérateur à dilution, sous pression hydrostatique jusqu'à 2,2~GPa, et sous champ magnétique jusqu'à 16~T. La transition métamagnétique se termine sous pression et champ magnétique au niveau d'un point critique quantique terminal. Dans cette région, il se produit une forte augmentation de la masse effective, et une différence intrigante entre champ montant et descendant apparaît dans la résistivité transverse. Ce pourrait être la signature d'une nouvelle phase, éventuellement reliée aux phénomènes de relaxation observés dans les mesures d'aimantation, et résultant de frustrations au sein du réseau quasi-Kagomé que forment les atomes d'uranium dans cette structure cristalline. / In this thesis we explore the ferromagnetic quantum criticality in three uranium-based ternary compounds, by means of thermodynamical and transport measurements on single crystal samples, at low temperature and high pressure. URhSi and URhAl are itinerant ferromagnets, while UCoAl is a paramagnet being close to a ferromagnetic instability. All of them have Ising-type magnetic ordering. In the orthorhombic compound URhSi, we show that the Curie temperature decreases upon applying a magnetic field perpendicular to the easy magnetization axis, and a quantum phase transition is expected around 40~T. In the hexagonal system URhAl, we establish the pressure--temperature phase diagram for the first time, indicating a quantum phase transition around 5~GPa. In the isostructural compound UCoAl, we investigate the metamagnetic transition with measurements of magnetization, Hall effect, resistivity and X-ray magnetic circular dichroism. Some intriguing magnetic relaxation phenomena are observed, with step-like features. Hall effect and resistivity have been measured at dilution temperatures, under hydrostatic pressure up to 2.2 GPa and magnetic field up to 16~T. The metamagnetic transition terminates under pressure and magnetic field at a quantum critical endpoint. In this region, a strong effective mass enhancement occurs, and an intriguing difference between up and down field sweeps appears in transverse resistivity. This may be the signature of a new phase, supposedly linked to the relaxation phenomena observed in magnetic measurements, arising from frustration on the quasi-Kagome lattice of uranium atoms in this crystal structure.

La supraconductivité dans la famille des composés de type fermions lourds tel le CeCoIn5 se développe à proximité d’une instabilité antiferromagnétique. La proximité de cette instabi- lité indique un point quantique critique (anglais pour ”quantum critical point” QCP) entre la phase antiferromagnétique et un liquide de Fermi. À ce point, les deux états fondamentaux du système sont en compétition et peuvent être perturbés par une variation de la pression ou de la composition chimique. Dans cette proposition, nous étudions la réciprocité entre les deux méthodes de perturbation du point quantique critique. Pour ce faire, on change la composition chimique du CeCoIn5 en dopant le cristal avec des atomes d’ytterbium qui prennent la place du cérium dans la structure. La substitution de certains atomes de cérium par de l’ytterbium est équivalent électroniquement à enlever un électron de la couche 4f car l’ytterbium est bivalent dans la structure CeCoIn5 . Ainsi, on détruit des moments magné- tiques dans le réseau fortement corrélé de centres de Kondo et pousse le matériau vers la phase antiferromagnétique. Dans la même optique, on utilise un accélérateur de particules pour implanter des atomes d’hélium dans la maille du cristal. Les atomes d’hélium agissent comme une source de pression négative qui dilatent le réseau et réduisent la cohérence entre certaines quasi-particules de Kondo. On propose alors que cette implantation pourrait induire l’ordre antiferromagnétique puisqu’elle favorise l’interaction magnétique longue portée. Dans un premier ordre, on a dopé les échantillons de CeCoIn5 dopé à l'Yb avec une concentration de 5%, 10% et 15%. Tel qu’attendu, suite aux mesures de la chaleur spécifique en fonction de la température, on s’aperçoit que la valeur de la température de transition de phase supraconductrice diminue lorsqu’on augmente le dopage dans le monocristal. On montre ainsi la dépendance entre la concentration de dopant dans le cristal et la destruction inhomogène de l’état corrélé. Lorsqu’on remplace des électrons de l’orbitale 4f par des trous de cette bande, on détruit la cohérence entre les centres de Kondo qui induit la supraconductivité. Cette variation chimique peut être utilisée comme un paramètre de réglage qui favorise le régime de l’interaction magnétique près du QCP. Similairement, suite à une implantation d’atomes d’hélium de 0.1%, 0.5% et 1% des mailles dans les premiers 15 micromètre de CeCoIn5 , on constate que la dilatation du réseau réduit linéairement l’intéraction globale du régime fortement corrélé entre les singulets de Kondo. Cependant, la cohérence entre les centres de Kondo est plus difficile à obtenir, ce qui diminue la température critique (Tc) de la transition de phase supraconductrice. On associe cette diminution de Tc proche d’un QCP à la suppression inhomogène du régime liquide de Fermi. Alors, l’application d’une pression négative par implantation d’hélium est considérée comme un paramètre de réglage qui avantage l’interaction magnétique longue portée et conduit le cristal vers l’ordre AFM. / Superconductivity in the family of heavy fermion compounds such as CeCoIn5 develops near an antiferromagnetic instability. The proximity of this instability indicates a quantum critical point (QCP) between the antiferromagnetic phase and a Fermi liquid ground state. At such a point, the two ground states of the system are in competition and applying pressure or changeing the chemical composition moves the system away from the QCP. In this work, we study the reciprocity between the two methods of perturbation of the QCP. In this sense, the chemical composition of the CeCoIn5 is changed by doping the system with ytterbium atoms, which replace the cerium. The substitution of cerium which is trivalent and carries a magnetic moment atoms by the bivalent ytterbium is electronically and non-magnetic electron of the shell 4f by a hole of the same orbital and removing a magnetic moment. Thus, we destroy magnetic moments causing the Kondo coherence and push the material towards the antiferromagnetic phase. In the same vein, an accelerator is used to implant helium atoms in the lattice of the crystal. Helium atoms act as a source of negative pressure which expands the lattice and which destroys the coherence between certain Kondo singlets. It is then proposed that this implantation should eventually induce antiferromagnetic order since this is favoring the long-range magnetic interaction. First, Ce1−xYbxCoIn5 samples were doped with an Yb concentration of x = 5%, 10% and 15%. As expected, following the measurements of the specific heat as a function of temperature, it is found that the value of the temperature of the superconducting phase transition (Tc) decreases when the level of doping increases in the single crystal. Thus, we conclude that the more electrons in the 4f orbital are replaced by holes of this band, the more we destroy the coherence between the Kondo center which induces superconductivity We also show that this inhomogeneous destruction of the correlated state is linear with the concentration of induced holes in the crystal. we conclude that the more electrons in the 4f orbital are replaced by holes of this band, the more we destroy the coherence between the Kondo center which induces superconductivity. In this sense, this chemical variation used as a tunning parameter favors the magnetic state near the QCP. Similarly, following a helium atom implantation of 0.1%, 0.5% and 1% of the lattices in the first 15 μm of CeCoIn5 , we find that lattice expansion linearly decreases the correlation between Kondo singlets. Thus, the coherence between Kondo centers is more difficult to achieve, which decreases the critical temperature (Tc) towards the superconducting phase transition. This linear decrease of Tc close to a QCP is associated to the suppression of the Fermi liquid regime and thus is expected to lea the crystal to the AFM order. Then, the application of a negative pressure by helium implantation can be considered as a tunning parameter which benefits the long-range magnetic interaction

Orientador: Nathan J. Berkovits / Banca: Victor de Oliveira Rivelles / Banca: Chris Hull / Banca: Abraham Hirsz Zimerman / Banca: José Abdalla Helaÿel-Neto / Resumo: Nesta tese, mostramos a equivalência dos formalismos de Green-Schwarz e de espinores puros para a supercorda. Partindo da ação de Green-Schwarz no semi-gauge de cone de luz e adicionando graus de liberdade fermiônicos, relacionamos os operadores BRST do formalismo de espinores puros e de Green-Schwarz no semi-gauge de cone de luz através de transformações de similaridade, indicando a equivalência das respectivas cohomologias. Esta prova de equivalência é uma generalização do procedimento usado para relacionar a superpartícula de Brink-Schwarz e a superpartícula do formalismo de espinores puros. / Abstracts: In this thesis, we have shown the equivalence of the Green-Schwarz and pure spinor formalisms for the superstring. Starting from the Green-Schwarz action in the semi-light-cone gauge additional fermionic degrees of freedom, we have related the BRST operator of pure spinor formalism to the semi-light-cone Green-Schwarz operator through similarity transformations, indicating the equivalence of the cohomologies. This equivalence proof is a generalization of the procedure used to related the Brink-Schwarz and pure spinor's superparticle. / Doutor

Orientador: Marcelo Batista Hott / Banca: Álvaro de Souza Dutra / Banca: Julio Marny Hoff da Silva / Banca: Adalto Rodrigues Gomes dos Santos Filho / Banca: Carlos Alberto Santos de Almeida / Resumo: Nesta tese analisamos a localização de campo de matéria em bramas duplas. Estudamos a localização de férmions não-massivos em paredes de domnio (3-brana) imersa no espaço de 4+1 dimensões em cenários Randall-Sundrum (espaço warped), e Rubakov-Shaposhnikov (espaço plano), respectivamente. Abordamos a localização do campo fermiônico, acoplando os férmions com uma função de campo escalar, cuja solução tipo kink simples é deformada a uma solução tipo kink duplo. No contexto de nosso estudo, este tipo de configuração kink duplo permite ilustrar o fenômeno da separação das branas. Construímos novos modelos não-lineares em teoria de campos que forneçam configurações do tipo kink duplo. Estes modelos são construídos a partir da deformação do modo-zero associado 'a equação de estabilidade de outros modelos bem estabelecidos. Por sua vez, estes modelos são aplicáveis na descrição de fenômenos críticos e em cenários de mundos-brana. Além disso, temos conhecimento de que não 'e possível a localiza¸c˜ao de campo de gauge por meio unicamente da curvatura (warped). Propomos um mecanismo que leve à localização do modo-zero do campo de gauge abeliano em branas espessas por meio de uma função suave e contínua que torna a ação normalizável. Esta função suave funcionaria como uma função dielétrica. Neste mesmo contexto, aplicamos este mecanismo para a localização do modo-zero do campo de Kalb-Ramond em branas espessas / Abstract: In this thesis we analyze the localization of matter field in double branes. We study the localization of massless fermions in domain wall (3-branes) immerse in a space 4+1 dimensions in Randall-Sundrum (warped space), and Rubakov-Shaposhnikov (flat space) scenarios, respectively. We approach the fermions localization, coupling the fermions to a scalar field functional, whose kink-like solutions are deformed to double kink solutions. In the context of our study, this double kink (two-kink) allows to illustrate the brane splitting phenomenon. We construct new non-linear models in field theory which provides double kink configurations. These models are constructed from the deformation of the zero mode associated to the stability equations of well-established models. In turn, these models are applicable in the description of critical phenomena and brane-worlds scenarios. Moreover, we know that it is not possible to achieve gauge fields localization on brane by means of only the warped curvature. We propose a mechanism that leads to the localization of zero mode of Abelian gauge field in thick branes by means of a smooth and continuous function which turns out the action normalizable. This smooth function would work as a dielectric function. In this same context we apply this mechanism for the localization of zero mode of Kalb-Ramond field in thick branes / Doutor

Orientador: Júlio Marny Hoff da Silva / Banca: Álvaro de Souza Dutra / Banca: José Abdalla Helayël Neto / Resumo : O século passado é considerado como a era das Teorias Quânticas de Campos. Desta forma, neste trabalho, forneceremos todos os detalhes de uma descoberta teórica inesperada de uma partícula de matéria de spin 1/2 com dimensão de massa 1. Esses espinores recebem o nome de ELKO, o qual vem do acrônimo alemão Eigenspinores des Ladungskonjugationsoperators, e são fundamentados em um conjunto completo de autoespinores de helicidade dual do operador conjugação de carga. O ELKO pertence a um subgrupo do grupo completo de Lorentz. Portanto, a lei de transformação entre suas componentes não é dada pela simetria de paridade, e desta maneira não satisfaz a equação de Dirac. Intrinsicamente nas somas de spin para o ELKO aparece um termo que quebra a simetria de Lorentz, levando então à apreciação da Very Special Relativity, que nada mais é do que um subgrupo do grupo de Lorentz, cuja álgebra deixa as somas de spin invariantes ou covariantes. Pela razão do propagador do ELKO ser o mesmo de Klein-Gordon a menos de um fator, a lagrangiana associada é a do campo escalar, por esta razão o ELKO é dotado de dimensão de massa 1 / Abstract: The last century is considered as the era of Quantum Field Theories. Thus, in this work, we provide all the details of an unexpected theoretical discovery of a matter particle spin 1/2 endowed with mass dimension 1. These spinors are the so called ELKO, which comes from the German acronym Eigenspinores des Ladungskonjugationsoperators, based on a complete set of a dual helicity eigenspinors of the charge conjugation operator. ELKO belongs to a subgroup of the full Lorentz group. Therefore, the law of transformation between its components is not given by the parity symmetry, and thus it does not satisfies the Dirac equation. It appears, intrinsically in the spin sums a Lorentz symmetry breaking term, then it will be better analysed within the Very Special Relativity, which is a subgroup of the Lorentz group, whose algebra leaves the spin sums invariant or covariant under transformations. Since the ELKO propagator is the same of Klein-Gordon propagator apart from a term, than the associated lagrangian is the scalar field one, for this reason ELKO is endowed with mass dimension 1 / Mestre

Orientador: Antonio Carlos Ferreira Seridonio / Banca: Ricardo Egydio de Carvalho / Banca: Rafael Zadorosny / Resumo: Nós investigamos teoricamente uma cadeia topológica de Kitaev conectada a dois pontos quânticos (QDs) hibridizados a terminais metálicos. Neste sistema, observamos o surgimento de dois fenômenos marcantes: (i) uma decriptografia do Férmion de Majorana (MF), que é detectado por meio de medições de condutância devido ao estado de vazamento assimétrico do qubit de MFs nos QDs; (ii) criptografia desse qubit em ambos os QDs quando o vazamento é simétrico. Em tal regime, temos portanto a criptografia proposta, uma vez que o qubit de MFs separa-se nos QDs como estados ligados no contínuo (BICs), os quais não são detectáveis em experimentos de condutância / Abstract: We theoretically investigate a topological Kitaev chain connected to a double quantum-dot (QD) setup hybridized with metallic leads. In this system, we observe the emergence of two striking phenomena: i) a decrypted Majorana Fermion (MF) - qubit recorded over a single QD, which is detectable by means of conductance measurements due to the asymmetrical MF-leaked state into the QDs; ii) an encrypted qubit recorded in both QDs when the leakage is symmetrical. In such a regime, we have a cryptography-like manifestation, since the MF-qubit becomes bound states in the continuum, which is not detectable in conductance experiments / Mestre

Orientador: Antonio Carlos Ferreira Seridonio / Banca: Valdeci Pereira Mariano de Souza / Banca: Claudio Luiz Carvalho / Resumo: Nós estudamos teoricamente como o calor e a eletricidade são afetados pela sobreposição de dois férmions de Majorana (MFs, de Majorana fermions em Inglês), os quais estão isolados nas bordas de um fio topológico de Kitaev, em particular, na forma de "ferradura". É considerado que esse fio está assimetricamente acoplado a um único ponto quântico (QD, de Quantum dot em Inglês) hibridizado com contatos metálicos. Em baixas temperaturas e dependente do nível de energia desse QD, nós mostramos que ao ajustar a assimetria acima, as respostas ressonantes das condutâncias termoelétricas mudam inesperadamente de forma drástica. Assim, propomos como aplicação, um sintonizador termoelétrico em nanoescala assistido por MFs / Abstract: We study theoretically in a topological U-shaped Kitaev wire, with Majorana fermions (MFs) on the edges, how heat and electricity are affected by them when found overlapped. The asymmetric regime of their couplings with a single quantum dot (QD) hybridized with metallic leads is considered. At low temperatures and dependent upon the QD energy level, we show that by tuning this asymmetry, the resonance positions of the thermoelectrical conductances change drastically. Thereby, the tuner of heat and electricity here proposed is constituted / Mestre

Second-order phase transitions involve critical fluctuations just below and above the transition temperature. Macroscopically, they manifest in the power-law behaviour of many physical properties such as the susceptibility and the specific heat. The power-laws are predicted to be universal, i.e. the same exponents are expected for a certain class of transitions irrespective of the microscopic details of the system. The underlying commonality of such transitions is the divergence of the correlation length ξ and the correlation time ξ_τ of the critical fluctuations at the transition temperature. Both ξ and ξ_τ can be directly observed by neutron scattering experiments, making them an ideal tool for the study of critical phenomena. At classical phase transitions, the critical fluctuations will be thermal in nature. However, if a second-order transition occurs at T = 0, thermal fluctuations are frozen, and the transition is driven by quantum fluctuations instead. This is called a quantum critical point. The quantum nature of the fluctuations influences observable properties, also at finite temperatures, and causes unusual behaviour in the vicinity of the quantum critical point or the existence of exotic phases, e.g. unconventional superconductivity. Heavy-fermion compounds are a class of materials that is well suited for the study of quantum criticality. They frequently show second-order transitions into a magnetically ordered state at very low temperatures, which can easily be tuned to T = 0 by the application of pressure, magnetic fields or element substitution. In this thesis, fluctuations near a quantum critical point are investigated for three heavy-fermion systems. CeCu2Si2 shows unconventional superconductivity close to an antiferromagnetic quantum critical point. Results from single-crystal neutron spectroscopy and thermodynamic measurements are discussed and some details are also given about the synthesis of large single crystals. The focus of the study is the comparison of the inelastic response of magnetic and superconducting samples, which are found to be very similar for ΔE > 0.2 meV. CePdAl has an antiferromagnetic state with partial magnetic frustration. The ordering temperature can be suppressed by Ni substitution towards a quantum critical point. Single-crystal neutron diffraction experiments of three members of the substitution series were analysed. They revealed several unusual effects of the frustrated state in the pure sample, and show that magnetic order and frustration persist in the substituted samples. YbNi4P2 is a rare example of a compound with ferromagnetic quantum criticality, which has only been studied in the last few years. The aim of the powder neutron spectroscopy experiments presented here was to obtain an overview of the relevant energy scales, i.e. the crystal electric field, local magnetic fluctuations and ferromagnetic fluctuations. Simulations using the program McPhase were performed for a thorough understanding of the crystal electric field.

On étudie la limite thermodynamique pour un système de particules quantiques en interaction dans un milieu aléatoire dans le formalisme de l'ensemble microcanonique. L'existence de la limite est démontrée pour l'énergie interne ainsi que pour l'entropie sous des conditions assez générales sur le modèle à une particule. Ensuite, la limite thermodynamique est étudiée pour le modèle des pièces à une dimension dans le cas des fermions et pour une densité de particules faible. On donne une caractérisation de l'état fondamental en terme d'espaces fonctionnels, on démontre sa non dégénérescence presque sûre et on décrit sa fonction d'autocorrélation. Ces résultats permettent d'obtenir une estimée de l'énergie fondamentale par particule comme fonction de la densité de particules dans la limite thermodynamique.