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<div>The quantum phase transitions and exotic excitations are exciting and important topics of nowadays condensed matter theory. Topologically protected excitations are of great interest for potential applications in quantum computing. This Thesis explores two examples of exotic topologically protected excitations, Majorana fermions and parafermions in hybrid superconductor/semiconductor systems.</div><div><br></div><div>In the first part of the thesis, after a brief review of ideas on Majorana zero modes in solid state systems obtained by researchers over the past decade, I present our study of the emergence of Majorana fermions in charge carrier holes doped quantum wires. Study of Majorana modes in this system requires understanding Luttinger holes in low dimensions, which is also crucial for numerous spin-dependent phenomena, emerging field of spintronics and nanotechnology. We find that hole-doped quantum wires that are proximity coupled to a conventional s-wave superconductor is a promising system for the observation of Majorana fermions. We advanced understanding of Luttinger holes in quantum wells and quantum wires. We have shown that the vast majority of earlier treatments of Luttinger holes ignored an important effect, a mutual transformation of heavy and light holes at the heteroboundaries. We have derived the effective hole Hamiltonians in the ground size-quantized sub-bands of quantum wells and quantum wires. The effect of mutual transformation of holes is crucial for understanding Zeeman and spin-orbit coupling, and results in several spin-orbit terms linear in momentum in hole-doped quantum wires. We discuss the criterion for realizing Majorana modes in charge carrier hole systems and show that GaAs or InSb hole wires shall exhibit stronger topological superconducting pairing, providing additional opportunities for its control compared to intensively studies InSb and InAs electron systems.</div><div><br></div><div>In the second part of the thesis, I first introduce the basic facts of the current theoretical understanding of the fractional quantum Hall effect and a theoretical model of parafermion excitations. Parafermion zero modes are promising for universal quantum computing. However, physical systems that are predicted to host these exotic excitations are rare and difficult to realize in experiments. I present our work on modeling domain walls on the boundary between gate-induced polarized and unpolarized domains of the fractional quantum Hall effect system near the spin transitions, and the emergence of the parafermion zero modes when such domain wall is proximity coupled to an s-wave superconductor. Exact diagonalization of the Hamiltonian in a disk and torus geometries proves formation of the counter-propagating edge states with different spin polarizations at the boundaries between areas of the electron liquid in polarized and unpolarized filling factor $\nu=2/3$ phases. By analytical and numerical methods we find the conditions for emergence of parafermion zero modes in hybrid fractional quantum Hall/s-wave superconductor system. The phase diagram indicates that the parafermionic phase, which is represented by the six-fold ground state degeneracy, is separated from other phases by a topological phase transition. Such parafermion modes are experimentally feasible. They present a vital step toward the realization of Fibonacci anyons that allow a full universal set of quantum operations with topologically protected quasiparticles.</div><div><br></div>

Orientador: Pascoal José Giglio Pagliuso / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin / Made available in DSpace on 2018-09-24T15:46:53Z (GMT). No. of bitstreams: 1 Adriano_Cris_D.pdf: 6784336 bytes, checksum: d7c200af40255398764228130bc8b93d (MD5) Previous issue date: 2009 / Resumo: Este trabalho apresenta estudos sistemáticos das propriedades magnéticas dos compostos Ce2MIn8 (M = Rh, Ir) dopados com Cd, Sn e Ga no sítio cristalográfico do In. Foram utilizadas as técnicas de medidas macroscópicas de susceptibilidade magnética, calor específico e resistividade elétrica, além de medidas de caracterização estrutural pelo método de difração de pó de raios-x e medidas microscópicas da determinação da estrutura magnética usando a técnica de espalhamento magnético de raios-x e nêutrons para os compostos dopados com Cd. Os compostos Ce2MIn8 (chamados de 218) são tetragonais (grupo espacial P4/mmm) e são a versão bi-camada da família de férmions pesados supercondutores Cem MnIn3m+2n(M = Co, Rh, Ir; m = 1,2; n = 0,1), na qual os compostos do tipo CeMIn5 (chamados de 115) foram muito estudados por apresentarem uma variedade de propriedades físicas interessantes, tais como efeito Kondo, supercondutividade não convencional, ordenamento magnético, comportamento non-Fermi-Liquid, e ocorrência de pontos críticos quânticos. Mais interessante ainda é o fato de que estas propriedades podem ser controladas por dopagem, pressão externa e/ou campo magnético gerando diagramas de fases bastante interessantes. O objetivo de se estudar os parentes Ce2MIn8 é entender o papel da dimensionalidade nas propriedades físicas destes compostos e comparar os resultados encontrados com aqueles observados para os 115. Foram construídos os diagramas de fase inéditos para as séries de Ce2RhIn8-xCdx, Ce2IrIn8-xCdx, C e2Rh0.5Ir0.5In8-xC dx, Ce2RhIn8-xSnx e Ce2RhIn8-xGax a partir de dados obtidos utilizando as técnicas mencionadas acima. Foi visto que a dopagem de Cd nos compostos Ce2MIn8 favorece o AFM através do aumento da TN em função da concentração de Cd. Os resultados sugerem que o Cd está agindo de modo a diminuir a densidade de carga local e isso está favorecendo o ordenamento magnético. Porém, resultados da variação da temperatura do máximo da resistividade elétrica em função da concentração de Cd, sugerem que efeitos de campo cristalino também estão presentes nestes compostos. A estrutura magnética dos compostos de Ce2RhIn8-xCdx e C e2IrIn8-xCdx dopados com x = 2.6 % de Cd foram estudados em baixas-T e encontrou-se um vetor de propagação do tipo (½ ½ 0) consistente com ordenamento AFM abaixo de TN. Verificou-se que a orientação do momento magnético tende a ir na direção do plano-ab com dopagem de Cd nestes compostos. A substituição de In por Sn nos compostos de Ce2MIn8 mostrou que esta dopagem está desfavorecendo o ordenamento magnético através da diminuição do valor da TN em função da concentração de Sn. Os resultados sugerem que o Sn está favorecendo o efeito Kondo e que efeitos de campo cristalino são menos observáveis nos compostos dopados com Sn. Foi visto que a dopagem com Ga no sítio do In igualmente diminui a temperatura de ordenamento magnético e favorece o efeito Kondo. Porém, os resultados sugerem que efeitos de campo cristalino estão presentes pela variação não usual da temperatura do máximo das curvas de resistividade elétrica em função da dopagem com Ga. Neste trabalho também são apresentados estudos da evolução do magnetismo dos elétrons 4f, em compostos relacionados que não são férmions pesados para R2CoGa8, para R = Gd, Tb, Dy, Ho, Er e Tm. Nestes compostos podemos observar a evolução do magnetismo e dos efeitos de campo cristalino sem a presença do efeito Kondo / Abstract: This thesis describes the investigation of the physical properties of the (Cd, Sn, Ga)-doped Ce2MIn8 (M = Rh, Ir) intermetallic compounds. Temperature dependent magnetic susceptibility, heat capacity and electrical resistivity measurements were performed to characterize the macroscopic properties of the synthesized compounds. X-ray powder diffraction were used to determine their phase purity and crystal structure and X-ray and neutron magnetic scattering techniques were used to study the microscopic magnetic structure in low temperature. The Ce2MIn8 (M = Rh, Ir) compounds belong to the family of the heavy-fermions Ce-based compounds CenMIn3n+2 (M = Co, Rh, Ir; n = 1, 2), where the occurrence of unconventional superconductivity (USC) in many of its members has been motivating intense work in past few years. In particular these compounds present a wide range of interesting properties as Kondo effect, USC, magnetism, non Fermi liquid and Fermi liquid behavior and the occurrence of quantum critical points. Particularly interesting is the tunability of their ground state by pressure and chemical doping that revealed very interesting and rich phase diagrams with properties that are unprecedented for this class of compounds. Indeed the study of the 218 parent compounds is a great opportunity to further study the relationship between magnetism, USC and crystal structure in this family. We report in this work five unpublished phase diagrams of this family: Ce2RhIn8-xCdx, Ce2IrIn8-xCdx, Ce2Rh0.5Ir0.5 In8-xCdx, Ce2RhIn8-xSnx e Ce2RhIn8-xGax. Our results revealed that Cd-doping Ce2MIn8 enhances the antiferromagnetic ordering temperature as a function of the Cd concentration. The results suggest that the Cd-doping in these compounds is inducing an electronic tuning by locally decreasing the Ce 3+ density of states and this is favoring the AFM ordering according com a Doniach-like scenario. However the evolution of the maximum in the resistivity as a function of the Cd concentration and the small variation of the magnetic moment orientation of the doped compounds suggest that Cd-doping is also changing the crystal field (CEF) parameters in these compounds. The magnetic structure studied by X-ray and neutron magnetic scattering showed the Cd-doped samples present just below TN a commensurate antiferromagnetic structure with a propagation vector (½ ½ 0). The magnetic structure determination indicates that the magnetic moment orientation of the Cd doped samples tend going to the ab-plane. The Sn chemical substitution in Ce2MI n8 (M = Rh, Ir) showed Sn-doping is decreasing the magnetic order by favoring the Kondo effect. This is the opposite of the Cd-doping effect because Sn is now increasing the local density of states of the Ce3+ions. As Sn-doping drives 4f to a more itinerant character the CEF effect are less important for this compounds. On the other hand, the Ga-doped Ce2RhI n8 similarly show a decreasing of the magnetic order due to the enhancement of the Kondo effect by chemical pressure. However the unexpected evolution of the maximum in the resistivity as a function of the Ga suggests in this dopant is changing the crystal field is still an important effect in this compound. Finally we present the 4f magnetism evolution studies on the series of the Ga-based R2CoGa8 for R = Gd ¿ Tm compounds, where one can follow the evolution of the magnetism and the CEF parameters without the presence of the Kondo effect / Doutorado / Física da Matéria Condensada / Doutor em Ciências

Orientador: Alex Gomes Dias / Dissertação (mestrado) - Universidade Federal do ABC. Programa de Pós-Graduação em Física, 2014

The constituents of a quantum many-body system can be inextricably linked, a phenomenon known as quantum entanglement. Entanglement can be used as a resource for quantum computing, quantum communication and detecting phase transitions, among others. The amount of entanglement can be quantified via the von Neumann and Rényi entropies, which have their origins in information theory. In this work, the quantum entanglement between subsystems of a one dimen- sional lattice model of fermions is quantified. The von Neumann and Rényi entropies were calculated for two types of subsystems. In the first study, the subsystems were treated as two subsets of particles, and in the second, as two spatial subregions. Finally, by considering particle superselection rules, the amount of entanglement that can actually be accessed as a resource was calcu- lated. In all cases, the quantum entanglement served to detect phase transitions in the model.

For almost forty years our comprehension of the metallic behavior in many materials has been founded on the Landau physical intuition about interacting Fermi systems. The idea of Landau, that interacting fermions could be regarded as free particles with renormalized parameters, is at the basis of the standard picture of the solids in terms of single independent electrons delocalized throughout the systems. The extraordinary success of this scenario is demonstrated by the impressive number of predictions and results, on which has root a large part of the actual technology.<br />The Fermi-liquid concept has been also extended to systems showing a strong electron-electron interaction, i.e. strongly correlated electrons systems. Under suitable conditions the low temperature metallic properties of these systems can be interpreted in terms of renormalized quasiparticles.<br /><br /> Nevertheless, recent experiments on some strongly correlated materials have shown remarkable deviations from the Fermi liquid predictions concerning different physical observables, such as specific heat C, resistivity ρ or susceptibility χ. The theoretical understanding of the breakdown of the Fermi liquid paradigm observed heavy fermion systems or in high Tc superconductors is one of the open challenges in the correlated electrons physics. Many ideas have been put forward to explain the observed non-Fermi liquid behavior, without finding an absolute consensus so far. Among them we can distinguish three main directions: overscreening in Kondo models, Kondo disorder and quantum criticality.<br /> <br /> A common feature can be recognized among some of these ideas, namely the existence of a physical mechanism pushing to zero the coherence temperature below which the Fermi liquid forms. In one case (Kondo disorder) this mechanism is associated to the presence of a certain degree of disorder. However, a more widely accepted mechanism for the formation of a non-Fermi liquid state is the proximity to a quantum phase transition (QPT) or to a quantum critical point (QCP). Within this scenario the breakdown of the Fermi liquid properties occurs in the neighborhood of T = 0 transition between a magnetically ordered phase (e.g. antiferromagnetic) and a paramagnetic one. In this regime the strong coupling between the fluctuations of the order parameter and the electrons may prevent the formation of a Fermi liquid phase with long-lived quasiparticles.<br /><br />Among the different approach to non-Fermi liquid problem based on quantum criticality we can mention the Hertz-Millis theory, where the paramagnons of the ordered phase “dress” the conduction electrons to produce the NFL behavior. Another approach is the local quantum critical theory, in which the competition between local Kondo screening and long wavelength magnetic fluctuations drives the system into a critical regime where non-Fermi liquid properties can arise. This approach is based on a suitable extension of the dynamical mean-field theory. However, local quantum criticality, even providing useful insights to the non-Fermi liquid problem, recquires some simplifying approximations to solve the mean-field equations, spoiling DMFT approach of many of its benefits. Dynamical Mean Field Theory is a powerful theoretical tool to investigate strongly correlated electrons systems. Among other things, this method has permitted to obtain a satisfactory description of the Mott metal-insulator transition in simplified models, such as Hubbard. Lately, the application to realistic calculations, thru an ab-initio plus<br />DMFT algorithm, has greatly increased our knowledge about real materials.<br /><br /> At the heart of the DMFT approach are the simplifications on the lattice quantum many-body problem arising in the limit of infinite dimension. These simplifications permit to map the lattice problem onto an effective single impurity problem, that has to be solved in a<br />self-consistent way. In this respect DMFT can be considered as the quantum generalization of the classic mean-field theory, introduced so far to deal with spin models.<br /> <br />In this thesis we shall show that a new approach to the heavy fermions physics can be based on the DMFT solution of one of the canonical model of this area, namely the periodic Anderson<br />model. In particular we demonstrate that, contrary to conventional expectations, a non-Fermi liquid state is readily obtained from this model within the DMFT framework. In agreement with the quantum criticality scenario, this novel NFL state is located in the neighborhood of a quantum phase transition, but unlike the standard quantum criticality scenario sketched before, the relevant quantum transition here is a Mott transition. Thus, the present study sheds a different light onto the NFL problem, showing that the coupling to long wavelength magnetic fluctuations (absent in DMFT) is not a prerequisite for the realization of a NFL scenario. Local temporal magnetic fluctuations alone can provide sufficient scattering to produce an incoherent metallic state. The presence of such large local magnetic fluctuations in our model has origin in<br />the competition between magnetic interactions, namely the super-exchange antiferromagnetic interaction between the correlated electrons and the ferromagnetic interaction indirectly driven<br />by the delocalization of the doped charges. Thus, we are able to obtain a DMFT description of the non-Fermi liquid phase in heavy<br />fermion systems which is based on the proximity to a Mott point, i.e. Mottness scenario. Our study shows that the PAM, solved within DMFT, may be considered as a “bare bones” or min-<br />imal approach able to capture the physical scenario for the formation of a NFL state and that is in qualitative agreement with some observed phenomenology in heavy fermion systems.

Cette thèse est divisée en deux parties. La première est consacrée à l'étude des angles de mélange des fermions en Théorie Quantique des Champs (TQC). Nous montrons que, du fait de la non-orthonormalité de ses états propres de masse, la matrice de mélange d'un système non-dégénéré de fermions couplés ne peut pas être considérée comme unitaire ; puis, dans le cadre du Modèle Standard, que les angles de mélange des quarks et des leptons se révèlent compatibles avec une structure précise des courants neutres, où universalité et absence des courants changeant la saveur sont violées avec la même amplitude. Puis nous retrouvons de manière perturbative la non-unitarité de la matrice de mélange par l'annulation des transitions non-diagonales à une boucle entre états propres de masse. Nous étudions enfin les transformations de saveur pertinentes dans cette démarche, et esquissons un lien entre les courants neutres et la matrice de masse considérée habituellement pour des systèmes couplés. La deuxième partie présente les premiers résultats d'une étude générale des contraintes apportées en TQC par les symétries discrètes (parité P, conjugaison de charge C et renversement du temps T) sur le Lagrangien et le propagateur fermioniques. Nous montrons, dans le cas d'une génération, que ces derniers, écrits de la manière la plus générale compatible avec l'invariance de Lorentz, sont naturellement invariants sous le produit PCT, puis que les états propres d'un propagateur invariant sous C sont des fermions de Majorana.

Les systèmes métalliques unidimensionnels possèdent une physique bien particulière désignée par le terme de «liquide de Luttinger». Les propriétés d'un tel système sont bien comprises du point de vue théorique et diffèrent énormément du comportement métallique en deux et trois dimensions qui est décrit par le liquide de Fermi. En outre, il existe de nombreuses réalisations expérimentales potentielles susceptibles d'être décrites dans ce cadre. Néanmoins, le rôle du couplage interchaîne reste encore mal compris et peut, en pratique, limiter l'observation du comportement de liquide de Luttinger à certains domaines des paramètres physiques (température, pression, etc.). Il a été proposé que le couplage interchaîne était fortement réduit du fait des interactions. Nous démontrons, par des calculs numériques et grâce à l'utilisation de lois d'échelles, la validité de cette hypothèse pour des modèles microscopiques sur réseau et nous obtenons de manière quantitative la renormalisation du couplage interchaîne dans un certain régime. De surcroît, nous mettons en évidence, pour la première fois pour des modèles microscopiques, l'existence de processus à deux particules dans la physique des chaînes fortement corrélées couplées. Nous étudions également les autres types d'excitations qui existent au voisinage de la transition métal-isolant. Nous discutons également, de façon générale, les propriétés de transport de ces matériaux à la lumière des résultats théoriques obtenus à partir d'un hamiltonien adéquat. Là encore, la présence des interactions fortes produit un effet essentiel par exemple en réduisant l'absorption optique de ces matériaux en accord avec les observations.

Nous étudions certains aspects de la physique des fermions en deux dimensions, pertinente pour les conducteurs organiques quasi unidimensionnels et les supraconducteurs à haute température critique. En particulier, nous nous intéressons au calcul de la surface de Fermi de systèmes électroniques en interaction, qui est une des informations cruciales du point de vue des propriétés de basse énergie de ces systèmes. Nous commençons par donner une interprétation énergétique, sur un toy model, de la déformation de la surface de Fermi due aux interactions entre électrons, en insistant sur la nécessité d'une méthode auto-cohérente. Puis nous expliquons comment faire le même calcul dans un cadre de théorie des champs, et comment améliorer les résultats grâce à un groupe de renormalisation. Nous appliquons ce formalisme aux composés quasi unidimensionnels. Un des chapitres est un résumé d'un article dans lequel nous analysons la pertinence d'une transition d'un état onde de densité de spin à un état supraconducteur, observée dans les flots de renormalisation d'un modèle de fermions à deux dimensions, dont la surface de Fermi est un carré avec des coins arrondis.