Eine Vielzahl von interessanten Phänomenen entsteht durch die quantenmechanischeWechselwirkung einer großen Zahl von Teilchen. In den meisten Fällen ist die Beschreibung der relevanten physikalischen Eigenschaften extrem schwierig, da die Komplexität des Systems exponentiell mit der Anzahl der wechselwirkenden Teilchen anwächst und das Lösen der zugrunde liegenden Schrödingergleichung unmöglich macht. Trotzdem gab es in der Geschichte der Festkörperphysik eine Reihe von bahnbrechenden Entdeckungen, die unser Verständnis von komplexen Phänomenen deutlich voran gebracht haben. Dazu zählt die Entwicklung der Landau’schen Theorie der Fermiflüssigkeit, der BCS-Theorie der Supraleitung, der Theorie der Supraflüssigkeit und der Theorie des fraktionalen Quanten-Hall-Effekts. In all diesen Fällen ist ein theoretisches Verständnis mithilfe sogenannter Quasiteilchen gelungen. Anstatt ein komplexes Phänomen durch das Verhalten von fundamentalen Teilchen wie der Elektronen zu erklären, ist es möglich, die entsprechenden Eigenschaften durch das simple Verhalten von Quasiteilchen zu beschreiben, die allein auf Grund der komplexen kollektiven Wechselwirkung entstehen. Eines der seltenen Beispiele, bei dem ein stark korreliertes quantenmagnetisches Problem analytisch lösbar ist, ist das Kitaev Modell. Es beschreibt wechselwirkende Spins auf einem Sechseck-Gitter und zeichnet sich durch einen Spinflüssigkeits-Grundzustand aus. Auch hier gelang die Lösung mittels spezieller Quasiteilchen, den Majorana Fermionen. Experimentell ist es jedoch noch nicht gelungen eine Spinflüssigkeit eindeutig nachzuweisen, da diese sich gerade durch das Fehlen jeglicher klassischer Ordnung und üblicher experimenteller Kenngrößen auszeichnet. Dagegen kann die Beobachtung von Quasiteilchenanregungen einen Hinweis auf den zugrunde liegenden Zustand liefern. Aber auch der definitive Nachweis von Majorana Fermionen in jeglicher Art System, bleibt ein ausstehendes Ziel in der modernen Festkörperphysik. Diese Arbeit befasst sich daher mit der Frage, wie solche Quasiteilchen experimentell sichtbar gemacht werden könnten. Dazu untersuchen wir den Einfluss von Unordnung auf die Zustände und Messgrößen des Kitaev Modells. Dies ist in zweierlei Hinsicht relevant. Einerseits ist Unordnung in der Natur allgegenwärtig, andererseits kann sie auch strategisch herbeigeführt werden, um die Reaktion eines System gezielt zu testen. Das zentrale Ergebnis dieser Arbeit ist, dass den Majorana Fermionen dabei in der Tat eine physikalische, messbare Bedeutung zukommt. Die Arbeit beginnt mit einer Einführung in frustrierte quantenmagnetische Systeme und Spinflüssigkeiten und diskutiert einige Effekte, die durch Gitterverzerrungen oder Verunreinigungen entstehen können. Anschließend zeigen wir, wie sich durch die frustrierte Wechselwirkung im Kitaev Modell ein Spinflüssigkeits-Grundzustand herausbildet. Die analytische Lösung des Modells gelingt mit Hilfe von Majorana Fermionen, jedoch verdoppelt sich der Hilbertraum pro Spin durch die Einführung dieser Quasiteilchen. Ein zentraler Aspekt dieser Arbeit ist daher die richtige Auswahl der „physikalischen“ Zustände, also solcher, die einem Zustand im ursprünglichen Spin Modell entsprechen. Dabei unterscheiden wir zwischen offenen und periodischen Randbedingungen. Wir konnten beweisen, dass sich, in der Phase ohne Bandlücke und für periodische Systeme, stets ein angeregtes Fermion befindet. Dies führt zu großen Effekten in endlichen Systemen, wie wir anhand der Suszeptibilität und der Anregungslücke für magnetische Flüsse zeigen. Außerdem berechnen wir numerisch die statische und dynamische Suszeptibilität abhängig von der Unordnung in der Wechselwirkungsstärke. Diese Art der Unordnung entsteht beispielsweise durch unregelmäßige Gitterstrukturen oder chemische Verunreinigungen auf den nicht-magnetischen Gitterplätzen. Insbesondere ergibt die Verteilung der lokalen Suszeptibilitäten das Linienspektrum, welches sich in Kernspinresonanz Experimenten messen lässt. Für große Unordnung postulieren wir einen Übergang zu einem Zustand mit einer zufälligen Verteilung magnetischer Flüsse. Ein weiterer Kern der Dissertation ist die Untersuchung eines magnetischen Defekts im Kitaev Modell. Diese Situation beschreibt den ungewöhnlichen Fall eines Kondoeffekts in einer Spinflüssigkeit. In der Majorana Fermionen Darstellung gelingt es uns, das Problem in eine Form zu bringen, die mit Hilfe von Wilson’s numerischer Renormalisierungsgruppe untersucht werden kann. Es zeigt sich, dass dadurch eine Nullpunktsentropie des Defekts entsteht, die durch lokalisierte Majorana Fermionen erklärt werden kann. Durch die Darstellung des Kitaev Modells mithilfe von Quasiteilchen ist es möglich eine elegante Beschreibung eines komplexen, stark wechselwirkenden Systems zu finden. Die Ergebnisse dieser Arbeit zeigen, dass den Majorana Fermionen dabei durchaus eine physikalische Bedeutung zukommt. Gelingt es sie z.B. durch magnetische Störstellen zu lokalisieren, wäre ein direkter experimenteller Nachweis möglich. / Many interesting phenomena in quantum physics arise through the quantum mechanical interaction of a large number of particles. In most cases describing the relevant physical properties is extremely difficult, because the complexity of the system increases exponentially with the number of interacting particles and solving the underlying Schrödinger equation becomes impossible. Nevertheless, our understanding of complex phenomena has progressed through some groundbreaking discoveries in the history of condensed matter physics. Examples include the development of Landau’s theory of Fermi liquids, the BCStheory of superconductivity, the theory of superfluidity and the theory of the fractional quantum Hall effect. In all these cases a theoretical understanding was achieved with so-called quasi-particles. Instead of explaining a phenomenon through the behavior of fundamental particles, such as electrons, the corresponding properties can be described by the simple behavior of quasi-particles, which are themselves a result of the complex collective interaction. One of the rare examples, where a strongly correlated quantum mechanical problem can be solved analytical, is the Kitaev model. It describes interacting spins on a honeycomb lattice and exhibits a spin liquid ground state. Here the solution was achieved by means of certain quasi-particles, called Majorana fermions. However, it has not been possible to clearly identify such a spin liquid experimentally, because its defining feature is the absence of any conventional order, in particular magnetic order. In contrast, the observation of quasiparticle excitations may hint at the nature of the ground state. But also a definite detection of Majorana fermions in any kind of system remains one of the outstanding issues in modern condensed matter physics. Therefore this thesis is devoted to the question how such quasiparticles may be found experimentally. For this reason we study the influence of disorder on the states and observables of the Kitaev model. This is relevant in two respects: Firstly, disorder is ubiquitous in nature and secondly, it may be used strategically to probe the response of a system. The central result of this work is that Majorana fermions hereby indeed obtain a true physical and observable significance. The thesis starts with an introduction of frustrated quantum mechanical systems and spin liquids, and discusses some of the effects that arise through lattice distortions or impurities. Afterwards we show how the frustrated interactions in the Kitaev model lead to a spin liquid ground state. The analytical solution of the model is achieved through the introduction of Majorana fermions. However, resulting from the introduction of these quasi-particles the Hilbert space per spin doubles. A central aspect of this thesis is therefore the right selection of the “physical” states, which correspond to a state of the original spin Hamiltonian. To do this, we distinguish between periodic and open boundary conditions explicitly. We were able to prove that there is always one excited fermion in the gapless phase of the periodic system. This leads to large finite-size effects, as we will illustrate for the susceptibility and the magnetic flux gap. Moreover we compute the static and dynamic spin susceptibilities for finite-size systems subject to disorder in the exchange couplings. In a possible experimental realization, this kind of disorder arises from lattice distortions or chemical disorder on nonmagnetic sites. Specifically, we calculate the distribution of local susceptibilities and extract the lineshape, which can be measured in nuclear-magnetic-resonance experiments. Further, for increasing disorder we predict a transition to a random-flux state. Another core of this dissertation is the investigation of a magnetic impurity in the Kitaev model. This setup represents the unusual case of a Kondo effect in a quantum spin liquid. Utilizing the Majorana representation we are able to formulate the problem in a way that can be analyzed using Wilson’s numerical renormalization group. The numerics reveal an impurity entropy which can be explained by localized Majorana fermions. Through the representation of the Kitaev model in terms of quasi-particles an elegant description of a complex, strongly correlated system is possible. The results of this thesis indicate that these Majorana acquire a relevant physical meaning. If one can localize them, for example with the help of magnetic impurities, a direct experimental observation would be feasible.

The XX century witnessed the quantum and relativistic revolutions in physics. The development of these two theories, namely, Quantum Mechanics and Relativity, was the inception of many crucial discoveries and technological advances. Among them, one stands out due to its uniqueness, the neutrino discovery. However, several neutrino properties are still obscure. Neutrinos are the only fundamental particles whose nature is currently unknown. Such fermions can either be different from their antiparticles, i.e., Dirac fermions, or be their own antiparticles, that is, Majorana fermions. On the other hand, the smallness of neutrino masses is a problem seemingly related to the neutrino nature; thus, as essential task consists in addressing the phenomenologically viable models in both cases. Furthermore, it is important to search for other physical process in which the neutrino nature may manifest through different experimental signatures. A rather difficult but promising method corresponds to the detection of the cosmic neutrino background, viz. neutrinos which are relics from the Big Bang. Previous works have shown that detection rates for Dirac and Majorana neutrinos can give different results. Nevertheless, this distinction was obtained considering the Standard Model framework only. Therefore, it is important to understand the consequences of having Non-Standard Interactions contributing to the detection of neutrinos from the cosmic background. Another remarkable relic predicted by Cosmology is the unidentified Dark Matter, composing ~25% of the Universe. All searches regarding the Weakly Interacting Massive Particle, one of the principal candidates for Dark Matter, have given negative results; this has compelled experiments to increase their sensitivity. Notwithstanding, neutrinos may stand in the way of such experimental searches given that they may constitute an irreducible background. In this thesis, we will address these three different phenomena, neutrino mass models, detection of the cosmic neutrino background and the neutrino background in Dark Matter searches, by considering the different characteristics in each case. In the study of neutrino mass models, we will consider models for both Majorana and Dirac neutrinos; specifically, we will probe the neutrinophilic two-Higgs-doublet model. Regarding the detection of relic neutrinos, we will analyse the consequences of the existence of the beyond Standard Model physics in the capture rate by tritium. Finally, we will scrutinize the impact of neutrinos in Direct Detection WIMP searches, by considering Standard Model plus additional interactions in the form of simplified models. / Ao longo do século XX testemunhamos as revoluções quântica e relativista que aconteceram na Física. O desenvolvimento da Mecânica quântica e da teoria da relatividade foi o prelúdio de inúmeras descobertas e avanços tecnológicos fundamentais; em particular, a descoberta dos neutrinos. No entanto, a sua total compreensão ainda é um mistério para a física de partículas. Entendidos como partículas fermiônicas fundamentais, os neutrinos possuem sua natureza desconhecida. Podendo ser diferentes de suas antipartículas, denominadas férmions de Dirac, ou também podendo ser as suas próprias antipartícula, sendo conhecidas como férmions de Majorana. Por outro lado, o valor de sua massa continua sendo um problema em aberto, supostamente relacionado à sua natureza. Portanto, é importante estudarmos modelos fenomenológicos viáveis para as duas naturezas possíves dos neutrinos. Além disso, é necessário procurar outros processos físicos cujos resultados experimentais sejam distintos de acordo com a natureza do neutrino. Um método bastante difícil, mas promissor, corresponde à detecção do fundo de neutrinos cósmicos, isto é, os neutrinos relíquia do Big Bang. Análises prévias mostraram que as taxas de detecção para neutrinos de Dirac e de Majorana resultam em valores distintos. Porém, este resultado foi obtido supondo como base o Modelo Padrão; assim, é crucial entender as possíveis consequências da existência de interações desconhecidas na detecção dos neutrinos da radiação cósmica de fundo. Outra relíquia notável prevista pela Cosmologia é a desconhecida Matéria Escura, que compõe ~25% do Universo. Todas as buscas por WIMPs (do inglês Weakly Interactive Massive Particles), um dos principais candidatos a Matéria Escura, tem dado resultados negativos. Isto tem forçado a criação de experimentos cada vez mais sensíveis. Contudo, os neutrinos poderão ser um obstáculo nessas buscas experimentais, pois estes convertir-se-ão em um fundo irredutível. Na presente tese, abordaremos estes três fenômenos diferentes, modelos de massa para os neutrinos, a detecção do fundo de neutrinos cósmicos e o fundo de neutrinos em experimentos de detecção direta de Matéria Escura, considerando as distintas características em cada caso. No estudo dos modelos de massa para os neutrinos consideraremos modelos para neutrinos de Majorana e Dirac; exploraremos modelos neutrinofílicos com dois dubletos de Higgs. Enquanto à detecção dos neutrinos relíquia, analisaremos as consequências da presença de física além do Modelo Padrão na taxa de captura pelo trítio. Finalmente, examinaremos o impacto dos neutrinos em experimentos de detecção direta de WIMPs, supondo as interações do Modelo Padrão junto com interações adicionais na forma de modelos simplificados.

Submitted by ANDRE RAMALHO DOS SANTOS null (ramalho_inf@yahoo.com.br) on 2018-02-14T03:20:16Z No. of bitstreams: 1 Dissertação André Ramalho.final.pdf: 2789018 bytes, checksum: d4170ea3aaec8f302b447a0aac5e5986 (MD5) / Approved for entry into archive by Ana Paula Santulo Custódio de Medeiros null (asantulo@rc.unesp.br) on 2018-02-14T16:54:15Z (GMT) No. of bitstreams: 1 santos_ar_me_rcla.pdf: 2620534 bytes, checksum: cb88b11f48c3fc7b2fef3c938febb8e0 (MD5) / Made available in DSpace on 2018-02-14T16:54:15Z (GMT). No. of bitstreams: 1 santos_ar_me_rcla.pdf: 2620534 bytes, checksum: cb88b11f48c3fc7b2fef3c938febb8e0 (MD5) Previous issue date: 2017-11-30 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / 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. / 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.

The XX century witnessed the quantum and relativistic revolutions in physics. The development of these two theories, namely, Quantum Mechanics and Relativity, was the inception of many crucial discoveries and technological advances. Among them, one stands out due to its uniqueness, the neutrino discovery. However, several neutrino properties are still obscure. Neutrinos are the only fundamental particles whose nature is currently unknown. Such fermions can either be different from their antiparticles, i.e., Dirac fermions, or be their own antiparticles, that is, Majorana fermions. On the other hand, the smallness of neutrino masses is a problem seemingly related to the neutrino nature; thus, as essential task consists in addressing the phenomenologically viable models in both cases. Furthermore, it is important to search for other physical process in which the neutrino nature may manifest through different experimental signatures. A rather difficult but promising method corresponds to the detection of the cosmic neutrino background, viz. neutrinos which are relics from the Big Bang. Previous works have shown that detection rates for Dirac and Majorana neutrinos can give different results. Nevertheless, this distinction was obtained considering the Standard Model framework only. Therefore, it is important to understand the consequences of having Non-Standard Interactions contributing to the detection of neutrinos from the cosmic background. Another remarkable relic predicted by Cosmology is the unidentified Dark Matter, composing ~25% of the Universe. All searches regarding the Weakly Interacting Massive Particle, one of the principal candidates for Dark Matter, have given negative results; this has compelled experiments to increase their sensitivity. Notwithstanding, neutrinos may stand in the way of such experimental searches given that they may constitute an irreducible background. In this thesis, we will address these three different phenomena, neutrino mass models, detection of the cosmic neutrino background and the neutrino background in Dark Matter searches, by considering the different characteristics in each case. In the study of neutrino mass models, we will consider models for both Majorana and Dirac neutrinos; specifically, we will probe the neutrinophilic two-Higgs-doublet model. Regarding the detection of relic neutrinos, we will analyse the consequences of the existence of the beyond Standard Model physics in the capture rate by tritium. Finally, we will scrutinize the impact of neutrinos in Direct Detection WIMP searches, by considering Standard Model plus additional interactions in the form of simplified models. / Ao longo do século XX testemunhamos as revoluções quântica e relativista que aconteceram na Física. O desenvolvimento da Mecânica quântica e da teoria da relatividade foi o prelúdio de inúmeras descobertas e avanços tecnológicos fundamentais; em particular, a descoberta dos neutrinos. No entanto, a sua total compreensão ainda é um mistério para a física de partículas. Entendidos como partículas fermiônicas fundamentais, os neutrinos possuem sua natureza desconhecida. Podendo ser diferentes de suas antipartículas, denominadas férmions de Dirac, ou também podendo ser as suas próprias antipartícula, sendo conhecidas como férmions de Majorana. Por outro lado, o valor de sua massa continua sendo um problema em aberto, supostamente relacionado à sua natureza. Portanto, é importante estudarmos modelos fenomenológicos viáveis para as duas naturezas possíves dos neutrinos. Além disso, é necessário procurar outros processos físicos cujos resultados experimentais sejam distintos de acordo com a natureza do neutrino. Um método bastante difícil, mas promissor, corresponde à detecção do fundo de neutrinos cósmicos, isto é, os neutrinos relíquia do Big Bang. Análises prévias mostraram que as taxas de detecção para neutrinos de Dirac e de Majorana resultam em valores distintos. Porém, este resultado foi obtido supondo como base o Modelo Padrão; assim, é crucial entender as possíveis consequências da existência de interações desconhecidas na detecção dos neutrinos da radiação cósmica de fundo. Outra relíquia notável prevista pela Cosmologia é a desconhecida Matéria Escura, que compõe ~25% do Universo. Todas as buscas por WIMPs (do inglês Weakly Interactive Massive Particles), um dos principais candidatos a Matéria Escura, tem dado resultados negativos. Isto tem forçado a criação de experimentos cada vez mais sensíveis. Contudo, os neutrinos poderão ser um obstáculo nessas buscas experimentais, pois estes convertir-se-ão em um fundo irredutível. Na presente tese, abordaremos estes três fenômenos diferentes, modelos de massa para os neutrinos, a detecção do fundo de neutrinos cósmicos e o fundo de neutrinos em experimentos de detecção direta de Matéria Escura, considerando as distintas características em cada caso. No estudo dos modelos de massa para os neutrinos consideraremos modelos para neutrinos de Majorana e Dirac; exploraremos modelos neutrinofílicos com dois dubletos de Higgs. Enquanto à detecção dos neutrinos relíquia, analisaremos as consequências da presença de física além do Modelo Padrão na taxa de captura pelo trítio. Finalmente, examinaremos o impacto dos neutrinos em experimentos de detecção direta de WIMPs, supondo as interações do Modelo Padrão junto com interações adicionais na forma de modelos simplificados.

Cette thèse est dédiée à l’étude de la violation CP dans les processus ūd→tb̄ e⁻ μ⁻ et W⁻→ l-1 l-2 (q′¯ q)⁺. Il y a des expériences qui cherchent à identifier ces processus au grand collisionneur de hadrons, ou LHC (Large Hadron Collider). Une conséquence de l’observation de ces désintégrations impliquait une brisure de la conservation du nombre leptonique, car ∆L = 2. Si le neutrino est de type Majorana, il est sa propre antiparticule et on peut observer la double désintégration bêta sans émission de neutrino (0νββ). Ce processus est caractérisé par ∆L = 2. Si nous observons des processus similaires à 0νββ, ∆L = 2, au LHC, il y a aussi la possibilité de chercher la violation CP. La mesure de ce type de violation CP nous donnerait des informations sur de la Nouvelle Physique (NP) qui ne pourraient pas être facilement obtenues autrement. Il existe trois types de violation CP : directe, indirecte et cinématique (produit triple). Ce travail relève essentiellement mes études sur deux processus de violation CP, l’un direct et l’autre produit triple. Elles sont présentées dans deux articles qui sont inclus dans cette thèse. Le premier article est consacré au produit triple dans le processus : ūd→tb̄ e⁻ μ⁻ . Le modèle que nous avons considéré n’implique pas de neutrino de Majorana. À l’aide de MadGraph, nous avons étudié la violation CP pour les deux processus mentionnés pour deux versions du LHC, haute luminosité HL-LHC (14 TeV) et haute énergie HE-LHC (27 TeV),et pour un futur collisionneur FCC-hh (100 TeV). Nous trouvons que le produit triple n’est pas mesurable au HL-LHC, peut être mesurable au HE-LHC, et est certainement mesurable au FCC-hh. Dans le deuxième article, nous avons examiné comment générer la violation CP avec des neutrinos droitiers. Le deuxième article porte sur l’étude de la violation CP directe dans la désintégration W⁻→ l-1 l-2 (q′¯ q)⁺ en impliquant deux neutrinos N1 et N 2. Nous avons trouvé que la valeur de l’asymétrie CP peut être mesurée avec une précision de 3σ et que 0.1% ≤ ACP ≤ 10%. / This thesis is dedicated to the study of CP violation in these processes ūd→tb̄ e⁻ μ⁻ et W⁻→ l-1 l-2 (q′¯ q)⁺. There are experiments which search to identify these processes at the "Large Hadron Collider" (LHC). The outcome of the observation of these decays would imply violation of lepton number conservation, ∆L = 2. If the neutrino is a Majorana particle, it is its own antiparticle and we can observe processes that violate the conservation of the lepton number, ∆L = 2. The neutrinoless double beta decay (0νββ), is a process which is characterized by ∆L = 2, occurs when the neutrinos are Majorana particles. If we observe 0νββ-like processes at the LHC, there is also the possibility of looking for CP violation. Measuring this type of CP violation would give us information about New Physics that could not be easily obtained using other methods. There are three types of CP violation, namely: direct, indirect and kinematic (triple product). This research presents studies concerning direct and triple product CP violation. The first paper is devoted to triple products in the process: ūd→tb̄ e⁻ μ⁻. In addition, the model considered does not involve a Majorana neutrino. Using MadGraph, we have numerically studied and evaluated the CP violation for the two mentioned processes for three types of accelerators: high luminosity HL-LHC (14 TeV), high energy HE-LHC (27 TeV) and for a future FCC-hh collider (100 TeV). We found that the triple product is not measurable at the HL-LHC, may be measurable at HE-LHC, and is certainly measurable at FCC-hh. In the second article, we investigated to see how to generate CP violation with right-handed neutrinos. The second article is on the study of direct CP violation the decay W⁻→ l-1 l-2 (q′¯ q)⁺ by involving two neutrinos N1and N2. It is also observed that the value of CP asymmetry can be measured with an accuracy of 3σ and as 0.1% ≤ ACP ≤ 10%.

La série de détecteurs NEMO est conçue pour la recherche de la double désintégration β sans émission de neutrino qui prouverait que le neutrino est une particule de Majorana (i.e. identique à son antiparticule) et massif. Après avoir présenté l’état des lieux en physique des neutrinos et les détecteurs NEMO 3 et SuperNEMO, cette thèse s’articule en deux parties indépendantes. La première concerne l’étude du bruit de fond provenant des neutrons pour optimiser le blindage destiné au premier module de SuperNEMO. La conclusion de cette étude montre que l’ajout de plaques de polyéthylène boré par rapport au blindage de NEMO 3 (de part et d’autre du blindage en fer) permet d’obtenir un bruit de fond négligeable provenant des neutrons, dans la fenêtre en énergie du canal deux électrons où la double désintégration β sans émission de neutrino du sélénium-82 est attendue, en cinq ans de prise de données de ce premier module. La seconde partie, via l’analyse des données du détecteur NEMO 3, permet une indication de la désintégration double β standard du néodyme-150 vers l’état excité 0+1 du samarium-150. La feuille de néodyme qui est placée dans le détecteur est analysée en détail pour obtenir cette indication à 3, 7σ avec une demi-vie mesurée de : T1/2 (150 Nd0+ →0+1 ) = [7, 12 ± 1, 28 (stat.) ± 0, 91 (syst.)] × 10E19 ans / The NEMO detector series is designed to search for the neutrinoless double β decay, which would prove that the neutrino is a Majorana particle (i.e. identical to its own antiparticle) and has a nonzero mass. After an introduction to neutrino physics and a description of both the NEMO 3 and SuperNEMO detectors, this thesis is articulated in two independent parts.The first provides an investigation of the neutron background in order to optimize the shielding for the first SuperNEMO module. The outcome of the study recommends the addition of borated polyethylene to the NEMO 3 shielding (on both sides of the iron shielding) to obtain a negligible background, coming from neutrons in the energy window of the two-electron channel where the neutrinoless double β decay of selenium-82 is expected, for the duration of five years for which data will be taken with this first module. In the second part, the neodymium foil located in the NEMO 3 detector is deeply analyzed to obtain an indication of the standard double β decay of neodymium-150 to the 0+1 excited state of samarium-150. The measured half-life, with a significance of 3.7σ, is: T1/2 (150 Nd 0+ →0+1 ) = [7.12 ± 1.28 (stat.) ± 0.91 (syst.)] × 10E19 years

Submitted by LUCIANO HENRIQUE SILIANO RICCO null (luciano.silianoricco@gmail.com) on 2016-03-03T12:32:48Z No. of bitstreams: 1 Dissertação_LucianoRicco.pdf: 7937141 bytes, checksum: 4631857aac8f308808dda1e44b0c0f03 (MD5) / Approved for entry into archive by Ana Paula Grisoto (grisotoana@reitoria.unesp.br) on 2016-03-04T16:21:23Z (GMT) No. of bitstreams: 1 ricco_lhs_me_ilha.pdf: 7937141 bytes, checksum: 4631857aac8f308808dda1e44b0c0f03 (MD5) / Made available in DSpace on 2016-03-04T16:21:23Z (GMT). No. of bitstreams: 1 ricco_lhs_me_ilha.pdf: 7937141 bytes, checksum: 4631857aac8f308808dda1e44b0c0f03 (MD5) Previous issue date: 2016-01-29 / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Investigou-se teoricamente um sistema composto por um interferômetro do tipo Aharonov- Bohm com dois pontos quânticos, onde um deles encontra-se acoplado à um fio de Kitaev na fase topológica, nos casos em que se desconsidera a interação de Coulomb entre os pontos quânticos (caso não interagente) e quando a mesma é levada em conta (caso interagente). Na primeira situação, verificou-se a presença robusta da anomalia de voltagem zero para ambos os regimes de interferência Fano adotados. Além do mais, constatou-se que o estado de Majorana isolado possui uma maneira singular de quebrar a simetria dos perfis de densidade de transmitância em função da diferença simétrica de energia dos pontos quânticos e da energia de Fermi dos terminais metálicos. Tais perfis podem ser obtidos experimentalmente por medidas de condutância. Na situação de pontos quânticos interagentes em ressonância, verificou-se que a razão entre a magnitude da repulsão de Coulomb e o acoplamento fio-ponto quântico altera a largura da anomalia de voltagem zero em ambos os regimes Fano analisados. Esse fato sugere que a correlação eletrônica influencia o tempo de vida do estado de Majorana no ponto quântico hibridizado diretamente com o fio. Ademais, para a situação de pontos quânticos não ressonantes, a inversão dos valores de energia dos mesmos também modifica a largura da anomalia de voltagem zero, fenômeno que não ocorre para o caso não interagente. Acredita-se que o dispositivo proposto neste trabalho constitui um mecanismo experimental alternativo para detectar excitações de Majorana. / We investigate theoretically a setup composed by an Aharonov-Bohm-like interferometer with two quantum dots, where one of them is coupled to a Kitaev wire within the topological phase, which is explored in two cases: (i) the interdot Coulomb correlation is disregarded (noninteracting case) and (ii) the same is taken into account (interacting case). In the situation (i), we verify the presence of the zero-bias anomaly for the both Fano regimes of interference adopted. Furthermore, we found that an isolated Majorana state has a particular way of breaking the symmetry in transmittance profiles, which can be accessed experimentally by performing electrical conductance measurements. In the situation (ii), for interacting quantum dots in resonance, we notice that the ratio between the Coulomb repulsion strength and the wire-dot coupling changes the width of the zero-bias peak for both Fano regimes analyzed. This feature suggests that the electronic correlation modifies the Majorana state lifetime in the dot directly coupled to the wire. Moreover, for the off-resonance situation, the swap between the energy levels of the dots also changes the width of the Majorana peak, which is not observed in the noninteracting case. The results obtained here can guide experimentalists that pursuit a way of revealing Majorana signatures. / FAPESP: 2014/14143-0

Submitted by GEOVANE MODENA PEREIRA null (geovanemodena@hotmail.com) on 2018-02-10T03:04:38Z No. of bitstreams: 1 Dissertação Geovane - Criptografia de Qubits de Férmions de Majorana por meio de Estados Ligados no Contínuo.pdf: 7524654 bytes, checksum: 0bd9409e8fa9c0c2da9190e44f4cfa33 (MD5) / Approved for entry into archive by Ana Paula Santulo Custódio de Medeiros null (asantulo@rc.unesp.br) on 2018-02-14T16:11:32Z (GMT) No. of bitstreams: 1 pereira_gm_me_rcla.pdf: 7420427 bytes, checksum: 0a0aec5beec2ecdd26883e0f4524844f (MD5) / Made available in DSpace on 2018-02-14T16:11:32Z (GMT). No. of bitstreams: 1 pereira_gm_me_rcla.pdf: 7420427 bytes, checksum: 0a0aec5beec2ecdd26883e0f4524844f (MD5) Previous issue date: 2017-12-01 / 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. / 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.

Made available in DSpace on 2015-05-14T12:14:15Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 4811188 bytes, checksum: e6a9d4d69f963d42f294d99b19a7c9fb (MD5) Previous issue date: 2014-07-30 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Dark Matter (DM) is a key piece for our understanding of the universe evolution. Its existence has been confirmed by gravitational effects on the known matter, and we do not know its constitution just yet. The assumption that DM is composed of particles demands an extension of the Standard Model of Elementary Particles (SM). There are many experiments searching for neutral, stable, weakly interacting particles so called WIMPs, but no conclusive positive signal has been observed so far. That being said, we propose a Majorana fermion to be our DM candidate in one of the simplest minimal extensions of the SM, which adds to the scalar sector a neutral scalar that mixes to the Higgs boson. Further, we study another model which supplements the former by adding a charged scalar, which mediates interactions between the DM particle and leptons. In both models, we compute the relic density, the scattering cross section off nucleon (Direct Detection), and its annihilation rate in Standard Model particles (Indirect Detection) using the numerical package micrOMEGAs. In conclusion, we interestingly find that such models have regions of the parameter space yielding the right abundance while compatible with direct and indirect detection limits. Lastly, we investigate the possibility having the Majoron risen in our extensions as dark radiation in the light of the recent CMB spectrum analyses. / A Matéria Escura (ME) é uma peça fundamental para nosso entendimento sobre a evolução do universo. Sua existência foi confirmada pelos efeitos gravitacionais que exerce sobre a matéria que conhecemos e até hoje não sabemos sua constituição. Assumir que ela seja constituída de partículas implica na necessidade de estender o Modelo Padrão das Partículas Elementares (MP). Há vários experimentos buscando partículas neutras, estáveis e pouco interagentes conhecidas como WIMPs, mas até agora nenhum sinal positivo é conclusivo. Em vista disso, propomos um férmion de Majorana como candidato à ME em uma das extensões mais simples do MP, adicionando ao setor escalar um escalar neutro singleto que se mistura com o bóson de Higgs. Em seguida, estudamos outro modelo que acrescenta ao anterior um escalar carregado singleto mediando interações entre as partículas de ME e os léptons. Nos dois modelos, computamos a abundância relíquia, a seção de choque de espalhamento com nucleons (detecção direta) e a taxa de aniquilação de ME em partículas do MP (detecção indireta) usando o pacote numérico micrOMEGAs. Em conclusão, mostramos que esses modelos têm uma interessante região de parâmetros que fornece a abundância relíquia correta estando de acordo com os limites das detecções direta e indireta. Finalmente, investigamos a possibilidade de o majoron que aparece em nossas extensões ser radiação escura, à luz de recentes análises do espectro da radiação CMB.

Topological phases of matter represent a new phase which cannot be understood in terms of Landau’s theory of symmetry breaking and are characterized by non-local topological properties emerging from purely local (microscopic) degrees of freedom. It is the non-trivial topology of the bulk band structure that gives rise to topological phases in condensed matter systems. Quantum Hall systems are prominent examples of such topological phases. Different quantum Hall states cannot be distinguished by a local order parameter. Instead, non-local measurements are required, such as the Hall conductance, to differentiate between various quantum Hall states. A signature of a topological phase is the existence of robust properties that do not depend on microscopic details and are insensitive to local perturbations which respect appropriate symmetries. Examples of such properties are the presence of protected gapless edge states at the boundary of the system for topological insulators and the remarkably precise quantization of the Hall conductance for quantum Hall states. The robustness of these properties can be under-stood through the existence of a topological invariant, such as the Chern number for quantum Hall states which is quantized to integer values and can only be changed by closing the bulk gap. Two other examples of topological phases of matter are topological superconductors and Weyl semimetals. The study of transport in various kinds of junctions of these topological materials is highly interesting for their applications in modern electronics and quantum computing. Another intriguing area to study is how to generate new kind of gapless edge modes in topological systems. In this thesis I have studied various aspects of topological phases of matter, such as electronic transport in junctions of topological insulators and topological superconductors, the generation of new kinds of boundary modes in the presence of granularity, and the effects of periodic driving in topological systems. We have studied the following topics. 1. transport across a line junction of two three-dimensional topological insulators, 2. transport across a junction of topological insulators and a superconductor, 3. surface and edge states of a topological insulator starting from a lattice model, 4. effects of granularity in topological insulators, 5. Majorana modes and conductance in systems with junctions of topological superconducting wires and normal metals, and 6. generation of new surface states in a Weyl semimetal in the presence of periodic driving by the application of electromagnetic radiation. A detailed description of each chapter is given below. • In the first chapter we introduce a number of concepts which are used in the rest of the thesis. We will discuss the ideas of topological phases of matter (for example, topological insulators, topological superconductors and Majorana modes, and Weyl semimetals), the renormalization group theory for weak interactions, and Floquet theory for periodically driven systems. • In the second chapter we study transport across a line junction which separates the surfaces of two three-dimensional topological insulators. The velocities of the Dirac electrons on the two surfaces may be unequal and may even have opposite signs. For a time-reversal invariant system, we show that the line junction is characterized by an arbitrary real parameter α; this determines the scattering amplitudes (reflection and transmission) from the junction. The physical origin of α is a potential barrier that may be present at the junction. If the surface velocities have the same sign, edge states exist that propagate along the line junction with a velocity and orientation of the spin which depend on α and the ratio of the velocities. Next, we study what happens if the two surfaces are at an angle φ with respect to each other. We study the scattering and differential conductance across the line junction as functions of φ and α. We also show that there are edge states which propagate along the line junction with a velocity and spin orientation which depend on φ. Finally, if the surface velocities have opposite signs, we find that the electrons must necessarily transmit into the two-dimensional interface separating the two topological insulators. • In the third chapter we discuss transport across a line junction lying between two orthogonal topological insulator surfaces and a superconductor which can have either s-wave (spin-singlet) or p-wave (spin-triplet) pairing symmetry. This junction is more complicated than the line junction discussed in the previous chapter because of the presence of the superconductor. In a topological insulator spin-up and spin-down electrons get coupled while in a superconductor electrons and holes get coupled. Hence we have to use a four-component spinor formalism to describe both spin and particle-hole degrees of freedom. The junction can have three time-reversal invariant barriers on the three sides. We compute the subgap charge conductance across such a junction and study their behaviors as a function of the bias voltage applied across the junction and the three parameters which characterize the barriers. We find that the presence of topological insulators and a superconductor leads to both Dirac and Schrodinger-like features in the charge conductances. We discuss the effects of bound states on the superconducting side on the conductance; in particular, we show that for triplet p-wave superconductors such a junction may be used to determine the spin state of its Cooper pairs. • In the fourth chapter we derive the surface Hamiltonians of a three-dimensional topological insulator starting from a microscopic model. (This description was not discussed in the previous chapters where we directly started from the surface Hamiltonians without deriving them form a bulk Hamiltonian). Here we begin from the bulk Hamiltonian of a three-dimensional topological insulator Bi2Se3. Using this we derive the surface Hamiltonians on various surfaces of the topological insulator, and we find the states which appear on the different surfaces and along the edge between pairs of surfaces. The surface Hamiltonians depend on the orientation of the surfaces and are therefore quite different from the previous chapters. We use both analytical methods based on the surface Hamiltonians (which are derived from the bulk Hamiltonian) and numerical methods based directly on a lattice discretization of the bulk Hamiltonian in order to find surface and edge states. We find that the application of a potential barrier along an edge can give rise to states localized at that edge. These states have an unusual energy-momentum dispersion which can be controlled by applying a potential along the edge; in particular, the velocity of these states can be tuned to zero. The scattering and conductance across the edge are studied as a function of the edge potential. We show that a magnetic field applied in a particular direction can also give rise to zero energy states on certain edges. We point out possible experimental ways of looking for the various edge states. • In the fifth chapter we study a system made of topological insulator (TI) nanocrystals which are coupled to each other. Our theoretical studies are motivated by the following experimental observations. Electrical transport measurements were carried out on thin films of nanocrystals of Bi2Se3 which is a TI. The measurements reveal that the entire system behaves like a single TI with two topological surface states at the two ends of the system. The two surface states are found to be coupled if the film thickness is small and decoupled above a certain film thickness. The surface state penetration depth is found to be unusually large and it decreases with increasing temperature. To explain all these experimental results we propose a theoretical model for this granular system. This consists of multiple grains of Bi2Se3 stacked next to each other in a regular array along the z-direction (the c-axis of Bi2Se3 nanocrystals). We assume translational invariance along the x and y directions. Each grain has top and bottom surfaces on which the electrons are described by Hamiltonians of the Dirac form which can be derived from the bulk Hamiltonian known for this material. We introduce intra-grain tunneling couplings t1 between the opposite surfaces of a single grain and inter-grain couplings t2 between nearby surfaces of two neighboring grains. We show that when t1 < t2 the entire system behaves like a single topological insulator whose outermost surfaces have gapless spectra described by Dirac Hamiltonians. We find a relation between t1, t2 and the surface state penetration depth λ which explains the properties of λ that are seen experimentally. We also present an expression for the surface state Berry phase as a function of the hybridization between the surface states and a Zeeman magnetic field that may be present in the system. At the end we theoretically studied the surface states on one of the side surfaces of the granular system and showed that many pairs of surface states can exist on the side surfaces depending on the length of the unit cell of the granular system. • In the sixth chapter we present our work on junctions of p-wave superconductors (SC) and normal metals (NM) in one dimension. We first study transport in a system where a SC wire is sandwiched between two NM wires. For such a system it is known that there is a Majorana mode at the junction between the SC and each NM lead. If the p-wave pairing changes sign at some point inside the SC, two additional Majorana modes appear near that point. We study the effect of all these modes on the subgap conductance between the leads and the SC. We derive an analytical expression as a function of and the length L of the SC for the energy shifts of the Majorana modes at the junctions due to hybridization between them; the energies oscillate and decay exponentially as L is increased. The energies exactly match the locations of the peaks in the conductance. We find that the subgap conductances do not change noticeably with the sign of . So there is no effect of the extra Majorana modes which appear inside the SC (due to changes in the signs of Δ) on the subgap conductance. Next we study junctions of three p-wave SC wires which are connected to the NM leads. Such a junction is of interest as it is the simplest system where braiding of Majorana modes is possible. Another motivation for studying this system is to see if the subgap transport is affected by changes in the signs of . For sufficiently long SCs, there are zero energy Majorana modes at the junctions between the SCs and the leads. In addition, depending on the signs of the Δ’s in the three SCs, there can also be one or three Majorana modes at the junction of the three SCs. We show that the various subgap conductances have peaks occurring at the energies of all these modes; we therefore get a rich pattern of conductance peaks. Next we study the effects of interactions between electrons (in the NM leads) on the transport. We use a renormalization group approach to study the effect of interactions on the conductance at energies far from the SC gap. Hence the earlier part of this chapter where we studied the transport at an energy E inside the SC gap (so that − < E < Δ) differs from this part where we discuss conductance at an energy E where |E| ≫ . For the latter part we assume the region of three SC wires to be a single region whose only role is to give rise to a scattering matrix for the NM wires; this scattering matrix has both normal and Andreev elements (namely, an electron can be reflected or transmitted as either an electron or a hole). We derive a renormalization group equation for the elements of the scattering matrix by assuming the interaction to be sufficiently weak. The fixed points of the renormalization group flow and their stabilities are studied; we find that the scattering matrix at the stable fixed point is highly symmetric even when the microscopic scattering matrix and the interaction strengths are not symmetric. Using the stability analysis we discuss the dependence of the conductances on the various length scales of the problem. Finally we propose an experimental realization of this system which can produce different signs of the p-wave pairings in the different SCs. • In the seventh chapter we show that the application of circularly polarized electro-magnetic radiation on the surface of a Weyl semimetal can generate states at that surface. The surface states can be characterized by their momenta due to translation invariance. The Floquet eigenvalues of these states come in complex conjugate pairs rather than being equal to ±1. If the amplitude of the radiation is small, we find some unusual bulk-boundary relations: the Floquet eigenvalues of the surface states lie at the extrema of the Floquet eigenvalues of the bulk system when the latter are plotted as a function of the momentum perpendicular to the surface, and the peaks of the Fourier transforms of the surface state wave functions lie at the momenta where the bulk Floquet eigenvalues have extrema. For the case of zero surface momentum, we can analytically derive interesting scaling relations between the decay lengths of the surface states and the amplitude and penetration depth of the radiation. For topological insulators, we again find that circularly polarized radiation can generate states on the surfaces; these states have much larger decay lengths (which can be tuned by the radiation amplitude) than the topological surface states which are present even in the absence of radiation. Finally, we show that radiation can generate surface states even for trivial insulators.