This thesis contains both physics analysis and hardware studies. It consists of two primary sections: the results of a search for heavy Majorana mass neutrinos, using the event signature of same (like) sign charged electron pairs ($e^{\pm} e^{\pm}$ ) and two jets, and the results of studies to upgrade the Hadronic Forward (HF) and Hadronic Endcap (HE) subdetectors in the Compact Muon Solenoid (CMS) detector in response to the high intensity proton-proton collisions generated at the Large Hadron Collider (LHC) at European Organization for Nuclear Research (CERN, Conseil Europ\'{e}en pour la Recherche Nucl\'{e}aire). In this search for Majorana mass neutrinos, same sign dielectron ($e^{\pm} e^{\pm}$) + dijet events in the final state have been considered as a signature for neutrino particles. The analyzed data corresponds to an integrated luminosity of 19.7 fb\textsuperscript{-1} of proton-proton collisions at a center of mass energy of \begin{math}\sqrt{s} = 8\ TeV \end{math}, collected using the CMS detector during the 2012 operation at the LHC. Monte Carlo simulations accounting for the theoretical expectations of the Standard Model (SM) and the detector limitations are used to prototype the experiment and to test proposed analysis steps. No excess of events is observed in the data beyond the expected SM background. Upper limits are set on the mixing element squared, $|{V}_{eN}|^{2}$, of the heavy Majorana neutrino with standard model neutrinos, as a function of Majorana neutrino mass for masses in the range of 40-500 $GeV/c^2$. The detector upgrade search comprises three sections of this thesis. The first section describes the test results of 1785 multianode Hamamatsu R7600U-200-M4 photomultiplier tubes (PMT) in numerous parameters such as gain, dark current, and timing characteristics, which provide insights on the expected performance of the upgraded CMS-HF detector. These PMTs replaced the previous single anode R7525 PMTs because the glass windows of previous PMTs are the source of Cherenkov radiation, which causes a background noise in the experiment. The second section reports characterization results of two types of PMTs in a novel operation mode for Secondary Emission (SE) Ionization Calorimetry, which is a novel technique to measure electromagnetic shower particles in extreme radiation environments. The third section presents the test results of novel scintillating materials for CMS experiment in specific and future particle accelerators in general. These materials are Polyethylene Naphthalate (PEN), Polyethylene Terephthalate (PET), high efficiency mirror (HEM) and quartz plates with various organic and inorganic coating materials such as p-Terphenyl (pTp), Anthracene and Gallium-doped Zinc Oxide (ZnO:Ga). We have investigated them for radiation hardness, light yield, timing characteristics, and scintillation and transmission properties.

Il y a 75 ans, Ettore Majorana montrait que le neutrino, seule particule élémentaire de matière de charge électrique nulle, pouvait théoriquement être identique a son antiparticule. Si tel est le cas, alors un phénomène naturel nouveau devrait apparaître pour quelques rares isotopes : leur double désintégration beta sans émission de neutrino (0). La signature expérimentale de ce processus est simple : l'observation de deux électrons émis par le noyau dont la somme de leur énergie correspond a l'énergie de transition. Mais ce processus, s'il existe, est infiniment rare. La principale difficulté dans cette recherche est donc instrumentale : réussir à développer un détecteur ultra basse radioactivité, sans aucun bruit de fond. J'ai choisi comme première partie de mon HDR, d'écrire une revue expérimentale relativement détaillée des différents projets, mon souhait étant de montrer pour chaque expérience, ses avantages et limitations en mettant l'accent sur les techniques utilisées pour supprimer les bruits de fond. Ayant été très impliqué dans l'expérience NEMO-3, et travaillant maintenant dans le nouveau projet SuperNEMO, j'ai davantage détaillé ces deux expériences. J'ai également détaillé les projets de bolomètres scintillants. C'est en effet une technique que j'avais particulièrement étudiée ces dernières années car elle me semble être très prometteuse. Le dernier chapitre de cette première partie est un résumé permettant au lecteur qui le souhaite une revue plus rapide des différents projets actuels. Depuis 5 ans, je développe un détecteur basse radioactivité, appelé BiPo, dont l'objectif est de mesurer la radiopureté en 238U et 232Th des futures feuilles sources émettrices double beta qui seront installées dans le détecteur SuperNEMO. J'ai donc choisi comme deuxième partie de mon HDR, de présenter ce détecteur et de résumer les différents résultats obtenus.

<p>Boundary quantum phases ---a special type of quantum phenomena--- occur in the boundary part of the system. The boundary part can be a surface of a bulk material, an interface between two distinct system, and even it can be a single impurity or a impurity cluster embedded into a bulk system. The properties of the boundary degree of freedom can be affected by many strong electron correlation effects, mesoscopic effects, and topological effects, which, therefore, induce a vast variety of exotic boundary quantum phases. Many techniques for precise fabrication and measurement in nanostructures had been developed,</p><p>which can provide ways to prob, understand, and control those boundary quantum phases.</p><p>In this thesis, we focus on three types of the boundary quantum phases : Kondo effects, boundary quantum phase transitions, and Majorana fermions. Our motivation is to design and prob those effects by using a important type of nanostructures, i.e. quantum dots. A vast variety of models related to quantum dots (QDs) are studied theoretically, which includes a QD coupled to a mesoscopic bath, a quadruple QD system with metallic leads, a QD with dissipative environments, and a QD coupled to a Majorana fermion zero mode.</p><p>Quantum dots provide a way to study the interplay of Kondo effects and mesoscopic fuctuations. In chapter 5, we consider a model including an Anderson impurity (small QD) coupled to a mesoscopic bath (large QD). Both the weak and strong coupling Anderson impurity problems are characterized by Fermi-liquid theories with weakly interacting quasiparticles. We find that the fluctuations of single particle properties in the two limits are highly correlated and universal : The distributions of the spectrum within the Kondo temperature collapse to universal forms; and the strong coupling impurity changes the wave functions corresponding to the spectrum within the Kondo temperature. </p><p>Quantum dots also bring the possibility to study more complex quantum impurities (multi-QDs) and the competition among dierent interactions, which may induce exotic effects: boundary quantum phase transitions and novel Kondo effects. In chapter 7, we design a quadruple quantum dot system to study the competition among three types of interactions: Kondo, Heisenberg, and Ising. We find a rich phase diagram containing two sharp features : a Berezinsky-Kosterlitz-Thouless type quantum phase transition between a charge-ordered phase and a charge liquid phase and a U(1)XU(1) Kondo state with emergent symmetry from Z2 to U(1). In chapter 8, we study a dissipative resonant level model in which the coupling of a fermionc bath competes with a dissipation-induced bosonic bath. we establish an exact mapping from this dissipative resonant level model to a model of a quantum dot embedded into a Luttinger liquid wire, and we also find two kinds of boundary quantum phase transitions (a Berezinsky-Kosterlitz-Thouless type and a second order type).</p><p>Finally, in chapter 9, we propose an experimental system to detect Majorana fermion zero modes. This system consists of a spinless quantum do coupled to a Majorana fermion which exists in the end of a p-wave superconductor wire. The Majorana Fermion strongly infuence the transport properties of the quantum dot. The zero temperature conductance peak value (when the dot is on resonance and symmetrically coupled to the leads) is e^2/2h. In contrast, if the wire is in its topological trivial phase, the result is e^2/h; if the side-coupled mode is a regular fermionic zero mode, the result is zero. Driving the wire through the topological phase transition causes a sharp jump in the conductance by a factor of 1/2. This result can be used to detect the existence of Majorana fermions.</p> / Dissertation

This thesis is a study of three categories of problems in fermionic systems for which topology plays an important role: (i) The properties of zero modes arising in systems of fermions interacting with a bosonic background, with a special focus on Majorana modes arising in the superconductor state. We propose a method for counting Majorana modes and we study a mechanism for controlling their number parity in lattice systems, two questions that are of relevance to the protection of quantum bits. (ii) The study of dispersionless bands in two dimensions as a platform for correlated physics, where it is shown the possibility of stabilizing the fractional quantum Hall effect in a flat band with Chern number. (iii) The extension of the hierarchy of quantum Hall fluids to the case of time-reversal symmetric incompressible ground states describing a phase of strongly interacting topological insulators in two dimensions. / Physics

Cette thèse poursuit deux directions dans le domaine des isolants et supraconducteurs topologiques.Dans la première partie de la thèse nous étudions des isolants en deux dimensions sur réseau, présentant un effet Hall quantique anormal (c'est-à-dire en l'absence d'un champ magnétique externe), induit par la présence d'un flux magnétique inhomogène dans la maille. Le système possède des phase isolantes caractérisés par un invariant topologique, le nombre de Chern, qui est lié à la conductance portée par le bord états. Nous montrons que les modèles à deux bandes admettent des phase à nombre de Chern arbitraire, ou, de façon équivalente, un nombre arbitraire d'états de bord, quand on augmente la portée des couplages sur réseau. Cette compréhension est rendue possible grâce à la démonstration d'une formule montrant que le nombre de Chern d'une bande dépend de certains propriétés d'un ensemble discret de points dans la zone de Brillouin, les points de Dirac en l'absence du gap. Ces idées sont rendues plus concrètes dans l'étude du modèle de Haldane et dans la création d'un modèle artificiel avec cinq phases de Chern dont les états de bord sont déterminés en détail. La deuxième partie de la thèse porte sur les supraconducteurs topologiques unidimensionnels qui exhibent des états exotiques d'énergie zéro: les états liés de Majorana. Nous étudions ici la présence de fermions de Majorana dans des fils de semiconducteurs à fort couplage spin-orbite sous l'effet de proximité d'un supraconducteur d'onde s. Nous montrons que la polarisation de spin des degrés de liberté électroniques dans la fonction d'onde Majorana dépend du poids relatif du couplage spin-orbite Dresselhaus et Rashba. Nous étudions également les fermions de Majorana dans des jonctions linéaires longues supraconducteur-normal et supraconducteur-normal-supraconducteur (SNS) où ils apparaissent comme des états étendus dans la jonction normale. En outre, la géométrie d'anneaux peut être mise en correspondance avec une jonction SNS, et, sous l'action de gradients dans la phase supraconductrice, des fermions Majorana étendus se forment encore à l'intérieur du fil normal. Enfin, un modèle à deux bandes avec des fermions de Majorana multiples est traité. Nous démontrons que les jonctions Josephson construites à partir de ce modèle maintiennent l'une des signatures remarquables des fermions de Majorana, à savoir la périodicité 4π de l'effet Josephson fractionnaire.

We investigate quantum resonant transport in two different systems: (i) a ferromagnetic Scanning Tunneling Microscope (STM) tip coupled to an adatom (interacting) on a host surface (metallic or semiconductor), and (ii) a quantum dot connected to source and drain leads and side-coupled to a superconducting nanowire sustaining Majorana zero modes (Kitaev chain). Both problems are studied within the Green&rsquo;s functions approach, which allows us to determine the transport properties of the system. In the first setup, due to the ferromagnetic and nonmagnetic &lsquo;natures&rsquo; of the tip and host, respectively, it is possible to obtain the spin-diode effect, which occurs only in the singly occupied regime. In addition, because of the presence of the adsorbed atom on the surface, Friedel oscillations are observed in the current. The second system differs from the first mainly because it is spinless and there is no Coloumb interaction. Interestingly, we find that the Majorana mode of the wire leaks into the dot thus giving rise to a Majorana (zero mode) resonance in the dot, pinned to the Fermi level of the leads. Surprisingly, this resonance occurs even when the gate-controlled dot level is far above or far below the Fermi level of the leads. We study three possible experimental scenarios to probe unambigoulsy this Majorana mode in wires via these leaked/pinned modes. / Nesta tese investigamos transporte quântico ressonante em dois sistemas diferentes: (i) uma ponta STM ferromagnética acoplada a um átomo (interagente) adsorvido em uma superfície metálica ou semicondutora, e (ii) um ponto quântico conectado a reservatórios de elétrons e lateralmente acoplado a um nanofio supercondutor que possui modos de Majorana (cadeia Kitaev). Ambos os problemas são estudados no contexto de funções de Green, o que nos permite determinar as propriedades de transporte do sistema. Na primeira configuração, devido à natureza ferromagnética e não magnética da ponta STM e da superfície e, respectivamente, é possível obter o efeito diodo de spin, que ocorre apenas no regime em que o adátomo está ocupado com um único elétron. Além disso, por causa da presença do átomo adsorvido sobre a superfície, oscilções de Friedel são observadas na corrente. O segundo sistema é diferente do primeiro, principalmente pela ausência da interação de Coloumb e pelo fato de não ter spin. Curiosamente, vemos que o modo de Majorana do fio vai para o ponto quântico dando origem assim a um modo com energia zero no ponto quântico localizado sempre no nível de Fermi dos contatos. Surpreendentemente, essa ressonância ocorre mesmo quando o nível do ponto quântico, controlado por uma tensão externa, está muito acima ou muito abaixo do nível de Fermi dos contatos. Propomos três possíveis cenários experimentais para identificar de maneira conclusiva este modo de Majorana em fios através do modo que aparece no ponto quântico.

Nanowires with Rashba spin-orbit coupling represent a promising platform for the realization of one-dimensional topological superconductivity and Majorana bound states. In this work we investigate Majorana bound states in hybrid normal-superconductor and short superconductor-normal-superconductor junctions based on nanowires with Rashba spin-orbit coupling. In particular, we explore consequences of the topological phase transition as well as the non-locality and self conjugation properties of the Majorana states on the low-energy spectrum and the Josephson effect in the case of superconductor-normal-superconductor junctions. Our work shows the great potential of hybrid junctions as a platform for the study of topological superconductivity and Majorana bound states.

Thesis advisor: Kevin S. Bedell / We present several results based upon non-trivial extensions of Landau-Fermi liquid theory. First proposed in the mid-20th century, the Fermi liquid approach assumes an adiabatic “switching-on” of the interaction, which allows one to describe the collective excitations of the many-body system in terms of weakly-interacting quasiparticles and quasiholes. At its core, Landau-Fermi liquid theory is often considered a perturbative approach to study the equilibrium thermodynamics and out-of-equilibrium response of weakly-correlated itinerant fermions, and therefore non-trivial extensions and consequences are usually overlooked in the contemporary literature. Instead, more emphasis is often placed on the breakdown of Fermi liquid theory, either due to strong correlations, quantum critical fluctuations, or dimensional constraints. After a brief introduction to the theory of a Fermi liquid, I will first apply the Landau quasiparticle paradigm to the theory of itinerant Majorana-like fermions. Defined as fermionic particles which are their own anti-particle, traditional Majorana zero modes found in topological materials lack a coherent number operator, and therefore do not support a Fermi liquid-like ground state. To remedy this, we will apply a combinatorical approach to build a statistical theory of self-conjugate particles, explicitly showing that, under this definition, a filled Fermi surface exists at zero temperature. Landau-Fermi liquid theory is then used to describe the interacting phase of these Majorana particles, from which we find unique signatures of zero sound in addition to exotic, non-analytic contributions to the specific heat. The latter is then exploited as a “smoking-gun” signature for Majorana-like excitations in the candidate Kitaev material Ag3LiIr2O6, where experimental measurements show good agreement with a sharply-defined, “Majorana-Fermi surface” predicted in the underlying combinatorial treatment. I will then depart from Fermi liquid theory proper to tackle the necessary conditions for the applicability of Luttinger’s theorem. In a nutshell, Luttinger’s theorem is a powerful theorem which states that the volume of phase space contained in the Fermi surface is invariant with respect to interaction strength. In this way, whereas Fermi liquid only describes fermionic excitations near the Fermi surface, Luttinger’s theorem describes the fermionic degrees of freedom throughout the entire Fermi sphere. We will show that Luttinger’s theorem remains valid only for certain frequency and momentum-dependencies of the self-energy, which correlate to the exis- tence of a generalized Fermi surface. In addition, we will show that the existence of a power-law Green’s function (a unique feature of “un-particle” systems and a proposed characteristic of the pseudo-gap phase of the cuprate superconductors) forces Luttinger’s theorem and Fermi liquid theory to be mutually exclusive for any non-trivial power of the Feynman propagator. Finally, we will return to Landau-Fermi liquid theory, and close with novel out-of-equilibrium behavior and stability in unconventional Fermi liquids. First, we will consider a perfectly two- dimensional Fermi liquid. Due to the reduction in dimension, the traditional mode expansion in terms of Legendre polynomials is modified to an expansion in terms of Chebyshev polynomials. The resulting orthogonality conditions greatly modifies the stability and collective modes in the 2D system. Second, we will look at a Fermi liquid in the presence of a non-trivial gauge field. The existence of a gauge field will effectively shift the Fermi surface in momentum space, resulting in, once again, a modified stability condition for the underlying Fermi liquid. Supplemented with a modernized version of Mermin’s condition for the propagation of zero sound, we outline the full effects a spin symmetric or anti-symmetric gauge would have on a Fermi liquid ground state. / Thesis (PhD) — Boston College, 2021. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

We study three different kinds of mesoscopic systems – in the intermediate region between macroscopic and microscopic scales consisting of many interacting constituents: We consider particle entanglement in one-dimensional chains of interacting fermions. By employing a field theoretical bosonization calculation, we obtain the one-particle entanglement entropy in the ground state and its time evolution after an interaction quantum quench which causes relaxation towards non-equilibrium steady states. By pushing the boundaries of the numerical exact diagonalization and density matrix renormalization group computations, we are able to accurately scale to the thermodynamic limit where we make contact to the analytic field theory model. This allows to fix an interaction cutoff required in the continuum bosonization calculation to account for the short range interaction of the lattice model, such that the bosonization result provides accurate predictions for the one-body reduced density matrix in the Luttinger liquid phase. Establishing a better understanding of how to control entanglement in mesoscopic systems is also crucial for building qubits for a quantum computer. We further study a popular scalable qubit architecture that is based on Majorana zero modes in topological superconductors. The two major challenges with realizing Majorana qubits currently lie in trivial pseudo-Majorana states that mimic signatures of the topological bound states and in strong disorder in the proposed topological hybrid systems that destroys the topological phase. We study coherent transport through interferometers with a Majorana wire embedded into one arm. By combining analytical and numerical considerations, we explain the occurrence of an amplitude maximum as a function of the Zeeman field at the onset of the topological phase – a signature unique to MZMs – which has recently been measured experimentally [Whiticar et al., Nature Communications, 11(1):3212, 2020]. By placing an array of gates in proximity to the nanowire, we made a fruitful connection to the field of Machine Learning by using the CMA-ES algorithm to tune the gate voltages in order to maximize the amplitude of coherent transmission. We find that the algorithm is capable of learning disorder profiles and even to restore Majorana modes that were fully destroyed by strong disorder by optimizing a feasible number of gates. Deep neural networks are another popular machine learning approach which not only has many direct applications to physical systems but which also behaves similarly to physical mesoscopic systems. In order to comprehend the effects of the complex dynamics from the training, we employ Random Matrix Theory (RMT) as a zero-information hypothesis: before training, the weights are randomly initialized and therefore are perfectly described by RMT. After training, we attribute deviations from these predictions to learned information in the weight matrices. Conducting a careful numerical analysis, we verify that the spectra of weight matrices consists of a random bulk and a few important large singular values and corresponding vectors that carry almost all learned information. By further adding label noise to the training data, we find that more singular values in intermediate parts of the spectrum contribute by fitting the randomly labeled images. Based on these observations, we propose a noise filtering algorithm that both removes the singular values storing the noise and reverts the level repulsion of the large singular values due to the random bulk.

<p dir="ltr">In this work we investigate the existence and experimentally measurable properties of Majorana quasiparticles in a few-body number conserving atomic system.</p>