Made available in DSpace on 2018-08-01T22:30:00Z (GMT). No. of bitstreams: 1 tese_6812_Tese final Thiago Oakes20141114-121507.pdf: 378469 bytes, checksum: 13e58c69ea83014550c9b1bd4e49cfd3 (MD5) Previous issue date: 2013-08-23 / CAPES / Neste trabalho calculamos a energia do estado fundamental do átomo de hidrogênio levando em conta as contribuições advindas da presença de um comprimento mínimo. O cenário de comprimento mínimo é introduzido pela modificação da equação de Dirac através da álgebra de Heisenberg modificada (álgebra de Kempf). Com a introdução do potencial Coulombiano no novo operador de energia de Dirac, calculamos a mudança na energia do estado fundamental do átomo de hidrogênio em primeira ordem do parâmetro relacionado ao comprimento mínimo via teoria de perturbação. / In this work we calculate the correction to the ground state energy of the hydrogen atom due to contribuitions arising from the presence of a minimal length. The minimal length scenario is introduced by means of modifying the Dirac equation truogh a deformed Heisenberg algebra (Kempf algebra). With the introduction of the Coulomb potential in the new Dirac energy Operator, we calculate the energy shift of the ground state of the hydrogen atom in first order of the parameter related to the minimal length via perturbation theory

Dans cette thèse, nous avons étudié les propriétés électroniques de WS2 et WSe2 par µ-PL, spectroscopie Raman, absorption optique inter bande et µ-PL résolue en temps combinées avec des champs magnétiques intenses. Nous montrons que l'émission de l'exciton par rapport au trion dans les monocouches de WS2 et WSe2 est fonction de la puissance du laser utilisé pour l'excitation de la µ-PL. De plus, nous montrons que l'intensité de l'émission du trion peut être contrôlée indépendamment en utilisant une énergie d'excitation plus basse que la bande interdite. Il s'agit d'une preuve du contrôle de la densité de porteurs dans ces systèmes 2D. Nous avons également étudié la diffusion Raman en résonance dans une monocouche de WS2. Nous observons un mode acoustique (2LA), seulement 4cm-1 en-dessous du mode E12g. Nous montrons qu'en fonction du rapport des intensité et la largeur de ligne de chacun de ces deux pics, toute analyse qui néglige la présence de la mode 2LA peut conduire à une estimation incorrecte du nombre de couche. Les propriétés électroniques de chaque vallée d'une monocouche de WSe2 ont été sondées par µ-PL via l'étude de l'émission et de la polarisation des excitons neutres et chargés. Nous montrons que le temps de diffusion de l'exciton entre les vallées de K+ et K- est de l'ordre de plusieurs ps. Enfin, grâce à la magnéto-spectroscopie, nous mettons en évidence différents types de porteurs de charges entre la monocouche et le cristal massif. Nous montrons que dans la monocouche, les porteurs de charge se comportent comme des fermions massifs Dirac, tandis que dans le monocristal de WSe2 nous observons un comportement excitonique, décrit par le modèle de l'atome d'hydrogène / In this thesis, we have studied tungsten dichalcogenides (WS2 and WSe2) by means of steady-state µ-photoluminescence (µ-PL) and Raman spectroscopy, optical interband absorption and time-resolved µ-PL techniques in the visible spectral range combined with high magnetic fields. We demonstrate that the ratio between the trion and exciton emission can be tuned by varying the power of the laser used for excitation of the µ-PL in ungated monolayer WS2 and WSe2 samples. Moreover, the intensity of the trion emission can be independently tuned using additional sub band gap illumination. This is a direct evidence that we can control the density of carriers in a 2D system. We have investigated the resonant Raman scattering in a WS2 monolayer. We observe a second order longitudinal acoustic mode (2LA) at only 4cm-1 below the first order E12g mode. We demonstrate, that depending on the intensity ratio and the respective line widths of these two peaks, any analysis which neglects the presence of the 2LA mode can lead to a potentially incorrect assignment for the number of layers. The valley dynamics in monolayer WSe2 has been probed by monitoring the emission and polarization dynamics of neutral and charged excitons in µ-PL. We demonstrate that the exciton inter valley scattering between the K+ and K- valleys is in the order of several picoseconds. Finally, using magneto-spectroscopy studies, we reveal the very different nature of carriers in monolayer and bulk dichalcogenides. We demonstrate that in monolayer WSe2, the carriers behave as massive Dirac fermions, while in bulk WSe2 we observe a distinctly excitonic behavior which is best described within the hydrogen model

Orientador: Waldyr A. Rodrigues Jr. / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Científica / Made available in DSpace on 2018-07-18T17:46:13Z (GMT). No. of bitstreams: 1 VazJunior_Jayme_D.pdf: 3696074 bytes, checksum: 38c75818b237a8ff519bd3727c669660 (MD5) Previous issue date: 1993 / Resumo: A relação entre a teoria do elétron e o eletromagnetismo é discutida com base no uso da álgebra do espaço-tempo e do spinor de Dirac-Hestenes. Desta relação surge uma equação não-linear como uma alternativa, a princípio mais satisfatória, à equação de Dirac. Este estudo é possível uma vez formulada a teoria do spinor de Dirac-Hestenes como uma classe de equivalência de elementos da sub-álgebra par da álgebra do espaço-tempo. / Abstract: The relationship between the theory of electron and electromagnetism is discussed by using the spacetime algebra and the Dirac-Hestenes spinor. From this relationship it emerges a non-linear equation which seems to be more satisfactory than Dirac equation. This study is possible once it is formulated the theory of Dirac- Hestenes spinor as an equivalence class of elements of the even subalgebra of the spacetime algebra. / Doutorado / Doutor em Matemática Aplicada

Thesis advisor: Kevin S. Bedell / One of the many achievements of renowned physicist L.D. Landau was the formulation of Fermi Liquid Theory (FLT). Originally debuted in the 1950s, FLT has seen abundant success in understanding degenerate Fermi systems and is still used today when trying to understand the physics of a new interacting Fermi system. Of its many advantages, FLT excels in explaining why interacting Fermi systems behave like their non-interacting counterparts, and understanding transport phenomena without cumbersome and confusing mathematics. In this work, FLT is applied to systems whose low energy excitations obey the massless Dirac equation; i.e. the energy dispersion is linear in momentum, ε α ρ, as opposed to the normal quadratic, ε α ρ². Such behavior is seen in numerous, seemingly unrelated, materials including graphene, high T[subscript]c superconductors, Weyl semimetals, etc. While each of these materials possesses its own unique properties, it is their low energy behavior that provides the justification for their grouping into one family of materials called Dirac materials (DM). As will be shown, the linear spectrum and massless behavior leads to profound differences from the normal Fermi liquid behavior in both equilibrium and transport phenomena. For example, with mass having no meaning, we see the usual effective mass relation from FLT being replaced by an effective velocity ratio. Additionally, as FLT in d=2 has been poorly studied in the past, and since the most famous DM in graphene is a d=2 system, a thorough analysis of FLT in d=2 is presented. This reduced dimensionality leads to substantial differences including undamped collective modes and altered quasiparticle lifetime. In chapter 3, we apply the Virial theorem to DM and obtain an expression for the total average ground state energy $E=\frac{B}{r_s}$ where $B$ is a constant independent of density and $r_s$ is a dimensionless parameter related to the density of the system: the interparticle spacing $r$ is related to $r_s$ through $r=ar_s$ where $a$ is a characterstic length of the system (for example, in graphene, $a=1.42$ \AA). The expression derived for $E$ is unusual in that it's typically impossible to obtain a closed form for the energy with all interactions included. Additionally, the result allows for easy calculation of various thermodynamic quantities such as the compressibility and chemical potential. From there, we use the Fermi liquid results from the previous chapter and obtain an expression for $B$ in terms of constants and Fermi liquid parameters $F_0^s$ and $F_1^s$. When combined with experimental results for the compressibility, we find that the Fermi liquid parameters are density independent implying a unitary like behavior for DM. In chapter 4, we discuss the alleged universal KSS lower bound in DM. The bound, $\frac{\eta}{s}\geq\frac{\hbar}{4\pi k_B}$, was derived from high energy/string theory considerations and was conjectured to be obeyed by all quantum liquids regardless of density. The bound provides information on the interactions in the quantum liquid being studied and equality indicates a nearly perfect quantum fluid. Since its birth, the bound has been highly studied in various systems, mathematically broken, and poorly experimented on due to the difficult nature of measuring viscosity. First, we provide the first physical example of violation by showing $\frac{\eta}{s}\rightarrow 0$ as $T\rightarrow T_c$ in a unitary Fermi gas. Next, we determine the bound in DM in d=2,3 and show unusual behavior that isn't seen when the bound is calculated for normal Fermi systems. Finally we conclude in chapter 5 and discuss the outlook and other avenues to explore in DM. Specifically, it must be pointed out that the physics of what happens near charge neutrality in DM is still poorly understood. Our work in understanding the Fermi liquid state in DM is necessary in understanding DM as a whole. Such a task is crucial when we consider the potential in DM, experimentally, technologically, and purely for our understanding. / Thesis (PhD) — Boston College, 2020. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

In this project a theoretical study of the so called gyromagnetic ratio was done by investigating classical mechanics, Dirac theory and string theory. The gyromagnetic ratio is a constant term appearing in the coupling between angular momentum and magnetic moment for a particle. A universality in quantum field theory claiming g = 2 regardless of spin is known to exist which also agrees with the found values (g = 2) of the Dirac and string theory. The proof of the aforementioned universality in quantum field theory was sketched in the project by showing that the W-boson Lagrangian is well behaved in the massless limit. Furthermore it is shown that the spin equations of motion for a particle is greatly reduced if g = 2 regardless of spin. / I det här projektet utfördes en teoretisk studie av den så kallade gyromagnetsika kvoten genom att undersöka klassisk mekanik, Dirac-teori och strängteori. Den gyromagnetiska kvoten är en konstant term som visar sig i kopplingen mellan rörelsemängsmoment och magnetiskt moment för en partikel. I kvantfältsteori existerar en universalitet som hävdar att g = 2 oberoende av spin. Denna universalitet stämmer överens med de funna värden på g från Dirac-teori och strängtoeri. Beviset för denna universalitet testades genom ett exempel där Lagrangianen för W-bosonen i kvantfältsteori visades bete sig som förväntat när massan för partikeln tilläts gå mot noll. Vidare undersöktes rörelseekvationerna för ett system helt bestämt av dess spin. I dessa kan det visas att ett universellt värde på g oavsett spin reducerar dessa ekvationer avsevärt.

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We study the effect of the so-called half-hound states on the Titchmarsh-Weyl M(λ)· function and the S-matrix for a one dimensional Dirac system. For short range potentials with finite first (absolute) moments, we gave an M(λ) characterization of half bound states and, as a corollary, we deduce the behavior of the spectral function near the spectral gap endpoints. Further, we establish community of the S-matrix in momentum space and prove the Levinson theorem as a corollary to this analysis. We also obtain explicit asymptotics of the S-matrix for power-law potentials / Ph. D.

Orientador: Antonio Carlos Ferreira Seridonio / Resumo: Embora o estado fundamental de moléculas covalentes diatômicas na natureza seja inevitavelmente ligante com primeiro estado excitado antiligante, foi demonstrado teoricamente que um par de impurezas, colocadas dentro de um semimetal de Dirac tridimensional, pode exibir um estado fundamental antiligante. Esse contraste com a natureza de moléculas isoladas surge devido a emergência de uma inesperada interação de longo alcance mediada pelos elétrons de condução com comportamento relativístico inerente ao semimetal de Dirac. Os perfis dos orbitais moleculares ligante e antiligante desse estado molecular são obtidos por meio da determinação teórica da densidade local de estados na superfície, cuja medida experimental pode ser realizada com auxílio da microscopia de corrente de tunelamento. Para o semimetal de Weyl, foi evidenciado que a quebra de simetria de reversão temporal é responsável por uma transição energética de s- para p-wave nos orbitais individuais das impurezas. Como consequência dessa transição e da característica direcional dos orbitais p-wave, a interferência entre as impurezas produz orbitais do tipo sigma quando frontais e do tipo \pi quando paralelas. Além disso, foi verificado que o surgimento do efeito magneto quiral, devido a separação dos nós de Weyl com quiralidades opostas, produz polarização nos orbitais moleculares via oscilações de Friedel. Por fim, foi analisado o efeito dos graus de liberdade de vibração da rede, presentes em qualquer sistema realísti... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: Although the ground state of the diatomic molecules in nature is inevitably bonding with its first excited state is antibonding, it was demonstrate theoretically that a pair of impurities, placed buried in three-dimensional Dirac semimetals, may exhibit an antibonding ground state. This contrast with the nature of isolated molecules emerges due to an unexpected long-range interaction mediated by the conduction electrons with relativist behavior inherent to Dirac semimetal. The bonding and antibonding molecular profiles were obtained by theoretical determination of the local density states on the system surface, whose experimental measurement can be performed with the help of tunneling current microscopy. For theWeyl semimetal, it was evidenced that the time reversal symmetry break is responsible for an energy transition from s- to p-wave in the individual orbitals of the impurities. As a consequence of this transition and the directional characteristic of the p-wave orbitals, the interference between the impurities produces p-type orbitals when frontal and -type orbitals when parallel. In addition, it was found that the appearance of the chiral magneto effect, due to the separation of the Weyl nodes with opposite chiralities, produces polarization in the molecular orbitals via Friedel oscillations. Lastly, it was addressed the effect of vibrational degrees of freedom, which are present in any realistic system, in the formation and features of (anti)bonding molecular state, ... (Complete abstract click electronic access below) / Doutor