Recentemente, tem sido questionada a validade do teorema de Migdal nos fuieretos dopados supercondutores. Motivados por esse problema, realizamos nesta dissertação uma revisão das propriedades físicas destes novos e notáveis materiais: os fulerenos e outros representantes desta família de compostos orgânicos que possuem estrutura geométrica de gaiola fechada. Em primeiro lugar abordamos, ainda que de maneira sucinta, alguns fundamentos da teoria microscópica BCS (Bardeen, Cooper e Schrieffer, 1961) da supercondutividade, tais como o problema da instabilidade do líquido de Fermi, a formação de pares de Cooper, o método da transformação canônica para demonstrar o aparecimento da interação efetiva atrativa entre os elétrons do par, as equações de Gor'kov demonstrando o surgimento do gap supercondutor, e a expressão BCS da temperatura crítica no limite de acoplamento fraco. Após, revisamos o trabalho realizado por Grimaldi, Cappelluti e Pietronero (1995), sobre a supercondutividade não adiabática nos fuieretos dopados, no qual são feitas correções de vértice para a interação elétron-fônon, usando o método perturbativo. Naquele trabalho eles utilizam um modelo de fônons de Einstein com uma única freqüência para caracterizar a função espectral de Eliashberg, necessária para obter tais correções de vértice Nossa proposta neste trabalho é generalizar este modelo por um constituído de várias Lorentzianas truncadas, centradas nas freqüências dos principais modos de vibração da rede cristalina: os intermoleculares, os ópticos e os intramoleculares. Encontramos como resultado deste estudo que as correções de vértice, com contribuição multifonônica, introduzem modificações substancias como um aumento da temperatura crítica e variação no coeficiente isotópico, dando resultados mais próximos dos obtidos experimentalmente, em contraste daqueles obtidos na teoria de Migdal-Eliashberg, sem correções de vértice.

Neste trabalho desenvolvemos um modelo efetivo para a descrição da matéria nuclear, que incorpora os resultados obtidos, para a descrição de um núcleon, pelo modelo de sacola difusa. O sistema nuclear será descrito via uma função de energia interna, que compreende um termo livre e outro que leva em conta a interação entre os núcleons. A parte livre, por se tratar de um sistema de férmions, corresponderá à energia de um gásde Fermi livre. Além disso, para evitar a superposição de dois ou mais núcleons, introduzimos um volume de exclusão a la Van der Waals. Na parte integrante, a troca de píons entre os núcleons será levada em conta via um potêncial efetivo. A função energia interna dependerá da densidade da matéria nuclear e também de um parâmetro que determinará o volume esperado de cada núcleon na matéria nuclear. O valor deste parâmetro será um pouco diferente do valor encontrado para um núcleons isolado, devido à interação entre eles. Obtém-se então resultados para a energia de ligação por núcleon para a matéria nuclear simétrica e para a matéria de nêutrons, bem como para a equação de estado da matéria de nêutrons.

The aim of this thesis was to identify topologically protected states in the materials SnTe and Fe3Sn2. Such states are currently receiving a large amount of interest due to their applications for spintronic devices. Recently SnTe was discovered to be a crystalline topological insulator, a state of matter where its surface is highly conducting while the bulk remains insulating. However detection of these surface states is difficult using transport measurements, since the bulk is not totally insulating but still contains a large number of free carriers. SnTe undergoes a rhombohedral structural distortion on cooling caused by a soft transverse optic phonon, with the exact Tc strongly dependent on the carrier concentration. The distortion acts to lower crystal symmetry removing some of the symmetries that protect the surface state. Single crystal samples displaying the structural transition were grown and investigated using inelastic X-ray scattering to measure the phonon softening previously reported by other authors. The soft phonon was seen to recover again after distortion indicative of a 2nd order ferroelectric transition. This is the first reported discovery of the recovery showing the distortion is ferroelectric in nature. Shubnikov de Haas quantum oscillations were measured to study the Fermi surface under ambient and high hydrostatic pressure conditions. A distortion of the Fermi surface caused by the structural transition was evident, resulting in 4 distinct oscillation frequencies. However at applied pressures above 6 kbar, the transition was suppressed and only 1 oscillation measured. A two component Hall response also becomes apparent under high pressure. The possible origin of this and its relation to possible surface states is discussed. The anomalous Hall effect was also measured in the ferromagnet Fe3Sn2 which has a bilayer Kagome structure. Previous measurements on polycrystalline Fe3Sn2 suggested a non-collinear spin rotation from the spins pointing along the c-axis at high temperature to lying in the a-b plane below 80 K. A spin glass phase is then expected below 80 K. Single crystal magnetisation measurements carried out in this thesis show the spins are in the a-b plane at high temperatures and begin to display a ferromagnetic component along the c-axis approaching 80 K. The difference is accounted for by considering the demagnetising factor in the plate shaped single crystals. For this temperature range an applied field along the c-direction however rotates the moments towards c. At intermediate fields there are strong features evident in both the anomalous Hall effect and magnetoresistance. These features may be due to a topological Hall effect caused by a non-collinear spin structure. The possible existence of Skyrmion excitations was also recently discussed theoretically in Fe3Sn2. Our data is more suggestive of static Skyrmions known to cause topological Hall effects in MnSi.

abstract: In this dissertation two kinds of strongly interacting fermionic systems were studied: cold atomic gases and nucleon systems. In the first part I report T=0 diffusion Monte Carlo results for the ground-state and vortex excitation of unpolarized spin-1/2 fermions in a two-dimensional disk. I investigate how vortex core structure properties behave over the BEC-BCS crossover. The vortex excitation energy, density profiles, and vortex core properties related to the current are calculated. A density suppression at the vortex core on the BCS side of the crossover and a depleted core on the BEC limit is found. Size-effect dependencies in the disk geometry were carefully studied. In the second part of this dissertation I turn my attention to a very interesting problem in nuclear physics. In most simulations of nonrelativistic nuclear systems, the wave functions are found by solving the many-body Schrödinger equations, and they describe the quantum-mechanical amplitudes of the nucleonic degrees of freedom. In those simulations the pionic contributions are encoded in nuclear potentials and electroweak currents, and they determine the low-momentum behavior. By contrast, in this work I present a novel quantum Monte Carlo formalism in which both relativistic pions and nonrelativistic nucleons are explicitly included in the quantum-mechanical states of the system. I report the renormalization of the nucleon mass as a function of the momentum cutoff, an Euclidean time density correlation function that deals with the short-time nucleon diffusion, and the pion cloud density and momentum distributions. In the two nucleon sector the interaction of two static nucleons at large distances reduces to the one-pion exchange potential, and I fit the low-energy constants of the contact interactions to reproduce the binding energy of the deuteron and two neutrons in finite volumes. I conclude by showing that the method can be readily applied to light-nuclei. / Dissertation/Thesis / Doctoral Dissertation Physics 2018

Neste trabalho desenvolvemos um modelo efetivo para a descrição da matéria nuclear, que incorpora os resultados obtidos, para a descrição de um núcleon, pelo modelo de sacola difusa. O sistema nuclear será descrito via uma função de energia interna, que compreende um termo livre e outro que leva em conta a interação entre os núcleons. A parte livre, por se tratar de um sistema de férmions, corresponderá à energia de um gásde Fermi livre. Além disso, para evitar a superposição de dois ou mais núcleons, introduzimos um volume de exclusão a la Van der Waals. Na parte integrante, a troca de píons entre os núcleons será levada em conta via um potêncial efetivo. A função energia interna dependerá da densidade da matéria nuclear e também de um parâmetro que determinará o volume esperado de cada núcleon na matéria nuclear. O valor deste parâmetro será um pouco diferente do valor encontrado para um núcleons isolado, devido à interação entre eles. Obtém-se então resultados para a energia de ligação por núcleon para a matéria nuclear simétrica e para a matéria de nêutrons, bem como para a equação de estado da matéria de nêutrons.

Recentemente, tem sido questionada a validade do teorema de Migdal nos fuieretos dopados supercondutores. Motivados por esse problema, realizamos nesta dissertação uma revisão das propriedades físicas destes novos e notáveis materiais: os fulerenos e outros representantes desta família de compostos orgânicos que possuem estrutura geométrica de gaiola fechada. Em primeiro lugar abordamos, ainda que de maneira sucinta, alguns fundamentos da teoria microscópica BCS (Bardeen, Cooper e Schrieffer, 1961) da supercondutividade, tais como o problema da instabilidade do líquido de Fermi, a formação de pares de Cooper, o método da transformação canônica para demonstrar o aparecimento da interação efetiva atrativa entre os elétrons do par, as equações de Gor'kov demonstrando o surgimento do gap supercondutor, e a expressão BCS da temperatura crítica no limite de acoplamento fraco. Após, revisamos o trabalho realizado por Grimaldi, Cappelluti e Pietronero (1995), sobre a supercondutividade não adiabática nos fuieretos dopados, no qual são feitas correções de vértice para a interação elétron-fônon, usando o método perturbativo. Naquele trabalho eles utilizam um modelo de fônons de Einstein com uma única freqüência para caracterizar a função espectral de Eliashberg, necessária para obter tais correções de vértice Nossa proposta neste trabalho é generalizar este modelo por um constituído de várias Lorentzianas truncadas, centradas nas freqüências dos principais modos de vibração da rede cristalina: os intermoleculares, os ópticos e os intramoleculares. Encontramos como resultado deste estudo que as correções de vértice, com contribuição multifonônica, introduzem modificações substancias como um aumento da temperatura crítica e variação no coeficiente isotópico, dando resultados mais próximos dos obtidos experimentalmente, em contraste daqueles obtidos na teoria de Migdal-Eliashberg, sem correções de vértice.

In the past decade the interest in molecular electronic devices has escalated. The synthesis of molecular crystals has improved, providing single crystals or thin films with mobility comparable with or even higher than amorphous silicon. Their mechanical flexibility admits new types of applications and usage of electronic devices. Some of these organic crystals also display magnetic effects. Furthermore, the fullerene and carbon nanotube allotropes of carbon are prominent candidates for various types of applications. The carbon nanotubes, in particular, are suitable for molecular wire applications with their robust, hollow and almost one-dimensional structure and diverse band structure. In this thesis, we have theoretically investigated carbon based materials, such as carbon nanotubes, pentacene and spiro-biphenalenyl neutral radical molecular crystals. The work mainly deals with the electron structure and the transport properties thereof. The first studies concerns effects and defects in devices of finite carbon nanotubes. The transport properties, that is, conductance, are calculated with the Landauer approach. The device setup contains two metallic leads attached to the carbon nanotubes. Structural defects as vacancies and bending are considered for single-walled carbon nanotubes. For the multi-walled carbon nanotubes the focus is on inter-shell interaction and telescopic junctions. The current voltage characteristics of these systems show clear marks of quantum dot behaviour. The influence of defects as vacancies and geometrical deformations are significant for infinite systems, but in these devices they play a minor role. The rest of the studies concern molecular crystals, treated with density-functional theory (DFT). Inspired by the enhance of the electrical conductivity obtained experimentally by doping similar materials with alkali metals, calculations were performed on bundles of single-walled carbon nanotubes and pentacene crystals doped with potassium. The most prominent effect of the potassium intercalation is the shift of Fermi level in the nanotube bands. A sign of charge transfer of the valence electrons of the potassium atoms. Semi-conducting bundles become metallic and metallic bundles gain density of states at the Fermi level. In the semi-conducting pristine pentacene crystals structural transitions occur upon doping. The herringbone arrangement of the pristine pentacene molecules relaxes to a more π-stacked structure causing more dispersive bands. The charge transfer shifts the Fermi level into the lowest unoccupied molecular orbital band and turns the crystal metallic. Finally, we have studied molecular crystals of spiro-biphenalenyl neutral radicals. According to experimental studies, some of these materials show simultaneous electrical, optical and magnetical bistability. The electronic properties of these crystals are investigated by means of DFT with a focus on the possible intermolecular interactions of radical spins.

Abstract This thesis deals with infrared spectroscopy investigations on the linear DCCI molecule. The high resolution spectra between 200–5200 cm-1 were measured with the Fourier transform spectrometer at the University of Oulu. The spectra were analyzed taking into account various types of resonances between rovibrational energy levels. As a result, a set of molecular constants and resonance parameters describing the rotational and vibrational energy states of the molecule were obtained. From the resulting molecular constants, together with previous results from literature for HCCI, the structure of monoiodoacetylene was calculated. In addition, eight harmonic force constants with estimated uncertainties for monoiodoacetylene were determined.

Stochastic differential equations are becoming a popular tool for modeling the transport and acceleration of cosmic rays in the heliosphere. In diffusive shock acceleration, cosmic rays diffuse across a region of discontinuity where the up- stream diffusion coefficient abruptly changes to the downstream value. Because the method of stochastic integration has not yet been developed to handle these types of discontinuities, I utilize methods and ideas from probability theory to develop a conceptual framework for the treatment of such discontinuities. Using this framework, I then produce some simple numerical algorithms that allow one to incorporate and simulate a variety of discontinuities (or boundary conditions) using stochastic integration. These algorithms were then modified to create a new algorithm which incorporates the discontinuous change in diffusion coefficient found in shock acceleration (known as Skew Brownian Motion). The originality of this algorithm lies in the fact that it is the first of its kind to be statistically exact, so that one obtains accuracy without the use of approximations (other than the machine precision error). I then apply this algorithm to model the problem of diffusive shock acceleration, modifying it to incorporate the additional effect of the discontinuous flow speed profile found at the shock. A steady-state solution is obtained that accurately simulates this phenomenon. This result represents a significant improvement over previous approximation algorithms, and will be useful for the simulation of discontinuous diffusion processes in other fields, such as biology and finance.

This thesis deals with systems of interacting particles with very low energy in the limit where the particle-particle scattering is much larger than the range of the interactions. We use a quantum-field-theory approach which allows us to study both few-body and dense-matter systems in a unified framework. This allows to introduce composite fields of two and three particles (when appropriate). The quantum corrections are calculated nonperturbatively with the Functional RenormalisationGroup. We deal with three types of systems. First we study systems with three and four scalar particles. For three-particle systems our framework describes the Efimov effect. During the FRG flow in the scaling limit, the four-particle system has an infinite sequence of (unphysical) four-particle states on top of each Efimov trimer. This is a case of super Efimov behaviour. Three of these four-particle states survive to the physical limit. Two of these three states have been found in exact quantum-mechanical calculations, and have also been observed in gases of ultracold atoms. Next, this thesis studies systems of three and four spin-1/2 particles. In the scaling limit, we find attractive fixed points for the three- and four-particle systems. Out of the scaling limit, we study atom-molecule scattering and molecule-molecule scattering, in particular their scattering length. Finally, we study dense-matter systems of spin-1/2 particles. This calculation includes all the two-, three-, and four-particle interactions. These systems show spontaneous symmetry breaking: the two-particle field has a finite classical value. We find the value of the atom gap in units of the chemical potential.