In the present work, we performed electronic structure calculations, based on the formalism of the Density Functional Theory, to investigate the electronic properties of nanoribbons obtained from the 2D structure of the carbon allotrope composed of rings of 5 and 8 atoms, known as OPG-Z . Nanoribbons were investigated for 5 types of edges and considering 5 units of different widths, totaling 25 systems. Results obtained by cohesive energy calculation indicated that all systems are energetically stable with negative energy in the range of -6.62 eV/Atom to -8.5 eV/Atom. The band structure and density of states results showed that the armchair-P1 nanoribbons are metallic for widths 1 and 2 and semiconductor for widths 3 to 5. The armchair- P2 for width 1 has a metallic behavior, and in the other widths the behavior is that of a semiconductor. The armchair-PO type nanoribbons showed topological insulator characteristics for all 5 widths. For armchair-O only the smallest width is a semiconductor and the other systems are metallic. Finally, the zigzag-PO nanoribbon of widths 1, 3 and 4 are semiconductors, while the units of width 2 and 5 are metallic. Combining Density Functional Theory with the Nonequilibrium Green Functions method to perform electronic transport calculations, we seek to propose applications of nanoribbons in molecular electronics. The electronic transport was carried out, for the voltage range from -1.0 V to 1.0 V, in the molecular devices of the nanoribbons considering up to the third unit of width that present zero gap or very small gap at the Fermi level in the analysis of density of states. The transport results, interpreted by analyzing the I-V, (dI/dV)-V and T(E,V) graphs, indicated the characteristic curve for the armchair-P1 nanoribbon devices of width 1 and 3 similar to a light-emitting diode for voltage values between -0.3 V and +0.3 V and almost ohmic resistance for the range of 0.3 V-1.0 V. 52acOPGZ-P1 and 91acOPGZ-P2 nanodevices, the exponential I-V characteristic is observed between 0.4 V-1.0 V, plus behavior similar to the field effect transistor in the range between -0.4 V and +0.4 V, with points of negative differential resistance in this voltage range. For the armchair-PO and armchair-O devices, the characteristic field-effect transistor-like I-V curve behavior is observed for 51acOPGZ-PO and 52acOPGZ-O, and the behavior almost ohmic linear becomes evident with the increase in the width of the devices and, therefore, the device width 3 for both types of edges presents a characteristic tendency of an ohmic resistor. For the molecular devices zigzag-PO of width 1 and 3 we have the I-V similarity to a light-emitting diode and, for the device zigzag-PO of width 2, we have a behavior with characteristic tendency of a field effect transistor. With these results, we verified possibilities in the development of molecular devices based on nanoribbons of the OPG-Z allotrope as an alternative for application in nanoelectronics.

Carbon allotropes are frequently applied in several areas of science and technology due to the versatility of their structural, thermal, electronic and magnetic properties, which changes with their hybridization and symmetry. POPGraphene is a 2D carbon allotrope designed with 5-8-5 carbon ring symmetry, which is predict to be energetic, dynamic and thermodynamic stable, and to presents great features like high thermal stability and superconductor behavior. Since carbon nanoribbons presents different properties from their 2D counterparts, in the present work we proposed and investigated five new carbon nanoribbons based on the armchair (two nanoribbons) and zigzag (three nanoribbons) cutting direction of POPGraphene structure, which results in nanoribbons with different edges shape. In the first part of this work, we analyzed the hydrogen edges passivation effect for one kind of POPGraphene nanoribbon, using its minimum width. In the second part, we investigated the effects of top and bottom edges shape, considering all different kinds of edge symmetry in zigzag and armchair directions. In the third part, we analyze the effect of nanoribbons width in all investigated systems in the second part. In the fourth part, we investigated the uniaxial strain applications’ effect on the electronic and transport properties of the different edges shape nanoribbons, but with the same width. To conduct this research, we implemented the Density Functional Theory to get the energetic, structural and electronic properties of all nanoribbons. Density Functional Theory combined with the Non-Equilibrium Green Function Method was implemented to compute the transport properties of the designed molecular devices based on the nanoribbons, under bias voltage application. The results shows that all nanoribbons are stable and feasible to be experimentally obtained, and that pentarings on edges termination is a parameter that improve the nanoribbons stability. The electronic properties shows that most of the nanoribbons have a metallic behavior, except for two armchair cases, which presents a very tiny band gap. Furthermore, in case of the hydrogen edges passivation effect, we have that the hydrogen breaks the superconductor behavior of the nanoribbon, extinguishing the high peak of density of states that was presented at Fermi level. The transport properties shows that the nanodevice behavior is strongly dependent of the chirality (zigzag or armchair) and edges termination (with pentarings, octarings or both) of the nanoribbons, having behaviors of Field Effect Transistor, Negative Differential Resistance (NDR) devices, Light Emitting Diode and Resonant Tunneling Diode, depending on these structural properties and the range of bias voltage application. We see that hydrogen edges passivation improve the transport properties leading to the arise of NDR regions in a specific operations range. Besides, we see that these NDR regions arise in this device and in other one cases, due to the presence of sub-bandgap regions in band structure of the unit cell which was used as a building block for design those molecular devices.

We briefly discuss the motivation and important results of modified theories of gravity and the different formalisms under the variational principle. Ricci based gravities (RBG) are described, showing their projective invariance, together with the action of such theories and the equations of motion under the Palatini formalism. The mapping between solutions of General Relativity (GR) and Ricci based gravities is shown, and the mapping of a scalar field theory coupled to a Ricci based theory is done.
Two important RBG's and their field equations are presented, the Eddington inspired Born-Infeld gravity (EiBI) and the quadratic Palatini gravity. In the context of the mapping of solutions, the Wyman solution for GR coupled to a free scalar field is shown in detail. This solution serves as a generator of solutions for both EiBI and quadratic Palatiny gravities. The asymptotic behaviour of the solutions generated for EiBi and quadratic gravity have the same approximate behaviour. The curvature analysis for this approximation is done for the Zakhary-Mcintosh complete set of curvature invariants, and all the invariants are shown to be regular in the interval of validity of the approximation. A geodesic analysis of the asymptotic approximation shows that the spacetime is geodesically incomplete, thus, is singular. Tidal forces are analysed and the strenght of the singularity is determined.

Understanding the thermodynamic properties of materials is a fundamental issue in physics, and its knowledge is crucial for targeting a specific material for possible applications. In this work, we present the Raman spectroscopy study dependent on the temperature and pressure of the GaSe0.5Te0.5 alloy in bulk form and its relevant thermodynamic parameters. Theoretical calculations were performed in collaboration to support the experimental results. Our results show a non-linear redshift for the 𝐴1𝑔 and 𝐸2𝑔 vibrational modes as the temperature increases in the temperature range from 10 to 748 K. Such behavior is well described by considering both thermal expansion and phonon-phonon coupling contributions. By combining DFT calculations and Raman spectroscopy experiments, the anharmonic constants relative to the three- and four-phonon decay processes, mode-Grüneisen parameters, Debye temperature, thermal expansion coefficient, and bulk modulus were estimated. Furthermore, the high-pressure measurements and DFT calculations, performed in the pressure range from 0 to 26.4 GPa, show a quadratic trend for the 𝜔𝐴1𝑔 and 𝜔𝐸2𝑔 modes as a function of pressure, with the 𝐴1𝑔 modes being more compressible than 𝐸2𝑔 one, i.e., 𝜕𝜔𝐴1𝑔/𝜕𝑃 > 𝜕𝜔𝐸2𝑔/𝜕𝑃. No structural phase transition is observed until the maximum pressure reached in the experiment. This study took a step forward in the understanding of mechanical and thermal properties related to GaSe0.5Te0.5 alloy, whose determined parameters are important for designing new applications.

Graphene, due to its exceptional optical, electrical, thermal and plasmonic properties, is currently one of the most studied nanomaterials worldwide and has promising applications in nanotechnology. In this sense, the carbon element is of inestimable importance for the development of modern science and the various applications that can be used in various technological areas. Its excellent interaction with a wide range of frequencies in the electromagnetic spectrum, mainly the Teraherz range, allows the material to be used in the development of several plasmonic nanodevices. In this sense, this work analyzes the possibility of developing a plasmonic nanodevice based on graphene, whose operating principle is the propagation of plasmonic waves over it, generating dipole resonances in the structure, in addition to the electromagnetically induced transparency effect. This consists of a silicon layer, a silica layer, a graphene waveguide and another silica layer, where two graphene nanoribbons will be deposited that will function as resonators. The two graphene resonators can be treated as light and dark. The Drude model was used to model graphene based on its conductivity. Through computer simulations using the Comsol Multiphysics software, the frequency response of the device was investigated, as well as the influence of the variation of several physical and structural parameters regarding its propagation characteristics, among which the gap d and the height hf of the resonators and the chemical potential µ_c. The electromagnetically induced transparency effect was observed when simulations were made for the device with the waveguide and the two resonators deposited on the silica above the guide, in which case the dipole mode is divided into two frequency bands at 8.96 THz and 9.85 THz, isolating the output port with isolation levels of 92%, in addition to a region between the isolation frequencies at 9.38 THz, where there is transmission of plasmonic waves from the input port to the devices output port, with transmission levels of 54% of the incident wave for a chemical potential µ_c = 0.15eV . The dynamic control of the device’s resonant frequencies is evidenced through the variation of the chemical potential of the graphene through the application of external tension in the structure, thus changing the operating range of the device. Based on this, from the obtained results it is possible to use the analyzed structure in the development of plasmonic devices such as sensors, switching filters, among others.

Active matter, particles that consume energy internally to generate motion, have a tendency to aggregate around solid surfaces. As a consequence, it is possible to form vortices around circular surfaces (obstacles). It was shown that, for models with hydrodynamic interactions, there is synchronization, that is, the occurrence of vortices rotating in opposite directions in neighboring obstacles, which in turn are arranged in a square network. Here, we show the same phenomenon for a model without hydrodynamic interaction of active matter in the presence of two or four circular obstacles. We compute, mainly, the correlation of the collective angular velocity, which is the parameter of the synchrony characterization, as a function of the density of the particles and the distance between the obstacles. We found, under certain combinations of density and distance between obstacles, there is synchronization of vortices.

Bandgap, Composites, Absorbance, Emission, Ferrites, Polymers, Raman, Infrared.

In this work, we investigate the existence of regular solutions in general relativity and alternative theories of gravity. In the context of general relativity, we briefly review Bardeen’s solution. We analyzed some aspects of the interpretations of this solution for when we have a source with a magnetic or electric charge. By inserting the cosmological constant, we study thermodynamics for a regular black hole. By imposing the energy conditions, we build new regular solutions that violate only the strong energy condition. In addition to the standard regular solutions, we also study the existence of black bounces in general relativity. We also study the possibility of generalizing electrically charged regular black hole solutions, built in general relativity, for f(R) theory and f(G) theory, where R is the curvature scalar G is the Gauss-Bonnet term. We build the formalism in terms of a mass function and this results in different gravitational and electromagnetic theories for each mass function, in the cases of f(R) and f(G) theories. By imposing the limit of some constant, we get again the results of general relativity.

In this research, we used the  ab initio Real Space - Linear Muffin Tin Orbital - Atomic Sphere Approximation (RS-LMTO-ASA) method, based on the Density Functional Theory (Density Functional Theory - DFT) and implemented for the calculation of collinear and non-collinear magnetic structures, in order to analyze the magnetic properties of linear dimers and trimers consisting of 3d metals (V, Cr, Mn, Fe, Co and Ni ) adsorbed on 5d-type metallic surfaces of (W(001) and Ta(001)), in addition to nanostructures composed of  3d and 5d metals on these same  5d(001) substrates. This work aimed to understand the fundamental characteristics of the Dzyaloshinskii-Moriya interaction (iDM) for these systems in collinear and non-collinear magnetic configurations. We obtained the ground state magnetic configurations of all systems verifying that in cases where the configuration was approximately collinear, the iDM contributions are originated from the spin-orbit coupling (SOC). It was shown that, for the non-collinear case in some of these systems, the Dzyaloshinskii-Moriya-type interaction, arising from non-collinearity, presents a significant contribution. Furthermore, it was shown that for some trimers composed of Fe-W-Fe/W(001) and Mn-W-Mn/W(001) there is a competition between the Heisenberg exchange interactions and the iDM generating a complex non-collinear magnetic configuration, showing that the interdiffusion of a 5d metal  between two 3d metals  in these systems decreases the exchange interaction and raises the iDM, where the physical origin of the DM interaction between 3d-5d-type metal pairs is related to the charge current,  while between pairs of 3d-3d-type metals, the iDM comes from the spin current. Other systems such as trimers V₃/Ta(001) and Fe₃/W(001) also showed a non-collinear magnetic configuration due to the high values of iDM, in which the physical origin of this interaction (iDM between 3d metals) is due to the spin current plus the SOC contribution.

In this thesis, initially, a reference potential method known as paradynamics is presented, the method is computationally implemented and tested in the reaction of the haloalkane dehalogenase enzyme with 1,2-dichloroethane (DCE). The second part of the work involves the application of a reference potential method to the study of RNA methylation of SARS-CoV-2. The inhibition of key enzymes that may contain the viral replication of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has assumed central importance in drug discovery projects. Nonstructural proteins (nsps) are essential for RNA capping and coronavirus replication since it protects the virus from host innate immune restriction. In particular, nonstructural protein 16 (nsp16) in complex with nsp10 is a Cap-0 binding enzyme. The heterodimer formed by nsp16-nsp10 methylates the 5'-end of virally encoded mRNAs to mimic cellular mRNAs and thus it is one of the enzymes that is a potential target for antiviral therapy. In this study, we have evaluated the mechanism of the 2'-O methylation of the viral mRNA cap using hybrid quantum mechanics/molecular mechanics (QM/MM) approach. It was found that the calculated free energy barriers obtained at M062X/6-31+G(d,p) is in agreement with experimental observations. Overall, we provide a detailed molecular analysis of the catalytic mechanism involving the 2'-O methylation of the viral mRNA cap and as expected the results demonstrate that the transition state stabilization is critical for the catalysis.

In this paper, we analyze a solution that mimics the Bardeen solution with a cosmological constant surrounded by quintessence. We obtained this by integrating the Einstein equations associated with nonlinear electrodynamics. We show what the conditions are for it to be regular throughout spacetime.

We also describe the thermodynamics associated with this solution. First by establishing the form of Smarr's formula and the first law of thermodynamics. Then we obtained relevant quantities such as the entropy, the thermodynamic potentials and coefficients, and the compressibility factor. We found that the Black Hole can undergo phase transitions, we named these as: small, small-large, and large. We define the Helmholtz free energy, and thus construct a graph showing the range of existence of each phase. Finally, we calculate the critical exponents of the solution, for a given set of parameter values, and conclude that they are the same as for the Van der Waals fluid.

In this thesis, we investigate generalizations of the Pseudo quantum electrodynamics (PQED) -- a nonlocal dimensional projection with pseudo operators developed to deal with mixed-dimensionality systems that has flourished after it was discovered it could properly describe 2d materials.

The description of projected photons have been extended to the case of massive photons of two different natures, one of them projected from the gauge-invariant Chern-Simons term and the other from Proca electrodynamics;  For the Pseudo-Chern-Simons formulation, we use Schwinger-Dyson equation to characterize the dynamical mass generation for the fermions and the critical limits in which  it produces a chiral symmetry breaking, while for the Pseudo-Proca, we calculate the quantum corrections that gives the Fermi velocity renormalization, interaction potential and -factor.

Mixed-dimensionality systems, however, covers essentially any material where one kind of particle is restricted to a smaller than the other particles dimensional subset. This motivates us to also extend PQED in the sense of projecting  the interaction onto fractal geometries, but to do that, we first discuss the main ideas behind fractional calculus, giving a few examples, and then we  start the discussion on the possibility of a Fractal-PQED in the perspectives.

Polarimetry is the technique employed for determining the polarization state of a light beam; i.e., the time-averaged trajectory pattern of the wave’s electric field on a plane orthogonal to propagation. Among many versions, the rotating-waveplate polarimeter has been implemented in several single-wavelength applications to determine the Stokes parameters of light through the Stokes-Mueller formalism. The extension of such technique to spectroscopic measurements is of great interest to the materials research community, and attempts have already been made towards dispersions of the polarization state. However, even though spectral measurements have been demonstrated possible, the need for achromatic polarizing elements requires special attention to their modeling, especially the quarter-wave plate. This dissertation establishes an account of the necessary corrections of the established Fourier analysis approach to determining the Stokes parameters, which fully describe any partially polarized light beam. In this work, we visit the literature’s state-of-the-art in polarimetry and implement the rotating-waveplate polarimeter for spectral measurements with achromatic polarizing elements over the visible range (400-800 nm). Initially using the simplistic ideal model available for such items, we are able to probe strong signs of artifacts in the spectral measurements. After analyzing the broadband calibration data and revisiting the literature, we develop a better model for the waveplate, such that the real Stokes parameters may be determined apart from the intrinsic dispersive properties of the retarder; the equivalent rotatory angle, the fast axis tilt, and the retardance. Here we present the mathematical and experimental procedure to have them properly characterized and taken as correction terms in the polarimetric measurements. We also show the enhancement in precision on simulated states, as well as on application examples of solution samples, which corroborates that the remodeling is necessary, and the approach developed here is essential for reliable and trustworthy spectropolarimetric data generation and analysis.

In this thesis, we research the behavior of the band gap on two-dimensional materials such as graphene and transition metal chalcogenides (TMD). These materials can be described using the pseudo-quantum electrodynamics (PQED), which is an effective theory suitable to depict the electromagnetic interaction between particles restricted to the plane. The low-energy excitations of the charge carriers in the graphene are describing massless Dirac fermions, while in the TMD these excitations are, approximately, depicting by massive Dirac fermions. We use the massive PQED to analyze the renormalization group functions at the large-$N$ limit, and we show that the band gap renormalization is determinate. Our theoretical result shown the function $m(n)/m_0 = (n/n_0)^{C_\lambda/2}$, being $m_0=m(n_0)$ and $C_\lambda$ a function of the coupling constant $\lambda= \pi \alpha/4$, where $\alpha$ is the fine-structure constant. Then, we compare our theoretical results with the experimental findings for tungsten diselenide (WSe$_2$) and molybdenum disulfide (MoS$_2$), and we conclude that our approach is in agreement with these experimental results for reasonable values of $\lambda$. We show that the renormalization of the Fermi velocity is similar to that found for graphene. We also investigate the role of the four-fermions interactions, which may represent the presence of impurities or disorders in the honeycomb lattice of two-dimensional materials. Firstly, we consider massless fermions in the PQED and introduce the Gross-Neveu (GN) interaction, and we take the broken phase of the chiral symmetry. Thus, we generate a mass term for the Dirac field through the gap equation. In this case, we show that there exists a critical coupling constant, namely, $\lambda \approx 0.66$ in which the beta function of the mass vanishes, providing a stable fixed point in the ultraviolet limit. For $\lambda > \lambda_c$, the renormalized mass decreases, while for $\lambda<\lambda_c $ it increases with the carrier concentration. Next, a complete set of four-fermion interactions is introduced. Under a suitable initial choice of these four-fermion interactions in the Lagrangian that defines the system, we find two possible critical values for $\lambda_c$, namely the minimal value $\lambda_c^{min}=0.26$ and the maximal value $\lambda_c^{max}=0.66$. Thus, the renormalized mass exhibits a transition in its behavior, providing a possible tuning and controlling mechanism for the renormalization of the band gap, depending on the type of material and its imperfections. We analyze the criticality of PQED coupled to the GN interaction, at both zero and finite temperatures, from dynamical mass generation. In the static regime, we show that the increase in temperature causes the system to recover the gapless phase. In the dynamical regime, we find an analytical solution for the mass function $\Sigma(p,T)$ in two different approximations for the GN coupling constant. As well as, a zero-external momentum solution for $p =0$, which the gapless phase is recovered for critical temperature. We compare our analytical results with numerical tests and a good agreement is found. Finally, to understand hybrid systems like Rhenium diselenide (ReSe$_2$) stacked on graphene, we consider PQED with massive Dirac fermions coupled with a set of four-fermion interactions treated as an effective theory at low-energy. Therefore, we perform an analysis of the functions of the renormalization group in the perturbative approach. We show that renormalized mass is described by $ m(\Lambda)/m_0 = \exp[\theta (\Lambda/\Lambda_0 -1) ] (\Lambda/ \Lambda_0)^{-\lambda/2}$, where $\lambda$ is the effective coupling constant from PQED, $\theta$ is a parameter which contains the coupling constant of the four-fermion interactions and $\Lambda$ is the energy scale (cutoff). Then, we find that for $\alpha \approx 0.15$ and $\theta \approx 1.22$ our theoretical result is in excellent agreement with the experimental measurements in the ReSe$_2$/graphene.

This work presents an analytical study of the electronic transport in dimerized trans- polyacetylene (Trans-PA) oligomers containing even and odd chains, symmetrically coupled to metallic electrodes (left and right), in T-shaped geometry using the Su-Schrieffer-Heeger (SSH) model via the Heisenberg equation of motion combined with the Keldysh formalism. We introduce disorder into the system through the dimerization force   demonstrating that chain dimerization can effectively lead to a reduction or increase in peak conductance.  The odd chain exhibits a trivial topological behavior, with the conductance peaks being considerably suppressed as the dimerization disturbance is varied. On the other hand, we have an opposite behavior in the even chain; for example, the string with dimming   has an almost perfect transmission. Furthermore, we observed for the odd chain the formation of a plateau in the I-V characteristic curve for high bias voltages and for an even chain it shows a current that has a linear behavior. This procedure presents an analytical study through the tuning of parameters in the device. Such parameters with tunneling amplitude are in accordance with the geometry described in experimental works.

The theory of General Relativity is one of the greatest achievements of the 20th century physics. Formulated by Einstein, General Relativity was established as a metric theory of gravitation. One of the main results of Einstein’s theory are Black Hole solutions. Black Holes started in General Relativity as controversial theoretical predictions to reach nowadays a remarkable scenario of experimental evidences. The study of fields defined in a Black Hole spacetime has shown to be a great area for testing new ideas, at both classical and quantum level. This dissertation is divided into two parts. In the first part, we investigate analytically the power radiated by a scalar particle in circular geodesic orbits around a Schwarzschild Black Hole. The radial scalar field modes are written in terms of confluent Heun functions. We obtain the emitted power using the framework of quantum field theory in curved spacetimes at tree level. We compare our analytical results with the numerical ones, obtaining excellent agreement. In the second part, we review recent theorems that show sufficient conditions for light-rings to exist around stationary, axisymmetric, asymptotically flat Black Holes. Although these results are quite generic, there are spacetimes that are not contemplated in the theorem hypotheses. We discuss how to work out the theorem for the non asymptotically flat Ernst spacetime.

In this work we evaluated the stability of Azithromycin dihydrate (AZM-DH) when subjected to high pressures and low temperatures using techniques of Raman spectroscopy, infrared spectroscopy, X-ray diffraction, scanning electron microscopy (SEM) an use of Density Functional Theory (DFT) for the classification of normal modes. AZM-DH is an antibiotic of the macrolide subclass generally used in antibacterial activity, and, like many drugs, it presents polymorphism which leads to the existence of several structural phases reported in the literature. Despite being a medicine that has been used for a long time, the lack of further information about it when subjected to different pressures and temperature led us to elaborate this work. In this work the AZM-DH crystal was studied under ambient conditions (temperature and pressure), at high pressures and low temperatures. The classification of normal modes of vibration was determined from quantum calculations via Density Functional Theory (DFT). According to the X-ray diffraction measurements, the crystalline phase of AZM-DH is found in the orthorhombic system of the P212121 space group and its lattice parameters were determined using the Rietveld method of structure refinement. Then, the stability of the AZM-DH crystal at low temperatures (300 -7 k) allowed us to admit that AZM-DH has a reversible behavior at low temperatures, with conformational changes and linear behavior of the modes. In general the bands become narrower as the temperature decreases and some modes appear. The modes in general present a linear behavior, there is a change in intensity of the bands and narrowing mainly from 220 K onwards. For the study at high pressures using Raman scattering with pressure values ranging from 0.0 to 6.1 GPa. From the analysis of the behavior of the band profile as a function of pressure, we observed several spectral changes associated with superposition and disappearance of modes. In addition, we evaluate the behavior of all normal modes (wavenumber) as a function of pressure (P) through wavenumber vs. plots. pressure which showed that all vibrational modes are linear and therefore could be adjusted with a straight line (ω = ω0 + α.P). therefore, almost all modes showed smooth discontinuities from the pressure of 1.1 GPa indicating that AZM molecules undergo conformational changes within the unit cell. Also, we can highlight that there is an indication of pre-amorphization for pressure values above 4.0 GPa. Another important point is regarding the crystal decompression experiment which shows the thermodynamic process is completely reversible.

In the last decades, raised a great interest in the planar theories study, mainly is due with its applications in condensed matter and in high energies physics. The discovery of massive and non-massive Dirac excitations in two-dimensional materials connected the physics of high-energy with condensed matter. In this context, we highlight the contributions of the pseudo quantum electrodynamics (PQED), also known as reduced quantum electrodynamics (RQED). This is an unitary U(1) gauge theory which describes the electromagnetic interaction in planar systems, preserving Coulomb's potential. The PQED has been used in the description of these materials and achieving results compatible with experimental measurements. In the present work, we study the perturbative and non-perturbative aspects of PQED added to terms that, in general, give mass to the mediating field excitations of the interaction. Such terms one Proca, Chern-Simons, and non-local Chern-Simons. We calculate the static interaction potentials, observing the screening effect and the electron-electron bound states formation, highlighting the deep connection between the dimensional reduction process and the mediating field mass. Moreover, the normalized mass and Fermi velocity for these theories were derived, extending PQED known results.

Recently, experimental nano-device composed by a semiconductor and superconductor hybrid nanowire structure has been used as a superconductive topological phase which have boosted the area of condensed matter physics to detect and control Majorana bound states (MBSs). In this work we obtain analytically the transport properties as current and conductance in a system formed by a quantum point with a single level connected to a Kitaev chain deposited on a superconductor s-wave to identify the signature of Majorana Zero Modes (Majorana fermions in solid state). For this, we use the Non-Equilibrium Green’s Functions (NEGF) also named as Keldysh formalism. Then, we derive the Meir-Wingreen formula to non-equilibrium situations similar the Landauer-Büttiker formula for the current (I-V curve) in equilibrium situations. With base in the Keldysh formalism, we use the matrix form to apply the computational method and obtain the I-V and conductance (G-V) curves to characterize the system under investigation. The characteristic of the 𝐼-𝑉 curve of the system identifies Majorana modes and the resonance in the G-V curve show a behavior of the system analogous to the behavior of the current in a field effect transistor (FET).

Neste trabalho, propusemos novas soluções de buracos negros regulares que possuem multihori-
zontes, as quais são formadas pelo produto direto de soluções já conhecidas na literatura, que são

descritas através do acoplamento da gravitação com a Eletrodinâmica não-Linear. Analisamos a

regularidade, o campo elétrico e as condições de energia de cada solução. A condição de energia
forte sempre é violada dentro do horizonte de eventos em todas as soluções, as outras condições
de energia dependem fortemente da razão entre as cargas extremas das soluções isoladas. Para as
soluções com até quatro horizontes, apresentamos dois exemplos, Bardeen-Culetu e Balart-Culetu.
Ambas soluções são regulares, mas a primeira nunca pode satisfazer todas as condições de energia,
com exceção da condição de energia forte, pois possui razão entre cargas extrema de 1.57581. Já a
segunda solução pode satisfazer todas as outras condições de energia, com exceção da condição de
energia forte, e possui razão entre cargas extrema de 1.09915, valor que permite essa característica.
Propusemos também uma solução regular com até seis horizontes, Balart-Culetu-Dymnikova, onde,
para um determinado valor de carga, podemos vericar que satisfaz todas as condições de energia,
com exceção da condição de energia forte. Isso foi possível devido a razão entre as cargas extremas
não serem muito elevadas. Propomos soluções com número de horizontes qualquer. Soluções com
multihorizontes podem apresentar propriedades exóticas, como densidade de energia negativa, ou
violação das condições de energia, mas que podem ser contornadas com uma escolha apropriada de
soluções isoladas e valores de cargas extremas, resultando em soluções de buracos negros regulares
que satisfazem as condições de energia com exceção da condição de energia forte.

The recent detection of gravitational waves and the first image captured of a black hole shadow has increased the interest in black holes. Around these black holes, we can study the strong field regime of gravitation, which constitutes an essential feature of the General Theory of Relativity (GTR). Furthermore, the study of solutions of the GTR field equations with non-zero cosmological constant is important, since experimental evidence indicates that our cosmological neighborhood is undergoing an accelerated expansion. We study the scalar field theory in a spherically symmetric spacetime with positive cosmological constant associated to the Schwarzschild-de Sitter black hole. The scalar field is quantized using the prescription of Quantum Field Theory in Curved Spacetimes. We calculate the emitted power from a scalar source orbiting a Schwarzschild-de Sitter black hole, using numerically obtained solutions for the scalar field. We compare our results with those obtained in the case of a scalar source orbiting a Schwarzschild black hole.

In this work, crystals of Bis(L-histidinate) Ni(II) monohydrate, L-asparagine monohydrate pure and with dopants (Mn(II), Fe(III), Ni(II) and Cu(II)) were obtained by the method of slow evaporation of solvent at controlled temperature. Crystal structures were confirmed by the Rietveld refinement method. Bis(L-histidinate) Ni(II) monohydrate crystal has monoclinic symmetry and C2 space group, while monohydrate L-asparagine crystals pure and with dopants have orthorhombic symmetry and P2₁2₁2₁ space group. All crystals have four molecules per unit cell (Z = 4). The structural properties of these crystals were investigated by X-ray powder diffraction at high temperatures using synchrotron radiation, in the range of 300 to 740 K. The thermal properties were investigated by thermal analysis (DTA and TG) at high temperatures, in the range of 300 at 773 K. At 409 K the Bis(L-histidinate) Ni(II) monohydrate crystal presents changes in its diffraction pattern that indicate the beginning of a structural phase transition. This phase transition is supported by discontinuities in the lattice parameters and the relative parameters indicate that the thermal expansion is anisotropic. The structure of the new phase has not yet been identified, but the arrangement must be non-hydrated. At 600 K the diffraction peaks lose intensities until they are extinguished. At 358 K, the monohydrate L-asparagine crystal presents changes in its diffraction pattern that indicate the beginning of a structural phase transition. This phase transition is supported by discontinuities in the lattice parameters and the relative parameters indicate that the thermal expansion is anisotropic and negative along the a-axis. The structure of the new phase presents monoclinic symmetry, space group P2₁ and two molecules per unit cell (Z = 2). At 474 K the diffraction peaks lose intensities until they are extinguished. Thermal analysis measurements confirm these transformations for all crystals, all being endothermic. The first transformation is associated with dehydration and the second with degradation. For crystals of L-asparagine monohydrate with dopants (Mn(II), Fe(III), Ni(II) and Cu(II)) these same structural phase transitions are observed, but start at different temperatures. The different transition temperatures, as well as the changes in the diffraction patterns of the different doped crystals were interpreted as being effects of metals on the structure of L-asparagine monohydrate.

In this work, a study on the vibrational properties of the molecule 5,10,15,20-tetra(4-pyridyl)-21H,23H-porphyrin (tetrapyridyl free base porphyrin or H₂TPyP) in crystalline form is addressed. X-ray diffraction measurements were performed and the analysis of the diffractogram confirms the crystalline structure of the sample. However, in the present work, no further conclusions about the crystal space group or its lattice constants were achieved. Raman spectroscopy measurements were performed and the assignment of the vibrational modes from H₂TPyP was accomplished by comparing the experimental Raman spectra obtained in ambient conditions and the spectra obtained by means of computational simulation considering an isolated molecule. In addition, the behavior of the vibrational modes of the molecule under different hydrostatic pressure conditions and different excitation laser lines was studied. In the latter, the Raman spectra obtained with laser lines 488 nm and 532 nm display different vibrational modes: the spectrum obtained with the 532 nm laser line present some modes with no correspondents in the spectrum obtained with the 488 nm laser line. This effect was understood as a manifestation of the molecule Raman scattering resonant character that responds differently when excited in different optical absorption bands. The molecule was also subjected to high pressures, until 7.7 GPa and, for each pressure, the Raman spectrum was obtained with the 488 nm laser line. It is observed that the Raman modes are, in general, shifted to higher wavenumbers with the increasing pressure. Furthermore, some Raman modes appear with the compression and those are compatible with the previously observed modes in the spectrum obtained with the 532 nm laser line under ambient pressure that initially had no correspondents in the spectra obtained with 488 nm laser line under ambient pressure as well. Such observation suggests that this effect occurs due to the change on the resonance conditions of the molecules that are associated to those modes. It was also observed the splitting of some Raman peaks into new peaks with different evolution rates ( ). This effect was attributed to a pressure-dependent symmetry lowering, which indicates a preferential direction to the molecular distortion with compression due to the presence of the central nitrogen-hydrogen bonds. The decompression analysis shows that this process follows a reverse path when compared to the compression, which indicates an almost complete reversibility.

In 1993, Marino proposed the Pseudo-Quantum Electrodynamics (PQED) [E. C. Marino, Nucl. Phys. B, Vol. 408, 551 (1993)], an effective gauge theory in (2+1)D, obtained through the dimensional reduction of the Quantum Electrodynamics (3+1)D (QED) and which, although being a non-local theory, it respects the causality and unitarity, describing the coulombian interaction between static charges in the plane. In the present work, we considered the dimensional reduction that leads us to PQED, such as made by Marino but incorporating the boundary conditions effects imposed by the presence of a partially reflective surface to the electromagnetic field. In this manner, We propose an effective model that fits with the theory recently denominated in the literature as cavity Pseudo-Quantum Electrodynamics. A direct application of this model, also developed in this present work, is the obtaining of the Fermi velocity renormalization for an electron in a graphene sheet near a conducting plate, which is approached in the static interaction regime of the theory.

In the present work, we investigated the electronic properties of structures based on a 2D carbon allotrope formed by rings 5 and 8 called POPGraphene, using the hydrogenation edges of POPGraphene nanoribbons and the doping with N, B, or N and B atoms, in order to propose applications in molecular electronics. For the study, the Density Functional Theory was implemented for the optimization of the structures, and the Density Functional Theory combined with the Non-Equilibrium Green Functions method to obtain the electronic transport properties. The band structure results show that, among the proposed unit cells, the POPGraphene cell has a topological insulator character, and the others have a metallic behavior. The results for the electronic transport properties shows that the POPGraphene nanodevice has characteristics that resemble a Field Effect Transistor in the analyzed range, the hydrogenated one presents a Field Effect Transistor behavior in the range of -0.07 V to 0.07 V and of a Resonant Tunneling Diode in the range from -0.70 V (0.70 V) to -1.00 V (1.00 V), the doped with B presents a Field Effect Transistor behavior in the analyzed range, the doped with N presents a Field Effect Transistor behavior in the range of -0.10 V (0.10 V) to -1.00 V (1.00 V), and the doped with B and N presents a Field Effect Transistor behavior in the range of -0.70 V to 0.70 V and of a Light Emitting Diode in the range of -0.70 V (0.70 V) to -1.00 V (1.00 V). The results show that structures based on POPGraphene appear as a great alternative for the development of nanodevices and applications in molecular electronics.

In the present work, we investigated, using the Pseudo Quantum Electrodynamics, how the renormalization of the Fermi velocity in a graphene sheet is affected by conductive at surfaces in its vicinity. First, we review the effect of a single grounded conductive surface, and later we investigate a cavity formed by two grounded conducting surfaces. We show that the inhibition of the renormalization of the Fermi velocity occurred in the first case is enlarged by the cavity in a non-additive manner. This means that the result of the cavity is not the simple sum of the isolated results coming from two conductive plates. In addition, we also discuss the case in which the graphene is in a dielectric medium with a dielectric constant  separated by a planar interface from another medium with a dielectric constant . For this case, we show that the inhibition of the renormalization of the Fermi velocity is larger for the case  than for the case . The influence of external media on the properties of two-dimensional systems, we call Cavity Pseudo Quantum Electrodynamics.

We investigate the behavior of the absorption cross section of the massless scalar field by a static and chargeless black hole in the context of the Einstein-dilaton-Gauss- Bonnet (EdGB) theories. For comparative purposes, we also present the results of the massless scalar field absorption cross section in the Schwarzschild geometry, which is the exterior geometry of a static and chargeless black hole in the context of the General Relativity (GR) theory. In the limit in which the frequency of the scalar field tends to zero, for a static and chargeless black hole, the absorption cross section tends to the value of the area of the event horizon, for both the GR theory (Schwarzschild) and the EdGB theories. We show that the greater is the value of the Gauss-Bonnet constant, the greater will be the value of the absorption cross section. We present plots of the absorption cross sections, which were obtained by computational methods. The results obtained in this work corroborate the fact that the EdGB theories belong to a very promising set as alternative theories to GR.

The material Ferrous Sulphate Ammonium Hexahydrate (NH⁺₄)₂Fe⁺²(SO^-2₄)₂.6(H₂O) SFA, which belongs to the family of materials known as Tutton's Salt is formed mainly by octahedrons of [Fe(H₂O)₆]²⁺ and tetrahedrons of SO^-2₄ and NH⁺₄. 243 vibrational modes are predicted by group theory at k = 0 including the 3 acoustic modes, which are distributed as follows: Γ₂₃₄ = 57Ag + 57Bg + 60Au + 60Bu. In Chapter 2, we discuss fundamental concepts and relationships that are used in the formulation of the techniques used to investigate the phenomena observed in this work, such as: Raman Spectroscopy, X-Ray Diffraction and Group Theory. Chapter 3 provides technical information on the equipment and materials used in this work, as well as the methodology of the experiments. In Chapter 4 we present the experimental results that are divided into sections, where in the first section we obtain results by X-ray diffraction and also information acquired through structure refinement (Rietveld). This refinement presents a great excellence in its parameters of quality. The results are consistent with the literature. For the section of group theory we present the results in two parts where, in the first part, we see how the vibrational contributions of each group of atoms that make up the crystal are divided and classified, according to the Groups Theory. In the second part, we provide information about the vibrational behavior of the SFA crystal and perform the assignment of modes in Raman spectra. Correlation is done for the internal vibrational modes of the octahedral and tetrahedral geometries through the sites of symmetry with the representations of the crystal factor group C_2h. In the section where the polarized Raman results are presented, we have seen how the change in the light scattering geometry can give us different information about the polarizations of a crystal, especially for the SFA. We found that in the region between 50 cm^-1 e 200 cm^-1, modes are presented in all geometries. We also conclude that only the mode in 300 cm^-1 belongs entirely to geometry y(zx)y. We verified the emergence of one of the modes  in geometry x(yy)x at 550 cm^-1 . The stretches  are observed in all polarization configurations. In the section on results of high temperatures, we analyzed the vibrational behavior of the SFA crystal and concluded that the exit of the water molecules of the structure, around 83 ºC, is the main responsible for the changes observed in the Raman spectra, in fact, the loss hydrogen bonds directly affect the folding and stretching of the molecular groups SO^-2₄ that make up the neighborhood of the complex [Fe(H₂O)₆]²⁺. When we reach the temperature of 93 ºC is observed the beginning of the degradation of the material, where we see that the translations and librations of the molecular groups NH⁺₄ and SO^-2₄, in the interval between 20 cm^-1 e 100 cm^-1, together with the  folding and stretching , both associated with the complex [Fe(H₂O)₆]²⁺, cease to exist in the Raman spectra. Finally, in the section with the results of high pressures, we have the possible identification of two phases in the following pressure ranges: from 0.1 GPa to 4.5 GPa, and between 6, 1 GPa to 10.1 GPa. The first phase being the most crystalline followed by an intermediate phase between 4.5 GPa and 6,1 GPa, leading to the second phase, less crystalline, but not totally amorphous. This hypothesis is not conclusive, it is necessary to perform some more experiments to obtain more enlightening results on this phenomenon, such as, for example, X-ray Diffraction with pressure. Finally we present the conclusions of the work, as well as its perspectives.

The draining bathtub is a three--dimensional (one time-like and two space-like) analogue model of a rotating black hole. Black holes are solutions of the Einstein's equations. These equations describe the dynamics of the gravitational field in the presence of matter and/or energy. Even though the draining bathtub is not a gravitational system nor satisfies the Einstein's equations, it possesses the same causal structure of a black hole. In the present work we obtain an analytical expression for the absorption cross length of the draining bathtub in all range of frequencies. Since we are dealing with the scalar field, we need to solve the Klein--Gordon equation, which radial solutions are given in terms of Heun functions, used to compose the expressions of our analytical results.

The Pseudo-Quantum Electrodynamics (PQED), proposed by E. C. Marino, is an electromagnetic theory which describes the interaction between charged particles confined in a plane. When we do the coupling of the PQED with a bosonic field of matter, we obtain a called Scalar Pseudo-Quantum Electrodynamics (SPQED). In this work, we make a perturbative analysis of SPQED via Feynman diagrams. In order to do so, we obtain Feynman's rules from this theory and compute the one loop Green functions: bosonic field self-energy, electromagnetic field self-energy and vertex corrections. After this, the divergences from the diagrams were systematically treated using a dimensional regularization and the divergences removed through techniques of renormalization.

This thesis consists is to obtain a deeper understanding of topics related to Gravitation and Cosmology, with an emphasis on obtaining solutions to black holes and study of the current phase of accelerated expansion of the universe. We have done this through the Modified Gravity Theories f(R), f(T) and f (T, T), in which we know to have reproduced some of the best known Einstein Relativity. Our starting point was the action to f(R) Gravity coupled to nonlinear Electrodynamics, where we obtained regular black holes solutions in 4-D for a spherically symmetric spacetime and recovered the black-hole regular solutions of general relativity. Later, choosing a function mass M(r) in metric coefficients and find solutions with regular behavior in geometric invariants. For both cases, analyze the energy conditions and showed that the solutions found violate at least one of the conditions of energy. In f (T) Gravity, we couple nonlinear Electrodynamics to its action and charged black hole solutions and a new class of solutions of regular black holes. With the results obtained for charged black holes in f(T) Gravity, showed the possibility of accretion of fluid by these black holes. Still in the context of f(T) Gravity, we construct a theory that generalizes the Teleparallel Theory preserving the invariance under local Lorentz transformations. Finally, we approach the theory of f(T, T) Gravity, reconstructing the ΛCDM model, where we verify that the conservation of the energy-moment tensor is related to the choice of a certain Fg [y] function; we have also seen that our reconstruction describes the cosmological eras until the present time. We investigate the stability of the reconstructed model and find the condition for validity of the laws of thermodynamics.

In this thesis, the magnetic properties of several materials were investigated using first principle calculations. The ab initio method real space linear muffin-tin orbitals atomic sphere approximation (RS-LMTO-ASA) was used to calculate the electronic structure and magnetic properties of bulk systems, surface and nanostructures adsorbed on surfaces.                       

We have implemented new features in the RS-LMTO-ASA method, such as the calculation of the (a) Bloch Spectral Function (BSF), (b) orbital resolved J_ij and (c) Dzyaloshinskii-Moriya interaction (DMI). Using (a), we have shown that one is able to calculate the dispersion relation for bulk system using a real space method. Furthermore, the dispersion relation was revealed to be existent even for finite one-dimensional structures, such as the Mn chain on Au(111) and Ag(111) surfaces. With (b), we have investigated the orbital resolved exchange coupling parameter J_ij for 3_d metals. It is demonstrated that the nearest neighbor (NN) interaction for bcc Fe has intriguing results. The well known ferromagnetic metal bcc Fe has a total J_ij that favours the ferromagnetic behavior, however, the contribution coming from the T_2g orbitals favours the anti-ferromagnetic coupling behavior. Moreover, the Fermi surface for bcc Fe is formed mostly by the T_2g orbitals and these are shown to be highly Heisenberg-like, i.e. do not depend significantly on the magnetic configuration. Later, the same approach was used to study other transition metals, such as Cr, Mn, Co and Ni. In the end, we have presented the results obtained with implementation (c). Our results have shown the large dependence of the DMI values, both the strength and direction, with respect to which magnetic configuration they are calculated from. We argue that, for the investigated systems, the non-collinearity induces currents (spin and charge) that will influence directly the DMI vectors.

During many decades black holes posed only as mathematical solutions of the equations of
the Theory of General Relativity, until the discovery of its first astrophysical candidate Cygnus
X-1. Currently, black holes are paradigms, both in theoretical Physics and in Astronomy. In Astronomy,
black holes provide a solution in galaxy formation scenarios, in active galactic nuclei
and in the remanent of core-collapse supernovae. The recent detection of gravitational waves,
generated by the fusion of two black holes, opened a new window to observe the Universe and
gave rise to the gravitational-wave Astronomy. These and other experimental advances motivate
a study of the interaction between waves and black holes. We can model this interaction
by considering plane waves impinging upon black holes and studying how they are absorbed
and scattered. The absorption and scattering of waves can be quantified into two quantities: the
absorption and scattering cross sections. In this thesis, we analyze how massless plane waves
are absorbed and scattered by distinct black hole configurations: (i) Schwarzschild surrounded
by thin shell of matter, (ii) Kerr, and (iii) Kerr-Newman. We compute numerically the absorption
and scattering cross sections, and show a selection of results. Our results were obtained for
arbitrary values of frequency and scattering angle of the incident waves, and present excellent
agreement with analytical results obtained in limiting cases.

In this thesis, we present an analysis by resonant Raman spectroscopy (RRS) in single wall carbon nanotubes (SWCNT) and multiple walls (MWCNT) under two different foci. The first investigates the influence of hydrostatic pressure on the mechanical properties of the single wall carbon nanotubes (SWCNTs) dispersed in aqueous sodium dodecyl sulfate (SDS) and fatty acids (Cn), as well as the evidence of their filling by these particles. In this part of the work, the experiments were carried out using two different compressor media, alcohol solution composed of 4 ml of methanol and 1 ml of ethanol (MET-ET) as well as mineral oil (Nujol). The Raman spectra were acquired in the spectral range of the RBM mode and showed that the CNT samples were composed of tubes with diameters varying from 0.85 nm to 1.3 nm. A blueshift to the RBM and G modes is observed due to the increase in pressure. The disappearance of RBM modes assigned to tubes with diameters greater than 1.0 nm indicates that these tubes lose resonance at 2.0 GPa and 3.4 GPa for Nujol and MET-ET, respectively. In the analysis, the G-band component assigned to SWCNTs showed the Breit-Wigner-Fano (BWF) line shape, indicating that the sample is composed mainly of metal tubes. Our results show a dependence on the mechanical properties of the CNTs with the compressor medium, which can be understood from a theoretical prediction previously reported under the filling effect of the tube by fatty acid molecules. The second focus of the work is related to the doping mechanism in MWCNTs filled with aluminum carbide (Al4C3-MWCNTs) where they were studied and interpreted in relation to the changes in their electronic and phonic structures. Unfilled MWCNTs served as standard samples to aid in the interpretation of the fill and doping process. In addition, in order to corroborate the results of Raman spectroscopy, the samples were also characterized by scanning electron microscopy (SEM), transmission electron microscopy (TEM), X-ray diffraction (XRD), through which electron-phonon coupling associated with the Raman intensities of G and G 'modes were studied and interpreted in the light of the doping mechanism in these multiple-walled systems. Our results, corroborated by theoretical calculations, indicate that Al4C3 particles transfer electrons to MWCNTs. These calculations were performed for a system of filled and unfilled tubes of MWCNTs where the calculated electron states density indicated that the two possible systems considered exhibit metallic behavior with the aluminum carbide doping the carbon nanotubes.

In the this work, we have studied the electron transport characteristics in molecular junctions based on opioid derivatives. Four molecules that differ by the presence of acetyl groups were connected as molecular bridges between two metallic Au (111) electrodes. The molecules studied are 3-monoacetylmorphine, 6-onoacetylmorphine, diacetylmorphine and morphine. The theoretical study was performed using the DFT-NEGF methodology.
The results obtained show sequential deacetylation changes drastically the response of the molecular systems to an applied voltage under the system. Rectification effects, Negative Differential Resistance and resonant tunneling are described in terms of transmissions and Density of States. Particularly, diacetylmorphine has electrical current in the microampere scale and rectification pattern to direct polarization, obtaining rectification peaks (R=9,1) at low voltages (0,6 V) and maximum of rectification (R=14,3) in 1,8 V. The deacetylation inverts the rectification for morphine.

The theoretical studies of several magnetic materials are presented in this thesis. To each of them, it was investigated the electronic structure, by means of density functional theory calculations, and/or magnetization dynamics, in the context of atomistic spin dynamics (ASD). For bulk properties, we evaluate the magnon spectra of the heavy rare earths (Gd, Tb, Dy, Ho, Er, and Tm), using the exchange parameters and magnetic moments from first-principles calculations in ASD simulations. Additionally, we performed Monte Carlo simulations that nicely reproduced the qualitative trend of lowering of the critical temperatures across the series. Next, we discuss about the microscopic mechanism of the vanishingly low magnetic anisotropy of Permalloy using the concept of the orbital moment anisotropy for Fe and Ni atoms in the alloy. Turning to surface magnetism, we discuss the use of exchange parameters computed by a non-collinear formalism for 6 monolayers of Fe on the Ir(001) substrate, in order to have a more accurate description of magnons at finite temperature and to obtain good comparison with experimental data. Besides that, we also studied surface magnons on 3 and 9 Ni monolayers on Cu(001) and Cu(111) in order to track the significant surface and/or interface effects and contrast it to properties that are fcc Ni bulk-like. Likewise, we used the Monte Carlo method to estimate the critical temperatures of Ni surfaces and compared with experimental data. Finally, in the field of low dimensional magnetism, we present the ab-initio calculations for the electronic structure of Cr nanostructures of diverse geometries adsorbed on the Pd(111) surface, with focus on the formation of non-collinear spin configurations, either due to geometric frustration or the spin-orbit coupling provided by the substrate.

In the present work, a brief discussion about the application of boundary conditions over electromagnetic vortex systems with gauge-symmetry breaking will be developed both directly over Maxwell-Proca-Chern-Simons model and indirectly through alternative representations of this model.
At first, some breakthrough scientific discoveries related to this research theme will be indicated to present the Maxwell-Proca-Chern-Simons model, per se, with its equations of motion and some of its alternative representation previously known. Posteriorly, the calculations of forces due to the vacuum fluctuations will be developed implementing some apparently different boundary conditions over the other representations mapped before. Since a coincidence between the forces for two supposedly distinct boundary conditions will be shown, an analysis of the system constraints will be deepened in a way to show that such a coincidence, actually, came from the equivalence of the boundary condition. A quantitative approach of the vortex contributions to the force was also made, displaying how strongly the presence of vortices suppresses the vacuum force.

In this work we studied composites formed by the polymers PVA, PVK and PS modified by the presence of ferrites Fe3O4, FeLiO2 and (La0,6Sr0,4) (Co0,2Fe0,8) O3. For the characterization of these composites, Raman, FT-Raman, FT-IR, Optical Spectroscopy (in the case of PVK, for this to absorb and emit light) and X-Ray Diffraction were used. Raman spectra showed the influences of the polymer bands (reduction of intensity generally) when they were doped with the ferrites, facts also observed in FT Raman spectra and in infrared spectra. Raman spectra also showed changes in the line width of PS + Fe3O4, PS + FeLiO2, PVK + Fe3O4 and PVK + FeLiO2 composites. Another important change observed was in the spectrum of PVA modified with FeLiO2, where we observed the displacements of some vibrational modes. In relation to the infrared spectra, we observed important changes in the spectra of the composites, such as the displacement of the modes of the ferrites inserted in the polymer matrices, besides the reduction of the intensity of the modes, with the exception of the composite formed by the PVA and lithium ferrite. Optical spectroscopy showed changes in the absorption and emission bands of the polymers when the ferrites were inserted in their matrices. The X rays diffraction showed changes in the sizes of the ferrite crystallites, when these were inserted in the polymer matrices, the results of this technique also showed that the magnetite inserted in the polymers did not change phase, a fact that occurred when submitted to the laser radiation 785 nm.

In the context of a real massless scalar field in 1+1 D, Muñoz-Castañeda and Guilarte [Phys. Rev. D 91, 025028 (2015)] calculated the Casimir force between partially reflecting mirrors modeled by a term μ δ (x)+ λ δ′ (x) in the Lagrangian, which, in the limit of perfect mirrors, reproduces the Robin boundary conditions. This model, however, presents a problematic aspect: for λ different of 0 the mirrors are not full transparent at high frequencies. In this work, in order to provide a more realistic feature for this model, we propose a modified δ - δ′ point interaction that enables full transparency in the limit of high frequencies. Taking this modified δ - δ′ model into account, we calculate the Casimir force comparing our results with those found in the literature. In addition, we propose a second modification in the δ - δ′ model, so that in the limit of perfect mirrors we obtain the generalized Robin boundary condition.

Temperature- and pressure-dependent studies of Raman and infrared spectra have been
performed on azetidinium zinc formate, [(CH2)3NH2][Zn(HCOO)3] (AZZn), dimethylammonuim
[(CH3)2NH2][Mg(HCOO)3] (DMMg) and [(CH3)2NH2][Cd(HCOO)3] (DMCd). Vibrational spectra
showed distinct anomalies in frequencies modes and bandwidths near 250 and 300 K, which were
attributed to structural phase transitions associated with gradual freezing of ring-puckering motions of
azetidinium cation. Pressure-dependent studies have revealed a transition below 0.94 GPa. Raman spectra
indicate that the structure of the room-temperature high-pressure phase is the same as the monoclinic
structure observed at ambient pressure below 250 K. A second phase transition has been found between
2.26 and 2.74 GPa. This transition has strongly first order character and is associated with strong
distortion of the zinc formate framework and azetidinium cations. For structure of DMMg, studies reveled
three pressure-induced transitions near 2.2, 4.0 and 5.6 GPa. Theses transitions are associated with
significative distortion of the anionic framework and the phase transition at 5.6 GPa has also great impact
on the DMA+ cátion. The DMCd undergoes two pressure-induced phase transitions, the first transition
occured betwee 1.2 and 2.0 GPa and second one near 3.6 GPa. The first transition leads to subtle
structural changes associated with distortion of anionic framework and the later leads to significant
distortion of the framework. In contrast to the DMMg; the third transition associated with distortion of
DMA+ cation is not observed for the DMCd up to 7.8 GPa. This difference can be most likely associated
with larger volume of the cavity occupied by DMA+ cation in the DMCd and thus weaker interactions
between anionic framework and DMA+ cations.

In this work we present the study of the structural stability of a mono crystal all-trans-β-carotene subjected to extreme low temperatures and high hydrostatic pressure through Raman spectroscopy using excitation line 632.8 nm. Computer calculations were performed using the density functional theory (DFT) to determine the vibration modes of molecule all-trans-β-carotene since the vast majority of vibration predicted by group theory for the crystal are related to internal modes. Temperature in the range between 20 and 300 K the Raman spectra exhibit clear changes in the spectral region comprising the lattice modes and the region containing the internal vibrational modes. The temperature dependence of the most intense vibrational modes ν1(1511 cm-1) and ν2(1156 cm-1), which are related with the stretching vibrations (stretch) of the C = C and C − C bonds, respectively, of the chain polyene suffer shift to higher values of wavenumbers. This behavior is similar to that exposed in the theoretical work of Wei-Long Liu et al. We conclude that the all-trans-β-carotene crystal undergoes a phase transition induced by temperature at around 219 K. This transition is interpreted as rotation (around the dihedral angle) experienced by groups known as β-rings, located at each end of molecule. At low temperatures, the new molecular configuration affects the sliding plane of the space group C52h (P21/n), the phase transition leads to an unchanged monoclinic structure. However, the original space group is possibly reduced to the space group C2. At temperatures of 200 and 220 K, the spectral ratio (S) of the intensities integrated of asymmetric and symmetric stretching modes of the methyl group (CH3) undergoes an abrupt change, such change is more an indication of a phase transition. Moreover, the results obtained by differential scanning calorimetry (DSC) showed the occurrence of an exothermic process temperature close to the transition observed by Raman spectroscopy. In regime of high pressures, the Raman spectra showed various modifications as, for example, the disappearance modes and discontinuities. Such changes have taken place both within the region regarding the modes of the crystal lattice and in the region concerning the purely modes of the molecule. Two phase transitions were observed, the first between 1.94 and 2.5 GPa, and the second between 3.76 and 4.78 GPa. The analysis of the characteristic modes ν1 and ν2 shows a behavior similar to that observed for at Wei-Long Liu et al model. Finally, the Raman spectra at different pressures for β-carotene crystal were not compatible to the Raman spectra of the forms cis presented in this work.

O estudo das propriedades de espalhamento de buracos negros de Schwarzschild em dimensões extras para o campo escalar não massivo restrito à brana quadridimensional é apresentado. O estudo de espaços-tempos extra-dimensionais tem aumentado bastante recentemente graças, em parte, aos trabalhos pioneiros de Randall e Sundrum (em cinco dimensões) e Arkani-Hamed, Dimopoulos e Dvali (em d dimensões). Em especial, os últimos conjecturaram a existência de dimensões extras com escala submilimétrica para resolver o problema de hierarquia. Nesta visão, apenas as pertubações gravitacionais são modicadas no espaço-tempo completo, chamado de bulk, sendo que os demais campos do modelo padrão cam restritos à brana. A partir destas ideias, aqui se discute o espalhamento do campo escalar não massivo, no contexto de dimensões extras, restrito à brana do espaço-tempo de Schwarzschild. Utiliza-se o método de ondas parciais para determinação numérica das seções de choque. Aproximações analíticas, tais como a aproximação de Born, a análise perturbativa de geodésicas e a aproximação para o efeito glória, são utilizadas. É mostrado que tais aproximações concordam muito bem com os resultados
numéricos dentro de seus limites de validade.

Neste trabalho foram crescidos os cristais de sulfato de níquel hexahidratado (NSH), o qual foi dopado com os íons Mn+2 e Cu+2, e posteriormente foram caracterizados por difração de raios X de policristais e difração múltipla de raios X (DMX) usando radiação Síncontron. Os cristais foram crescidos pelo m etodo de evaporação lenta e tendo como resultados cristais de boa qualidade, os quais foram utilizados para os experimentos de
difração de raios X de policristais, no laboraório de física experimental e computacional da UFPA, e para os experimentos de difração múltipla realizados no Laboratório Nacional de Luz Síncontron (LNLS). De acordo com os resultados obtidos da difração de raios X de policristais juntamente com o refinamento Rietveld, podemos perceber que apesar da presença do dopante na estrutura cristalina, os cristais dopados de NSH:Mn e NSH:Cu, apresentaram a mesma estrutura tetragonal e grupo especial do NSH puro. Mudanças no parâmetro de
rede foram observadas o que resultou em um aumento da célula unitária, essas mudanças foram anisotrópicas, ou seja, os parâmetros de rede sofreram variações de formas diferentes e foram constatadas, em comum acordo, pelas técnicas utilizadas. O objetivo deste trabalho foi crescer cristais de NSH e dopar com outros íons para entender o processo de dopagem de materiais e estudar suas propriedades físicas por intermédio dos experimentos de difração de raios X. No LNLS, foram realizados os experimentos de difração múltipla, utilizando energias diferentes na estação de trabalho XRD2. As varreduras renninger mostraram que
a introdução dos dopantes na estrutura cristalina provou mudanças nas posições dos picos, intensidades e na largura meia altura. Estas alterac~oes, observadas nos cristais dopados, podem gerar modificações nas propriedades físicas do material, de modo que, podem acentuar ou inibir alguma propriedade que o cristal possua. O estudo da estrutura destes materiais podem auxiliar outras pesquisas que por ventura utilizem estes cristais. Um exemplo disso é a existência de grupos de pesquisa dopando o NSH com outros materiais, a fim de que possam aumentar a temperatura de desidratação. Assim, as aplicações podem ser feitas nas mais diversas áreas como óptica, eletrônica, medicina e na indústria.

General relativity passed all experimental tests in the weak-field regime, what made it the standard theory of gravity. However, the characterization of strong field regime of general relativity is still a challenge, due to the lack of definitive observational data from high curvature regions. It is in the strong regime that general relativity shows its subtleties and where it is possible to test whether or not general relativity should be replaced by an improved theory of gravity. High curvature regions – and therefore regions of strong field – are possible in the vicinity of compact gravitating objects, such as neutron stars, exotic stars, and black holes. Therefore, these compact objects are excellent laboratories to put constraints and to test theories of gravity in the strong regime. The outcome of the investigation of phenomena around these objects may confront crucial characteristics of general relativity as well as rule out possible alternative theories of gravity. With the advent of potential gravitational wave detectors and new or improved telescopes, it is of utmost importance to study the phenomenology around compact astrophysical objects – to understand the nature of the gravitational objects, to improve the description of the current theoretical models, and to understand the theory of gravity itself. In this thesis, we present a collection of studies on compact objects in general relativity and alternative theories of gravity. The thesis is divided in three main parts. In the first part, we discuss some solutions associated with compact objects. In Chapter 1 we obtain, in closed analytic form, slowly rotating black hole solutions of a general class of theories of gravity, for which the Einstein-Hilbert action is supplemented by all possible quadratic, algebraic curvature invariants coupled to a scalar field. We also discuss possible implications of this solution to the description of accretion disk (thermal) emissions. In Chapter 2 we investigate slowly rotating anisotropic neutron stars in general relativity and in scalar-tensor theories of gravity. We discuss the effect of the fluid anisotropy in the so-called spontaneous scalarization of stars. We also discuss possible ways to constraint the anisotropy of neutron stars. In the second part, we discuss wave-emission processes around compact objects and quasinormal modes. In Chapter 3 we calculate the emission of scalar waves by a particle orbiting a Kerr black hole, within the context of quantum field theory in curved spacetimes at tree level. In Chapter 5 we discuss astrophysical signatures of a plausible supplant to black holes: boson stars. We obtain quasinormal modes – polar and axial – of boson stars within a fully relativistic approach. We also compute the emission of gravito-scalar waves by a particle in circular orbits around boson stars, showing that the star modes “resonate” for some orbits. In Chapter 4 we discuss two different methods to compute the quasinormal modes of spherically symmetric astrophysical environments, namely: the direct integration method and the continued fraction method. In Chapter 6 we discuss the effect of accretion and dynamical friction in the motion and gravitational wave emission of a particle orbiting around – and through – a dark matter star. We model the dark matter star using uniform density stars and using boson stars. We discuss the cases for which the motion of the particle is subsonic and supersonic. In the last part, we discuss planar massless scalar waves impinging upon compact objects, considering their absorption and scattering cross sections. In Chapter 8 we compute the absorption cross section of planar massless scalar waves on Kerr black holes. We consider different angles of incidence, such that we explore the role of the rotation of the black hole into the absorption cross section. We also use the “sinc” approximation to compute the absorption cross of Kerr black holes and compare it with our numerical results. In Chapter 9 we analyze a wave incident on a Schwarzschild black hole surrounded by a thin spherical shell. We show that in the low-frequency limit the absorption cross section approaches the area of the black hole, regardless of the shell characteristics (position and mass). However, in the mid-to-high-frequency limit we show, numerically and analytically, that the absorption cross section can considerably differ from the case of an isolated Schwarzschild black hole with the same ADM mass. In Chapters 10 and 11 we study the absorption and scattering of waves, respectively, incident upon a Bardeen regular black hole. We show that Bardeen black holes can mimic some properties of Reissner-Nordstrom black holes, considering absorption and scattering of fields.

Pesquisas  em  matéria  condensada  como  supercondutores  e  isolantes  topológicos   vem garantindo  avanços  principalmente  na  caracterização  das  propriedades  de  superfície. Consciente  da  importância  dessas  propriedades  na  modelagem  de  nano  dispositivo  que nessa  dissertação  apresentamos  um  modelo  de  uma  nova  classe  de  dispositivo nanoeletrônico. Utilizaremos as propriedades teóricas de transporte eletrônico  para estudar este  modelo  que será  investigado  através do método da Função de Green de Não-Equilíbrio [1] .  A  partir da função de Green obtivemos a  fórmula da condutância do sistema. Os gráficos  da  condutância  sinalizam  a  assinatura  eletrônica  do  sistema  com  a  detecção  de quasipartículas, ou seja, de  Férmions de Majorana . Partiremos  de  um ponto  quântico em contato com eletrodos metálicos, de um único nível, sem spin  acoplado a  uma cadeia de Kitaev [2] , sobre um supercondutor topológico com pareamento -wave.

In this work, we used a modied route of the aqueous sol-gel process to produce spinel
nickel manganite and NiO/NiMn2O4 composite in the powder form. This synthesis route
is quite simple and it is based on the use of sorbitol as a chelating agent. The samples
were characterized by X-ray diraction technique, Rietveld method, scanning electron
microscopy and X-ray photoelectron spectroscopy. The magnetic properties of the samples
were investigated by DC magnetization and AC susceptibility measurements. With
respect to the NiMn2O4 compound X-ray diraction data showed that the sample has
structure of a cubic spinel. Magnetization versus temperature data in low magnetic elds
displayed a signature of a spin glass-type state due to magnetic disorder and frustration.
One well dened peak in real part AC susceptibility curve was observed, indicative of the
spin glass-type transition. The frequency dependence of AC susceptibility clearly demonstrated
a spin glass-type behavior with the onset of spin glass freezing below to the Curie
temperature. From DC magnetization data, the NiMn2O4 compound can be identied
as a cluster spin glass or cluster glass with both ferrimagnetic and spin glass-type phases
coexisting together at low temperatures. Thus, the exchange bias eect observed in the
NiMn2O4 compund was proposed to be due to the pinning eect at the ferrimagnetic and
spin glass-type interface. In relation to the results of the pollycrystaline NiO/NiMn2O4
composite, the Rietveld renement data showed that the percentage of the NiMn2O4 phase
in the samples ranged from 62 to 89 wt% and the NiO phase ranged from 48 to 11 wt%.
Magnetic hysteresis cycles of the NiO/NiMn2O4 composite performed at T = 5 K after
cooling the samples in constant magnetic eld (H = 50 kOe) showed a displacement to
negative elds, which is typical of the exchange bias eect. This eect must be presumably
due to exchange coupling at the interfaces between the antiferromagnetic (NiO) and
ferrimagnetic (NiMn2O4) materials. It also investigated the eect of NiO concentration
in the exchange bias eld and the coervicity. The results showed that exchange bias eect
changed with increasing concentration of NiO.

A eletrodinâmica quântica (QED) é uma das teorias mais bem sucedidas da física, na qual descreve a interação entre a matéria e a radiação eletromagnética. Diante disso, certos fenômenos planares, por exemplo, a supercondutividade à altas temperaturas e o efeito Hall quântico, desencadearam interesses na comunidade científica nesse ramo de pesquisa. Nesta dissertação apresentaremos a Pseudo-Eletrodinâmica Quântica (PQED)
como a teoria apropriada para descrever a interação eletromagnética de partículas carregadas no plano. Mostraremos alguns resultados desta teoria quando aplicada ao estudo do grafeno. Em particular, mostraremos que a PQED abre um gap de energia quando a constante de acoplamento excede um valor crítico, e que esse resultado pode abrir a conjectura da existência de uma transição de fase semi-metal para semi-condutor no grafeno.
E analisando também a influência da velocidade de Fermi na geração deste gap.

Nós investigamos por meio da função de Green de não equilíbrio e teoria do funcional da densidade, as propriedades de transporte eletrônico de junções moleculares compostas de oligo-para-fenileno (com dois, três, quatro e cinco anéis de fenil) fazendo a ponte entre eletrodos do tipo nanotubos de carbono metálico. Verificou-se que a corrente está fortemente correlacionada com um parâmetro quiral puramente geométrico, tanto na ressonância como fora da ressonância. O gráfico de Fowler-Nordheim exibe mínimos, Vmin, que ocorrem sempre que a curva de transmitância em ressonância entra na janela de condução. Esse resultado corrobora com o cenário em que o modelo transporte coerente dá a interpretação correta de espectroscopia de voltagem de transição (TVS). Nós mostramos que Vmin corresponde a tensões, onde a resistência diferencial negativa (NDR) ocorre. A constatação de que Vmin corresponde a tensões que exibem NDR, o que pode ser explicado para a junção de uma única molécula dentro do modelo de transporte coerente, o que confirma ainda mais a aplicabilidade de tais modelos para interpretar adequadamente TVS. O fato dos eletrodos serem orgânicos da origem as diferenças do comportamento de Vmin, se comparado com o caso das junções moleculares com contatos não orgânicos. Na segunda fase da tese, investigamos teoricamente o transporte quântico de não equilíbrio em um ponto quântico acoplado a um estado ligado de Majorana. Baseado no formalismo da função de Keldysh-Grenn, que nos permite investigar a corrente elétrica de forma contínua a partir de zero voltagem até ao grande regime de voltagem. Em particular, nossos achados concordam totalmente com os resultados anteriores na literatura onde o cálculo do transporte é obtido usando a teoria de resposta linear. Nossas curvas I-V revelam uma inclinação característica dada por I = (G0/2)V em regime de resposta linear, onde G0 é a condutância balística e2/h como previsto em Phys. Rev. B 84, 201.308 (R) (2011). Os desvios deste comportamento também são discutidos quando o acoplamento é assimétrico para ambos, o eletrodo esquerdo e direito. A condutância diferencial obtida a partir das correntes da esquerda e direita pode ser maior ou menor do que G0/2, dependendo do acoplamento. Nós também comparamos a corrente através do ponto quântico acoplado a um férmion regular (FR) de modo zero e a um estado ligado de Majorana ou “Majorana bound state” (MBS). Os resultados diferem consideravelmente para toda a faixa de tensão de polarização analisada. Além disso, observa-se a formação de um platô na curva característica I-V para tensões de polarização intermediárias quando o ponto é acoplado a um MBS. Os efeitos térmicos são também considerados. Fazemos notar que, quando a temperatura dos reservatórios é grande tanto RF quanto MBS coincidem para todas as tensões de polarização.

A teoria de perturbações aplicada a gravitação de Einstein pode gerar resultados satisfatorios para muitos problemas em relatividade geral e teoria quântica de campos. A teoria de perturbações nos permite encontrar soluções aproximadas, que se desviam pouco de uma solução exata. Desta forma, a equação de Einstein e \linearizada" e estabelecemos uma teoria linear para a relatividade geral. Ao quantizarmos as perturbações gravitacionais, temos uma teoria linear para um campo tensorial de spin 2: o graviton. Devido a sua relevância para o estudo de cosmologias in acionarias, a analise de fenômenos no espaco-tempo de De Sitter tem aumentado. Perturbações gravitacionais quânticas no espaco-tempo de De Sitter podem ter impactado a evolução de um universo in acionario, que parece ser o caso de nosso proprio Universo, de acordo com observações recentes. As propriedades da função de dois pontos do graviton são especialmente importantes neste contexto. Devido a invariância de calibre da teoria linearizada, divergências na função de dois pontos do graviton podem possuir um carater não físico. Particularmente, divergências no infravermelho podem atuar como mecanismos relacionados a quebra da simetria de De Sitter e o metodo perturbativo perde sua validade. Alguns autores relatam que estas divergências no infravermelho levam a uma constante consmologica dependente do tempo, por exemplo. Nesta dissertação, estudamos perturbações gravitacionais em espacos-tempos de fundo curvos. Usando um formalism invariante de calibre para perturbações gravitacionais em espacos-tempos de fundo com simetrias especiais, particularmente simetria esferica, calculamos a função de dois pontos do graviton na região estatica do espaco-tempo de De Sitter. Analisamos suas propriedades, incluindo seu comportamento no limite infravermelho. A região estatica do espaco-tempo de De Sitter e sicamente relevante, pois representa a região acessvel a um observador inercial. No estado de vacuo tipo Bunch-Davies, o qual e um estado termico com temperatura H=2, em que H e a constante de Hubble, a função de dois pontos que encontramos e nita no limite infravermelho. Alem disso, esta função de dois pontos na região estatica e invariante por translações temporais.

Analisamos a estrutura dos pontos fixos para o modelo não-abeliano de interação de quatro férmions em (3+1) dimensões o qual possue a simetria SU(Nc)­SU(Nf )L ­SU(Nf )R a partir do cálculo perturbativo da função beta do sistema reduzido. Tratamos o modelo como uma teoria efetiva válida em uma escala de energia em que p<< M, onde p é o momento externo e M é uma parâmetro massivo que caracteriza o acoplamento. Usando o mecanismo de redução de Zimmermann, mostramos até a ordem de 1-loop, que alguém do ponto fixo infravermelho na origem existe uma linha de pontos fixos não triviais ultravioletas os quais dependem de Nc e Nf . Estudamos também a quebra de simetria de Lorentz no contexto de Horava-Lifshitz para o modelo de Yukawa e Gross-Neveu-Thirring, mostramos que a inserção de altas derivadas na parte espacial da lagrangeana livre pode melhorar o comportamento ultravioleta das teorias e determinamos as funções do grupo de renormalização para o modelo de Gross-Neveu-Thirring. Num segundo momento, estudamos a eletrodinâmica quântica em três dimensões, na qual verificamos a geração do termo de Chern-Simons e mostramos que a auto-energia do campo de calibre é transversal pela conservação da corrente.

Suspensões de nanotubos de carbono de parede única  (SWCNTs) em soluções aquosas de dodecil  sulfato  de  sódio  (SDS)  e  ácidos  graxos  saturados  (Cn)  são  estudadas.  A  qualidade  das dispersões  é  analisada  por  espectroscopia  de  fotoluminescência  (PL)  como  uma  função  do comprimento da cadeia de Cn. Medidas de espalhamento Raman Resonante (RRS) e simulações de dinâmica  molecular  (MD)  foram  também  realizadas  com o  objetivo  de  estudar  o  efeito  do  meio envolvente nas propriedades dos SWCNTs em suspensões. Ambos os dados de PL e RRS indicam um aumento da individualização de SWCNTs nas dispersões para Cn’s tendo um comprimento de cadeia alquílica maior do que o SDS. Simulações de MD mostraram a formação de misturados CnSDS agregados em torno de um nanotubo em água e umaenergia de ligação de Cn com a parede do nanotubo, que aumenta linearmente com o comprimentoda cadeia. O aumento da solubilização de SWCNTs  é  assim  interpretado  em  termos  da  redução  da repulsão  eletrostática  dentro  dos surfactantes agregados e do aumento da energia de ligação com a parede do nanotubo. Amostras em Pó preparadas pela evaporação de dispersões de Cn ebundles de SWCNT em etanol também foram estudados  por  RRS  na  faixa  de  freqüência  do  modo  de respiração  radial  (RBM).  Todas  as freqüências  RBM  medidas  exibem  um  deslocamrnto  para o  azul  (∆ω)  em  relação  aos  valores obtidos para o pó de SWCNTs puros. Notavelmente, osnanotubos com diâmetros menores do que 1,0 nm, mostram ∆ωno intervalo de 2,5-4,5 cm -1 , enquanto aqueles tendo diâmetros maiores do que 1,0 nm exibem ∆ωno intervalo de 6,5-8,0 cm -1 . Simulações de MD mostraram que os nanotubos de diâmetros  grandes  encapsulam  os  Cn’s  nos  seus  núcleos,  assim  justificando  o  aumento  do endurecimento do modo RBM.

No presente trabalho estudamos a renormalização da pseudo-eletrodinâmica quântica em (2+1)D (PEDQ3) na ordem de um laço. Proposta por E.C. Marino, a PEDQ3 descreve a interação eletromagnética completa entre         elétrons movendo-se em um plano, e recentemente tem sido proposta como a interação entre os elétrons
no grafeno. Usando férmions de quatro componentes e utilizando a regularização dimensional calculamos as funções de renormalização da teoria no caso isotrópico e anisotrópico, e mostramos que a identidade de Ward-Takahashi é preservada. Particularmente, a renormalização da velocidade de Fermi para o caso anisotrópico e o fator giromagn ético para o caso massivo e isotrópico são obtidos.

Nesta dissertação, determinamos a força de Casimir para o modelo de Maxwell-
Proca- Chern-Simons (MPCS) obtido a partir do modelo de Maxwell-Chern-Simons-Higgs
que representa vórtices quantizados em (2 + 1)D do espaço-tempo. No modelo inicial
(MCSH), os vórtices são representados por um campo escalar complexo associado a um
termo de massa dinâmica M. Em uma primeira aproximação, consideraremos o valor esperado
no vácuo (não nulo) deste campo, obtendo, deste modo, o modelo (MPCS). Então,
calcularemos a força de Casimir para o modelo resultante, associando este ao modelo de
dois campos escalares massivos não-interagentes. As massas de cada um dos dois campos
escalares estão adequadamente relacionadas com as constantes características do modelo
de (MPCS). Assim, a força de Casimir pode ser descrita como a soma das forças para
dois campos escalares, que são bem conhecidas na literatura. Contudo, a força de Casimir
depende das condições de contorno consideradas. Então, um problema que surge
naturalmente é que devemos mapear as condições de contorno consideradas para o campo
escalar em respectivas condições de contorno para o campo vetorial do modelo de MPCS
(ou vice-versa). Aqui, por uma questão de simplicidade, tentaremos denir corretamente
as condições de contorno que serão consideradas para o modelo de MPCS (associado a
dois campos escalares), a m de obter a força de Casimir para o modelo em termos das
expressões conhecidas para forças de Casimir para campos escalares.
De outra perspectiva, também, estudamos a força de Casimir para o modelo MPCS
fazendo uso de transformações duais, a m de expressar o modelo MPCS como uma
soma de dois modelos de Proca-Chern-Simons (PCS) vetoriais. O cálculo da força para
cada Proca-Chern-Simons é feito tomando o valor esperado no vácuo do tensor energiamomento,
escrito em termos dos propagadores dos campos auto-duais. A vantagem de
fazermos esta abordagem é que as equações diferenciais resultantes (para os propagadores
dos campos vetoriais) são mais simples do que as descrevem os propagadores do modelo
inicial de Maxwell-Proca-Chern-Simons. Discutimos também, o mapeamento da condição
de contorno do modelo inicial nas respectivas condições de contorno para os modelos vetoriais
resultantes.
Também, para complementar este trabalho, apresentaremos os passos iniciais para investiga
ção do efeito Casimir dinâmico para o modelo de MPCS associando este a campos
escalares massivos. Por simplicidade, começamos a estudar o campo escalar massivo em
(1 + 1)D, sujeito as condições de contorno de Dirichlet, considerando apena uma da fronteiras em movimento não relativístico.