This dissertation describes work carried out between June 1987 and October 1991, in the Low Temperature Physics Group at the Cavendish Laboratory, Cambridge. The aim of this work was to use electron tunnelling spectroscopy to measure the density of excitation states of the recently discovered high-temperature superconductors. Tunnelling is the most sensitive method for measuring a superconductor’s energy gap, and historically has provided important evidence for the microscopic mechanism of superconductivity in conventional metals. It was hoped that electron tunnelling would prove equally successful in revealing the mechanism of superconductivity in these new materials. Preliminary experiments showed that a thick, degraded surface layer prevented preparation of high-quality tunnel junctions by conventional evaporation techniques. For this reason, apparatus for the formation and fine control of low-temperature point-contact junctions was constructed, together with new measurement electronics and a computer-controlled data-acquisition system. To test this apparatus, point-contact junctions were formed on conventional superconductors. By increasing pressure of the tip on the sample the junction could be moved from the tunnelling to the metallic regime. Point-contact measurements were then made on a number of ceramic, single-crystal and thin-film high-temperature superconducting materials; some not previously investigated by tunnelling. Although ‘gap-like’ structure was occasionally observed, anomalous features (e.g., voltage-dependent background, broadening, large zero-bias conductance) were always present and usually dominated the tunnelling characteristics. These complicate estimation of the energy gap and preclude measurement of more subtle properties such as gap anisotropy or the effective phonon spectrum, α2F. The origins of these non-ideal features have been much debated in the literature and are reviewed in this dissertation. In the case of thin films deposited by laser ablation the tunnelling characteristics were dominated by single-electron tunnelling effects (Coulomb gap and staircase structure). The results suggest that the surface region consists of numerous, isolated normal metal particles.

Cette thèse expérimentale explore les propriétés supraconductrices du silicium très fortement dopé, en particulier au bore, ainsi que les propriétés physiques anormale observées à plus hautes températures. La supraconductivité de Si:B est obtenue sous 1K, pour des dopages en bore supérieurs à la limite de solubilité du bore dans le silicium. Le Si:B est métallique à ces taux de dopage. Dans une première partie, nous exposons les différentes techniques expérimentales exploitées au cours de cette thèse. Nous expliquons les différentes techniques de dopage hors équilibre identifiées pour doper du silicium au-delà de la limite de solubilité, puis les techniques de caractérisation pour contrôler la qualité des couches dopées obtenues, ainsi que les méthodes de mesures aux très basses températures. Dans une deuxième partie, nous exposons les résultats obtenus sur la supraconductivité de Si:B en faisant varier dans un premier temps le taux de dopage en bore, puis en renouvelant l'étude à différentes épaisseurs de couche dopée. Nous montrons notamment que l'évolution de la Tc avec le couplage électron-phonon $lambda$ ne suit pas une loi de McMillan classique, mais plutôt une loi de puissance comme celle observée dans le cas du diamant supraconducteur. Nous montrons que ce résultat peut être expliqué dans le cadre d'un modèle d'un supraconducteur à deux couches de $lambda$ différents. En étudiant la dépendance en température et angulaire de Hc2, nous montrons que Si:B est un supraconducteur intrinsèquement de type I, mais qui devient de type II sous effet d'impuretés, et que la supraconductivité est à caractère bidimensionnel. Dans une troisième partie, nous présentons des comportements anormaux de certaines caractéristiques physiques mesurées dans certaines séries de Si:B, à partir de 50K et qui persistent jusqu'à au moins 400K. Nous présentons des mesures de magnétotransport, d'effet Hall et de mesures thermoélectriques qui présentent toutes des caractéristiques hautement non linéaires, et donc anormales pour un métal. L'origine de ces anomalies est toujours ouverte. Enfin, nous présentons quelques perspectives de travail, en particulier les premières mesures sur un échantillon avec une géométrie de type SQUID. / This experimental PhD thesis explore the superconductivity of heavily boron doped epilayers as well as some unusual properties observed at high temperatures. The superconductivity of Si:B is observed below 1K and triggered by boron content exceeding the solubility limit of boron into silicon. For such high boron contents, the silicon layers are metallic. In a first part, we develop the various experimental techniques used. We explain the principles of the out-of-equilibrium doping techniques required to doped beyond the solubility limit. We develop also on the characterisation techniques used to control the quality of the samples, as well as the low temperatures measurement techniques. In a second part, we show the results obtained on the superconductivity of Si:B, obtained forst by varying the boron content at a given layer thickness, and then as a function of the layer thickness. We show that the evolution of Tc with the electron-phonon coupling constant lambda doesn't follow the classical McMillan law, but rather a power of law as it was reported for superconducting diamond. We show that this result can be explained by a double layer model with dislocations resulting in two different lambda values for each sublayer. The study of the temperature and angular dependency of the Hc2 also show that Si:B is an intrinsic type I superconductor turned into type II with defect effects, and that the superconductivity is bidimensionnal. In a third part, we present the anomalous high temperature behaviour of some Si:B epilayers, starting from 50K and observed at least up to 400K. We present magnetotransport, Hall effect and thermoelectric measurements that all show a highly non linear behaviour, unusual for a metal. The origin of these anomalies is still an open question. We finally present some future perspectives, including the first measurements on a Si:B SQUID-like geometry.

Des conducteurs mono- et multi-filamentaires de MgB2 dans une gaine de Nb/Cu ont été élaborés par la technique PIT (powder in tube) avec des dopages de carbone et de TiC. Les résultats montrent qu'il y a une couche de diffusion non supraconductrice à l'interface entre le Nb et MgB2 pour les échantillons traités à haute température, couche qui empêche la pénétration du courant dans le conducteur. Les traitements thermiques doivent être inférieurs à 750°C. Les effets des dopages au carbone amorphe et au TiC ont été étudiés par XRD,MEB et aimantation. La substitution du bore par du carbone diminue légèrement la Tc mais augmente la piégeage des vortex, conduisant à un optimum du courant critique. Des multi-filaments de 6, 12 et 36 filaments sans dopage ont été élaborés par la technique PIT. Les propriétés mécaniques de ces conducteurs ont été renforcées en utilisant un filament central en Nb. L'assemblage MgB2/Nb/Cu est très adapté pour obtenir de grandes longueurs de conducteurs par la méthode PIT. / The mono-filamentary and multi-filamentary MgB2 wires sheathed with Nb/Cu composite tube were fabricated by in-situ powder-in-tube (PIT) technique with the carbon and TiC doping. The results show that there is a diffusion layer at the interfacial region between the Nb sheath and MgB2, which is non-superconducting phase for the sample heat-treated at high temperature, and this diffusion layer obstructs the current transmission at high heat-treatment temperatures and the best heat-treatment temperature for the MgB2 wires with Nb as the barrier layer should be lower than 750°C. Effects of amorphous carbon and TiC doped MgB2 wires were investigated by XRD, SEM and magnetization. The results show that substitution of B for C enhances the flux pinning but depresses Tc slightly. By controlling the processing parameters, an optimized Jc(H) performance is achieved under a partial amorphous C substitution. The Cu-clad 6-, 12-, and 36-filamentary MgB2 wires with Nb buffer layer also have been fabricated by the in-situ PIT method. To improve the strength of wires, the Nb-core was used as the central filament. The results show that the in-situ PIT technique can be used to produce the certain long length MgB2/Nb/Cu wires. The superconducting filaments of MgB2/Nb/Cu composite tubes have well workability suitable for the MgB2 wires long length and multi-filament.

Comprendre la supraconductivité des pnictures et séléniures de fer nécessite de bien connaître leurs propriétés électroniques et magnétiques. Dans ce cadre, j'ai aidé à réaliser et j'ai automatisé un dispositif cryogénique capable d'étudier ces propriétés, à basse température (jusqu'à ~1 K) et sous application d'un champ magnétique statique (jusqu'à 2 T) ou oscillant. Les techniques implémentées sont la spectroscopie de pointe et la microscopie à sonde de Hall, et le dispositif est conçu de sorte qu'il soit possible de basculer de l'une à l'autre sans manipuler l'échantillon.J'ai ensuite utilisé ce dispositif pour étudier par spectroscopie de pointe les gaps supraconducteurs du pnicture Ba(Fe,Ni)2As2, puis rechercher la signature du couplage de ses électrons de conduction à des modes bosoniques. Ce faisant, il a été observé dans la conductance différentielle de jonctions métal-supraconducteur un signal oscillant dont la période varie en température comme le gap supraconducteur de l'échantillon. Ce signal dépend de la résistance de contact de la jonction d'une façon qui prouve clairement qu'il est issu d'effets hors équilibre.J'ai modélisé ce signal en étudiant théoriquement la physique de jonctions métal-métal-supraconducteur, dont la seconde région métallique serait formée par transition locale du supraconducteur vers l'état normal. Le modèle que j'ai ainsi construit permet de prédire la conductance différentielle d'une telle jonction, moyennant une connaissance préalable de la loi L(V) reliant la taille de la seconde région métallique à la tension aux bornes de la jonction. J'ai ensuite proposé plusieurs modèles pour cette loi.Après comparaison avec l'expérience, il semble possible que la région métallique se forme par dépassement local de la densité de courant critique Jd du supraconducteur associée à la brisure de paires de Cooper, ou "courant de depairing". Mais il serait aussi vraisemblable que l'injection d'électrons perturbe localement la distribution électronique f(E) de l'échantillon, au point de déstabiliser l'état supraconducteur. Cette dernière interprétation suppose une forte dépendance en température du couplage électron-boson à basse énergie.Enfin, je présente en annexe les fonctionnalités de microscopie magnétique du dispositif réalisé, ainsi que les premiers résultats scientifiques qu'elles ont permis d'obtenir : la mise en évidence du rôle joué par le fluage quantique dans la relaxation des vortex piégés au sein de Fe(Se,Te). / Reaching a good understanding of the superconductivity of iron pnictides and selenides requires an accurate knowledge of their electronic and magnetic properties. To this end, I helped building and I automated a cryogenic device that is suitable for the study of these properties, at low temperatures (down to ~1 K) and under the application of a magnetic field, either static (up to 2 T) or oscillating. The device implements the experimental techniques of point contact spectroscopy and scanning hall probe microscopy, and it allows switching between them without requiring sample manipulations.I subsequently used this device to study the superconducting gaps of Ba(Fe,Ni)2As2 by point contact spectroscopy, before I began looking for signatures of the coupling of conduction electrons to bosonic modes. However, in this process, the differential conductance of metal-superconductor junctions turned out to exhibit oscillating features, whose period evolves in temperature like the superconducting gap of the sample. This signal also depends on a junction's contact resistance in such a manner that it appears unmistakably out-of-equilibrium in nature.I derived a model of this signal by undertaking a theoretical study of metal-metal-superconductor junctions. In these junctions, the second metallic region would emerge from a local transition of the superconductor to the normal state. The resulting model is able to predict the differential conductance of such a junction, given prior knowledge of the L(V) law linking the size of the second metallic region to the voltage being applied across the junction. I subsequently derived several models for this law.Comparing these models to experimental data, it appears that the observed phenomenology could emerge from a local increase of current density above the "depairing current" Jd associated to Cooper pair breaking in the superconductor. Alternatively, electron injection could also locally alter the electron energy distribution f(E) of the sample to the point of destabilizing the superconducting state. This last explanation requires a strong temperature dependence of the electron-boson coupling at low energies.Finally, in an appendix, I describe the magnetic microscopy capabilities of the experimental device. Those capabilities enabled us to understand the role played by quantum creep in the relaxation of trapped vortices within Fe(Se,Te).

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Modelo disponível em: http://www.biblioteca.bauru.unesp.br/#!/servicos/ficha-catalografica/ Agradecemos a compreensão. on 2018-03-14T13:03:07Z (GMT) / Submitted by Nicolas Porto Vizarim (nicolasvizarim@gmail.com) on 2018-03-14T13:20:53Z No. of bitstreams: 1 Dissertação - Nicolas - Repositório.pdf: 7208823 bytes, checksum: 9075fa2e8a261a4f2a51a2946604cacc (MD5) / Approved for entry into archive by Maria Marlene Zaniboni null (zaniboni@bauru.unesp.br) on 2018-03-14T17:06:41Z (GMT) No. of bitstreams: 1 vizarim_np_me_bauru.pdf: 7208823 bytes, checksum: 9075fa2e8a261a4f2a51a2946604cacc (MD5) / Made available in DSpace on 2018-03-14T17:06:41Z (GMT). No. of bitstreams: 1 vizarim_np_me_bauru.pdf: 7208823 bytes, checksum: 9075fa2e8a261a4f2a51a2946604cacc (MD5) Previous issue date: 2018-02-26 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O estudo do comportamento de vórtices em supercondutores de tipo II com centros de aprisionamento (CAs) vem atraindo muita atenção nas últimas décadas devido a possibilidade de aumento da corrente crítica, assim como pela variedade de comportamentos que o sistema pode apresentar. Muito foi feito nos últimos anos na tentativa de compreender os mecanismos de aprisionamento, incluindo estudos de filmes infinitos sob influência de arranjos periódicos e quase-periódicos focando nos efeitos de comensurabilidade, correntes críticas e fases dinâmicas. No entanto, quando se trata de fitas supercondutoras muito trabalho ainda é necessário, especialmente para verificar como os CAs influenciam o sistema. Neste trabalho, foi simulado computacionalmente, utilizando técnicas de Dinâmica Molecular, o comportamento dinâmico de vórtices no interior de uma fita supercondutora do tipo II sob a influência de CAs com distribuição aleatória, hexagonal e dois tipos de arranjos conformes. A simulação foi feita considerando fitas imersas no plano xy, finita em x e infinita em y, com um campo magnético aplicado perpendicularmente ao plano das fitas e temperatura nula. Como resultado, encontramos que a fita com aprisionamento aleatório apresentou, na média, um decaimento suave da força de depinning (força necessária para libertar os vórtices dos CAs) em função do campo aplicado. Além disso, foi observada a presença de vórtices intersticiais fracamente ancorados, resultando em baixos valores de força de depinning. Já a fita com arranjo hexagonal apresentou efeitos significativos de comensurabilidade apenas no primeiro matching field, onde há um grande aumento da força de depinning, diferentemente do observado em filmes supercondutores infinitos, onde vários picos de comensurabilidade na corrente crítica são observados. Para os arranjos conformes, a força de depinning muda muito pouco em função do campo aplicado apresentando uma leve tendência decrescente, o que está de acordo com o que foi observado em filmes infinitos. Este comportamento está associado ao gradiente de defeitos e a simetria hexagonal que a rede conforme preserva, tornando o aprisionamento mais efetivo. Em um dos arranjos conforme foi obtido um aumento significativo nas forças de depinning em baixos campos, quando comparado aos outros arranjos. Com relação aos regimes dinâmicos, em fitas os vórtices tendem a formar canais devido a influência da corrente superfícial, que reduz o movimento transversal dos vórtices, diferentemente do observado em filmes infinitos. / The behavior of vortices in type II superconductors in the presence of artificial pinning centers has attracted much attention in the last two decades, due to the possibility of enhancing the critical currents, as well as the variety of behaviors that the system can exhibit. Much has been done in recent years to understand the pinning mechanisms, including studies of infinite films under the influence of periodic and quasi-periodic arrays focusing on the commensurability effects, critical currents and vortex dynamic phases. However, when it comes to superconducting strips a lot of work is still required, especially when the system is under the influence of pinning centers. In this work, we study the dynamic behavior of vortices inside a type II superconducting strip in the presence of pinning centers with random distribution, hexagonal and two types of conformal arrays. The simulation was performed considering strips using Molecular Dynamics technique, each with different arrays of defects, immersed in the xy plane, with finite dimension in x and infinite in y, under a magnetic field applied perpendicular to the plane of the strips and zero temperature. As a result, it was found that the strip with random pinning distribution showed a gentle decay of the depinning forces as a function of the applied field. In addition, the presence of weakly pinned interstitial vortices was observed, resulting in low values of depinning force. The hexagonal array showed significant commensurability effects only at the first matching field, where there is a great increase of the depinning force, unlike that observed in infinite superconducting films, where several commensurability peaks in the critical current is observed. For the conformal arrays, we observed a depinning force stability as a function of the applied field, which agrees with what has been observed in infinite films. This stability is associated to the gradient distribution of defects in the central region of the sample associated with sixfold symmetry that the conformal transformation preserves, resulting in a more effective pinning. In one of the conformal lattices, a significant increase in the depinning forces in low fields was obtained when compared to the other arrays. Concerning to the dynamic regimes, vortices in strips tend to form well defined channels due to the influence of the surface current, which reduces the transverse motion of the vortices, different to that observed in infinite films.

Made available in DSpace on 2014-12-17T14:55:45Z (GMT). No. of bitstreams: 1 HugoMCAM_DISSERT_partes autorizadas.pdf: 586809 bytes, checksum: e96d1467d4ab6c5fa6da39927cde0bca (MD5) Previous issue date: 2010-07-09 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / This work has as main objective to study the application of microstrip antennas with patch and use of superconducting arrays of planar and linear phase. Was presented a study of the main theories that explain clearly the superconductivity. The BCS theory, Equations of London and the Two Fluid Model are theories that supported the implementation of the superconducting microstrip antennas. Arrangements phase was analyzed in linear and planar configuration of its antennas are reported factors such arrays to settings and criteria of phase and the spacing between the elements that make the arrayst was reviewed in order to minimize losses due to secondary lobes. The antenna used has a rectangular patch Sn5InCa2Ba4Cu10Oy the superconducting material was analyzed by the method of Transverse Transmission Line (TTL) applied in the field of Fourier transform (FTD). The TTL is a full-wave method, which has committed to obtaining the electromagnetic fields in terms of cross-cutting components of the structure. The inclusion of superconducting patch is made using the boundary condition, complex resistive. Are obtained when the resonant frequency depending on the parameters of the antenna, radiation pattern of E-Plan and H-Plan for the M-phase arrangements of antennas in the linear and planar configurations for different values of phase and spacing between the elements. / Este trabalho tem como objetivo principal o estudo da aplica??o de antenas de microfita com patch supercondutor e uso dos arranjos de fase linear e planar. Foi apresentado um estudo das principais teorias que explicam com clareza a supercondutividade. As teorias BCS, Equa??es de London e modelo dos Dois Fluidos s?o as teorias que d?o suporte a aplica??o dos supercondutores nas antenas de microfita. Os arranjos de fase foram analisados em configura??es lineares e planares de suas antenas. Foram obtidos os fatores de arranjos para tais configura??es e os crit?rios da fase e do espa?amento entre os elementos que comp?e o arranjo, ao qual foram examinados com o objetivo de obter um l?bulo principal com alta diretividade e alto ganho. A antena utilizada tem como patch retangular o material supercondutor Sn5InCa2Ba4Cu10Oy foi analisada atrav?s do m?todo da Linha de Transmiss?o Transversa (LTT), aplicado no dom?nio da transformada de Fourier (FTD). O LTT ? um m?todo de onda completa, que tem como regra a obten??o dos campos eletromagn?ticos em termos das componentes transversais ? estrutura. A inclus?o do patch supercondutor ? feita utilizando-se a condi??o de contorno complexa resistiva. S?o obtidos resultados da freq??ncia de resson?ncia em fun??o dos par?metros da antena; diagramas de radia??o do Plano-E e Plano-H para os arranjos de fase de antenas nas configura??es lineares e planares para diferentes valores da fase e espa?amento entre os elementos.

Made available in DSpace on 2014-06-11T19:30:19Z (GMT). No. of bitstreams: 0 Previous issue date: 2010-04-28Bitstream added on 2014-06-13T19:39:47Z : No. of bitstreams: 1 pascolati_mcv_me_bauru.pdf: 4047066 bytes, checksum: cf327b8f4cd0447dc8dd5e7c4d6604a5 (MD5) / O interesse em conhecer o comportamento supercondutor tem sido cada vez maior nas últimas décadas. Na busca de melhores características supercondutoras, descobriu-se que amostras volumétricas apresentam características muito diferentes de amostras mesoscópicas (amostras com dimensões próximas dos comprimentos de penetração de London e coerência). Como exemplo, podemos citar a não formação de rede de Abrikosov, como consequência do efeito de confinamento (efeito associado às dimensões reduzidas da amostra) e também uma mudança considerável nos valores dos campos críticos. Neste trabalho foram resolvidas as equações de Ginzburg-Landau dependentes do tempo (TDGL), para fazer uma análise detalhada da dinâmica de vórtices em filmes finos mesoscópicos. Para revolvê-las, utilizamos o método das variáveis de ligação com invariância de calibre, adaptado para o algoritmo de diferenças finitas, utilizado para obter a densidade dos pares de Cooper e também curvas de magnetização. O estudo dessa dinâmica de vórtices, foi feito em três amostras com superfícies geométricas diferentes (côncova, convexa e rugosa). Observamos que na comparação entre as duas primeiras, há uma diferença considerável nos valores dos campos críticos, bem como no comportamento da magnetização comparado com um filme plano. Já para a amostra de superfície rugosa, observamos que existe uma competição entre o efeito de confinamento e a rugosidade em relação à configuração dos vórtices. Apresentamos também, uma tabela que mostra resumidamente os estados estacionários dos vórtices nas três amostras. / The interest to investigate the investigate the behavior of a superconductor has grown in the last few decades. Having in mind to search for better superconducting characteristics, it has been found that bulk samples present characteristics much more different than mesoscopic samples (samples with dimensions of the same order of the same order of the London penetration length and the coherence length). As an example, we can mention the non-formation of an Abrikosov vortex lattice as a consequence of the confinement effect (effect associated with the reduced dimensions of the sample) and also considerable change in the critical field values. In the present work we solved the time dependent Ginzburg-Landau equation (TDGL), in order to make a detailed analysis of the vortex dynamics in mesoscopic thin films. To solve these equations, we have used the link variables method which is gauge invariant. From this, we obtain the Cooper pair density and the magnetization curves. The vortex dynamics was investigated for three different surfaces of the film (concave, convex, and irregular). We have observed that, with respect to the parabolic geometries, there is a considerable difference for the critical fields, as well as for the behavior of the magnetization compared to a flat film. On the other hand, for a sample with an irregular surface, we have seen that there is a competition between the confinement effect and rugosity with respect to vortex configurations. We also present a table which summarizes the vortex stationary states for the three topologies mentioned above.

abstract: In this thesis, we present the study of several physical properties of relativistic mat- ters under extreme conditions. We start by deriving the rate of the nonleptonic weak processes and the bulk viscosity in several spin-one color superconducting phases of quark matter. We also calculate the bulk viscosity in the nonlinear and anharmonic regime in the normal phase of strange quark matter. We point out several qualitative effects due to the anharmonicity, although quantitatively they appear to be relatively small. In the corresponding study, we take into account the interplay between the non- leptonic and semileptonic weak processes. The results can be important in order to relate accessible observables of compact stars to their internal composition. We also use quantum field theoretical methods to study the transport properties in monolayer graphene in a strong magnetic field. The corresponding quasi-relativistic system re- veals an anomalous quantum Hall effect, whose features are directly connected with the spontaneous flavor symmetry breaking. We study the microscopic origin of Fara- day rotation and magneto-optical transmission in graphene and show that their main features are in agreement with the experimental data. / Dissertation/Thesis / Ph.D. Physics 2013

abstract: A series of Molybdenum-Copper bilayers were studied for use in 120mK superconducting transition edge sensors for spectrometer applications. The Transition temperature (T_C) was tuned to the desired temperature using the proximity effect, by adjusting the thickness of a normal copper layer in direct contact with the superconducting molybdenum layer in a proximitized bilayer structure. The bilayers have a fixed normal metal thickness d_Cu=1250 Å, on top of a variable superconductor thickness 650 Å ≤ d_Mo ≤ 1000 Å. Material characterization techniques including X-ray Diffraction (XRD), Rutherford Backscattering Spectroscopy (RBS), Atomic Force Microscopy (AFM), and 4-point electrical characterization are used to characterize the films. Film TC are compared with the results of the Usadel proximity theory. The results of RBS analysis demonstrated that some Argon-contamination is observed at the Mo film-substrate interface, which correlates with bilayer surface roughness (as observed with AFM), reduced crystalline quality (via XRD Rocking Curve), and a deviation from the theoretical expected TC for a bilayer. The Argon contamination is presumably the cause of interface roughness, reducing the interface transmission coefficient in the Usadel model, and producing the discrepancy from the expected TC. / Dissertation/Thesis / Masters Thesis Materials Science and Engineering 2014

Os supercondutores de alta temperatura crítica apresentam propriedades diferentes dos supercondutores convencionais, uma destas propriedades importantes é a simetria não isotrópica do parâmetro de ordem. Neste trabalho se apresenta um modelo que mostra a presença de simetria d-wave em uma classe de supercondutores de alta Tc, assim como a condição para a existência de ondas de densidade nos estados de equilíbrio. Se analisa primeiro um sistema de três corpos, um bipolaron e dois elétrons, com o objetivo de estudar o efeito da repulsão coulombiana local e não local sobre a simetria do parâmetro de ordem para o caso exato e também o limite de acoplamento forte. Se mostra também a construção de um Hamiltoniano efetivo que desacopla a interação el etron-bipolaron com o fim de abordar o problema coletivo de infinitos corpos e vemos como o modelo proposto prediz a formação de ondas de densidade para uma região especifica dos parâmetros físicos do Hamiltoniano estudado. / High-temperature superconductors have different properties than conventional superconductors, one of these important properties is non-isotropic symmetry of the order parameter. In this work we present a model that shows the presence of symmetry d-wave in a class of superconductors of high Tc , as well as the condition for the existence of density waves in the states of equilibrium. We first analyze a three-body system, a bipolaron and two electrons, in order to study the effect of local and non-local Coulomb repulsion on the symmetry of the order parameter for the exact case and also the strong coupling limit. It is also shown the construction of an effective Hamiltonian that decouples the electron-bipolaron interaction in order to approach the collective problem of infinite bodies and we see how the proposed model predicts the formation of density waves for a specific region of the physical parameters of the studied Hamiltonian.