In der vorliegenden Arbeit wird die Physik von Schwer-Fermion-Systemen, die durch Lanthanid- und Aktinid-Übergangsmetallverbindungen realisiert werden, untersucht. Die Basis für eine theoretische Beschreibung bildet das Anderson-Gitter, welches das Wechselspiel freier Leitungselektronen und stark korrelierter Elektronen aus lokalisierten f-Orbitalen charakterisiert. Als Zugang zu diesem Modell wird die von Wegner vorgeschlagene Flussgleichungsmethode verwendet, ein analytisches Verfahren, welches auf der Konstruktion eines effektiven Hamilton-Operators basiert. Ein zentrales Thema dieser Arbeit ist die Beschreibung der elektronischen Struktur von Schwer-Fermion-Systemen. Insbesondere wird die Abhängigkeit statischer Größen vom Einfluss verschiedener Systemparameter betrachtet. Die Dynamik kollektiver Anregungen in Schwer-Fermion-Systemen wird an Hand der elektronischen Zustandsdichten und dynamischen magnetischen Suszeptibilitäten untersucht. / The physical properties of heavy-fermion systems are examined. These systems are mainly formed by rare earth or actinide compounds. Their essential physics can be characterized by the periodic Anderson model which describes the interplay of itinerant metal electrons and localized, but strongly correlated f-electrons. The present calculations are based on the flow equations approach proposed by Wegner. This method uses a continuous unitary transformation to derive an effective Hamiltonian of an easy to treat structure. Within this framework the electronic structure of heavy-fermion systems is calculated and the influence of external parameters is studied. Beside the derivation of static properties the density of states and dynamic magnetic susceptibilities are investigated in order to characterize the nature of collective excitations.

[pt] Nesta tese estudamos as propriedades físicas de materiais fortemente correlacionados e desordenados, usando Hamiltonianos modelos para descrevê-los. A tese está dividida em duas partes. Na primeira, estudamos o modelo de Anderson periódico para descrever as propriedades de um isolante Kondo. Em particular tomamos o composto de Ce3Bi4Pt3 como paradigma deste tipo de materiais caracterizados por apresentar um pequeno gap(da ordem dos meV ). Na presença de pequenas concentrações de impurezas metálicas como íons de La substituindo os de Ce, como é o caso da liga (Ce1-xLax)Bi4Pt3, sofre uma transição metal-isolante. O Hamiltoniano de Anderson periódico é resolvido a partir da solução de um único sítio atômico que logo é embebido numa rede de Bethe. Este modelo consegue explicar qualitativamente os resultados experimentais como a resistividade em função da temperatura para diferentes concentrações de íons de La, assim como as propriedades óticas do sistema puro. A influência da localização de Anderson nesta transição é analisada a partir do estudo da condutividade elétrica do sistema. A segunda parte está dedicada ao estudo das propriedades de sistemas descritos pelo Hamiltoniano de Falicov- Kimball, largamente utilizado para estudar fenômenos como a transição de valência e metal- isolante, também em compostos de Metais de Transição e Terras Raras. Neste modelo, o caráter destas transições ainda não está bem estabelecido já que o resultado é muito dependente da aproximação utilizada. Utilizamos o Hamiltoniano de Falicov-Kimball sem spin onde a banda de condução é tratada de forma exata já que mostramos a sua equivalência com o problema de uma liga. Os estados f são resolvidos em forma aproximada a partir da equação de movimento, aproximação que chamamos de Aproximação do Estreitamento Dinâmico(AED). Estudamos as propriedades eletrônicas como a ocupação dos estados localizados em função da energia local. Também neste caso, analisamos um sistema desordenado estudando o contraponto entre a correlação eletrônica e a desordem. As diferentes fases que aparecem no sistema como, metálica, isolante de Anderson e de Mott são investigadas em função dos parâmetros que definem o sistema. / [en] In this thesis we study the properties of strongly correlated and disordered materials, using model Hamiltonians to describe them. The thesis is divided in two parts. The first one studies the periodic Anderson model used to describe the properties of a Kondo insulator. In particular we take Ce3Bi4Pt3 as a paradigmatic compound, characterized by a small gap(of the order of meV ). For small concentration of metallic impurities, ions of La substituting Ce, the alloy (Ce1-xLax)Bi4Pt3 suffers a metal- insulator transition. The periodic Anderson Hamiltonian is solved using the atomic solution that is embedded into a Bethe lattice. This model explains the experimental results as the resistivity as a function of temperature for different concentrations of ions of La, as well as, the optical properties of the pure system. The Anderson localization is analyzed studying the electric conductivity of the system. The second part of the thesis is dedicated to study the property of a system described by the Falicov- Kimball Hamiltonian. This Hamiltonian has been used to study the valence and metal-insulator transitions in Transitions Metal and Rare Earth compounds. In this model, the character of these transitions is still not well understood, since it is very dependent of the approximation used. We study the Falicov-Kimball Hamiltonian without spin. The conduction band is exactly described since we show its equivalence with the problem of an alloy. The f states are studied using the equation of motion for the Green functions, decoupling them in a way defined as the Dynamic Narrowing Approximation(DNA). We study the occupation of the local states as a function of energy and other electronic properties. For an alloy the interplay between the electronic correlation and disorder is analized. The different phases that appear in the system, as metallic and Anderson and Mott insulating, are investigated as a function of the parameters that define the system.

Cette thèse est consacrée à l’étude de deux aspects de la physique mésoscopique que sont le bruit quantique haute fréquence et l'effet de proximité supraconducteur en se focalisant toutefois sur un système modèle: le nanotube de carbone.Ainsi la première partie de cette thèse est dédiée à la mesure de bruit quantique haute fréquence. Afin de mesurer ces fluctuations nous avons développé un système de détection "on-chip" original dans lequel la source de bruit et le détecteur, une jonction Supraconducteur/Isolant/Supraconducteur, sont couplés par un circuit résonant. Cela nous a permis dans un premier temps de mesurer le bruit à l'équilibre du résonateur. Son bruit comporte une forte asymétrie entre émission et absorption reliée aux fluctuations de point zéro. Une seconde étape a été de mesurer le bruit hors équilibre d’émission du passage tunnel de quasi-particules dans une jonction Josephson. Ce bruit comporte une forte dépendance en fréquence en accord avec les prédictions théoriques et nous a permis de valider le principe de détection. Finalement, nous avons pu mesurer le bruit associé au régime Kondo hors équilibre d'une boîte quantique à nanotube de carbone (énergie caractéristique kBTK avec TK la température Kondo). Ce bruit d’émission à kBTK~hν possède une forte singularité à la tension V=hν/e (ν étant la fréquence de mesure). Cette singularité est reliée aux résonances Kondo dans la densité d’états de la boîte associés aux niveaux de Fermi de chaque réservoir. A plus haute fréquence hν~3kBTK, la singularité disparaît, ce qui est compris par des effets de décohérence induits par la tension.Dans la seconde partie, nous avons développé une technique permettant de mesurer à la fois la relation courant/phase et la caractéristique courant/tension d'un lien faible séparant deux supraconducteurs. Nous avons ainsi caractérisé une jonction à base de nanotube de carbone au travers de laquelle une relation courant-phase modulable par une tension de grille a été observée. Cette relation courant/phase exhibe une forte anharmonicité lorsque le supercourant présente une relativement grande amplitude. / This thesis discusses two experiments of mesoscopic physics regarding the high frequency quantum noise and the superconducting proximity effect. We nevertheless focused on a single model system: the carbon nanotube. The first experiment aims to measure the high frequency quantum noise of the tube. In order to measure those fluctuations we have designed an original on-chip detection scheme in which the noise source and the detector, a Superconductor/Insulator/Superconductor junction, were coupled through a resonant circuit. This first allowed us to measure the equilibrium noise of the resonator. It exhibits a strong asymmetry between emission and absorption related to zero point fluctuations. We have then measured the out-of-equilibrium emission noise of quasiparticles tunneling of a Josephson junction. It exhibits a strong frequency dependence in agreement with theoretical predictions and allowed us to validate the detection scheme. Finally, the out-of-equilibrium emission noise associated to the Kondo effect (characteristic energy kBTK with TK the Kondo temperature) in a carbon nanotube quantum dot was measured. We find a strong singularity at voltage V=hν/e (ν is the measurement frequency) for frequency ν~kBTK/h. This singularity is related to resonances in the density of states of the dot pinned at the Fermi energy of the leads. At higher frequency hν~3kBTK the singularity vanishes and understood in terms of decoherence effects induced by the bias voltage. In the second experiment, we have developed a technique allowing to measure in the same experiment the current-phase relation and the current-voltage characteristic of a weak link separating two superconductors. We have characterized a carbon nanotube based junction through which a gate tunable current-phase relation was observed. Jointly to a high critical current amplitude, an anharmonic current-phase relation was measured.

The study of transport in nano-structured devices and molecular junctions has become a topic of great interest with the recent call for quantum technologies. Most of our knowledge has been guided by experimental and theoretical studies of the single-electron transistor (SET), an elementary device constituted by a quantum dot coupled to two otherwise independent free electron gases. The SET is particularly interesting because its transport properties at low temperatures are governed by the Kondo effect. A methodological difficulty has nonetheless barred theoretical progress in describing accurately realistic devices. On the one hand, Density-Functional Theory (DFT), the most convenient tool to obtain the electronic structure of complex materials, yields only qualitatively descriptions of the low-temperature physical properties of quantum dot devices. On the other hand, a quantitative description of low-temperature transport properties of the SET, such that obtained through the solution of the Anderson model via exact methods, is nonetheless unable to account for realistic features of experimental devices, such as geometry, band structure and electron-electron interactions in the electron gases. DFT describes the electron gases very well, but proves inadequate to treat the electronic correlations introduced by the quantum dot. This thesis proposes a way out of this frustrating dilemma. Our contribution is founded on renormalization-group (RG) concepts. Specifically, we show that, under conditions of experimental interest, the high and low temperatures regimes of a SET corresponds to the weakly-coupling and strongly-coupling fixed points of the Anderson Hamiltonian. Based on an RG analysis, we argue that, at this low-temperature fixed point, the entanglement between impurity and gas-electron spins introduces non-local correlations that lie beyond the reach of local- or quasi-local-density approximations, hence rendering inadequate approximations for the exchange-correlation energy functional. By contrast, the weak-coupling fixed point is within the reach of local-density approximations. With a view to describing realistic properties of quantum dot devices, we therefore propose a hybrid self-consistent procedure that starts with the weak-coupling fixed point and takes advantage of a reliable numerical method to drive the Hamiltonian to the strong-coupling fixed point. Our approach employs traditional DFT to treat the weak-coupling system and the Numerical Renormalization-Group (NRG) method to obtain properties in the strongcoupling regime. As an illustration, we apply the procedure to a single-electron transistor modeled by a generalized one-dimensional Hubbard Hamiltonian. We analyze the thermal dependence of the conductance in the SET and discuss its behavior at low-temperatures, comparing our results with other self-consistent approaches and with experimental data. / O estudo de propriedades de transporte em dispositivos nano estruturados e junções moleculares tornou-se um tópico de grande interesse com a recente demanda por novas tecnologias quânticas. Grande parte do nosso conhecimento tem sido guiado por trabalhos experimentais e teóricos de um dispositivo conhecido como transístor de um elétron (SET), o qual é constituído por um ponto quântico acoplado a dois gases de elétrons independentes. O SET é particularmente interessante devido as suas propriedades de transporte a baixas temperaturas, as quais são governadas pelo efeito Kondo. Uma dificuldade metodológica, no entanto, tem barrado novos avanços teóricos para se obter uma descrição precisa de dispositivos realistas. Por um lado, a teoria do funcional da densidade (DFT), uma das ferramentas mais convenientes para calcular a estrutura eletrônica de materiais complexos, provê uma descrição apenas qualitativa das propriedades de transporte de transístores quânticos a baixas temperaturas. Por outro lado, uma descrição quantitativa satisfatória do SET a baixas temperaturas, tal como a modelagem e solução do modelo de Anderson via métodos exatos, é incapaz de levar em conta características realistas de dispositivos complexos, tal como geometria, estrutura de bandas e interações inter eletrônicas nos gases de elétrons. Embora a DFT os descreva bem, ela é inadequada para tratar correlações introduzidas pelo ponto quântico. Na presente tese propomos uma alternativa para este dilema. Nossa contribuição é fundamentada em conceitos de grupo de renormalização (RG). Especificamente, mostramos que, em condições de interesse experimental, os regimes de altas e baixas temperaturas em um SET correspondem aos pontos fixos de acoplamento fraco e forte do Hamiltoniano de Anderson. Baseando-nos em na análise do RG, mostramos que, no ponto fixo de baixas temperaturas, o emaranhamento entre a impureza e os spins dos gases eletrônicos introduz correlações não-locais que não podem ser descritas com abordagens DFT baseadas em aproximações locais ou quase locais para o potencial de troca e correlação. Em contraste, o ponto fixo de acoplamento fraco pode ser descrito por aproximações locais. Com o objetivo de obter uma descrição realista das propriedades de transístores quânticos, propomos um procedimento auto-consistente que começa do ponto fixo de acoplamento fraco e se aproveita de um método numérico eficiente para levar o Hamiltoniano para o ponto fixo de acoplamento forte. Nossa abordagem emprega DFT para tratar o sistema no limite de acoplamento fraco e o método de Grupo de Renormalização Numérico (NRG) para obter propriedades no regime de acoplamento forte. Como ilustração, aplicamos o procedimento para um transístor de um elétron modelado através do Hamiltoniano de Hubbard generalizado. Analisamos a dependência térmica da condutância no SET discutindo seu comportamento a baixas temperatura e comparamos nossos resultados com outras abordagens auto-consistentes e resultados experimentais.

In dieser Arbeit wird ein Modell für das Eu-reiche EuO formuliert. Es besteht in einer Erweiterung des Kondo-Gitter-Modells (KGM). Für das KGM existieren nur einige exakte Aussagen. In dieser Arbeit kommt eine neue hinzu, nämlich die exakte Abbildung des periodischen Anderson-Modells auf das antiferromagnetische KGM für beliebige Kopplungsstärke J. Reines EuO ist ein ferromagnetischer Halbleiter. Eu-reiches EuO zeigt einen gewaltigen Metall-Isolator-Übergang in der Nähe der Curie-Temperatur mit einem Sprung im Widerstand von bis zu 13 Größenordnungen. Das ist der größte Sprung im Widerstand, der jemals in der Natur beobachtet wurde. Wir reproduzieren diesen Sprung theoretisch mit der Kubo-Formel. Wir erzielen sehr gute Fits bereits in einer nicht vollständig selbstkonsistenten Theorie, bei der die Magnetisierung der Eu-Spins einer Brillouin-Funktion entnommen ist. In einer vollständig selbstkonsistenten Theorie bestimmen wir die Magnetisierung, die Curie-Temperatur, den spezifischen Widerstand und andere Transporteigenschaften. Wir berechnen Größen wie die elektronische Wärmeleitfähigkeit und die Thermokraft, für die weniger experimentelle Daten zum Vergleich vorhanden sind. Nichtsdestoweniger erscheinen z.B. die Rechnungen für die thermische Leitfähigkeit vertrauenswürdig, da das Wiedemann-Franz-Verhältnis mit der elektrischen Leitfähigkeit einen vernünftigen Wert liefert. Die Leitungselektronenzahl des Eu-reichen EuO kommt aus der Theorie unabhängig von der Leitfähigkeit heraus. Daher können wir aus der Leitfähigkeit und der Leitungselektronenzahl die durchschnittliche Drude-Mobilität (oder Streuzeit) berechnen. Diese Größe hat für höhere Impurity-(Sauerstoff-Leerstellen)-Konzentrationen einen Sprung in der Nähe der Curie-Temperatur von bis zu zwei Größenordnungen in Übereinstimmung mit dem Experiment. / In this thesis a model is formulated for Eu-rich EuO. It consists in an extension of the Kondo lattice model (KLM). For the KLM only a few exact statements exist. To those we add a new one, namely the exact mapping of the periodic Anderson model on the antiferromagnetic KLM for arbitrary coupling constant J. Pure EuO is a ferromagnetic semiconductor. Eu-rich EuO exhibits a huge metal--insulator transition near the Curie temperature with a jump in resistivity of up to 13 orders of magnitude. It is the biggest jump in resistivity ever observed in nature. We theoretically reproduce this jump. We achieve very good fits already within a not fully self-consistent theory where the magnetization of the Eu spins is taken from a Brillouin function. In a fully self-consistent theory we determine the magnetization, the Curie temperature, the resistivity and other transport properties. We calculate quantities like the electronic thermal conductivity and the thermopower, for which there are less experimental data to compare with. Nevertheless, e.g. the calculations for the thermal conductivity seem reliable since the Wiedemann-Franz ratio with the electrical conductivity gives a reasonable result. The conduction-electron number of Eu-rich EuO comes out of the theory independently of the conductivity. So we can calculate from the conductivity and the conduction-electron number the average Drude mobility (or scattering time). This quantitiy has a jump near the Curie temperature of up to two orders of magnitude for higher impurity (oxygen vacancy) concentrations in agreement with the experiment.

Die vorliegende Arbeit befasst sich mit dem ferromagnetischen Kondo-Gitter-Modell (s-d-, s-f-Modell) für Filmstrukturen. Die Spin-Fermion-Wechselwirkung des Modells kommt in Materialien vor, in denen lokalisierte Spins mit beweglichen Ladungsträgern wechselwirken, wie etwa in (verdünnten) magnetischen Halbleitern, Manganaten, oder Seltene-Erd-Verbindungen. Die durch die Ladungsträger vermittelte, indirekte Wechselwirkung zwischen den lokalisierten Spins reicht von der langreichweitigen, oszillierenden RKKY-Austauschwechselwirkung im Falle schwacher Kopplung bis zur kurzreichweitigen Doppelaustausch-Wechselwirkung bei starker Spin-Fermion-Kopplung. Beide Grenzfälle werden in dieser Arbeit durch die Abbildung des Problems auf ein effektives Heisenberg-Modell erfasst. Der Einfluss von reduzierter Translationssymmetrie auf die effektive Austauschwechselwirkung und auf die magnetischen Eigenschaften des ferromagnetischen Kondo-Gitter-Modells wird untersucht. Curie-Temperaturen werden für verschiedene Parameterkonstellationen berechnet. Die Auswirkungen von Ladungstransfer und von Gitter-Relaxation auf die magnetische Oberflächenstabilität werden betrachtet. Die Diskussion bezieht sich auf die Modifizierungen der Zustandsdichte und der kinetischen Energie im dimensionsreduzierten Fall, da die effektiven Austauschintegrale eng mit diesen Größen verknüpft sind. Die Bedeutung von Spinwellen für den Magnetismus dünner Filme und an der Oberfläche wird gezeigt. Die Interlagen-Austauschkopplung stellt ein besonders interessantes und wichtiges Beispiel der indirekten Wechselwirkung zwischen lokalisierten Momenten dar. Im Rahmen einer RKKY-Behandlung wird die Kopplung zwischen Monolagen in dünnen Filmen untersucht. Sie wird entscheidend durch die Art der ebenen und senkrechten Ladungsträgerdispersion bestimmt und ist jenseits eines kritischen Wertes der Fermi-Energie stark unterdrückt. Schließlich wird die temperaturabhängige magnetische Stabilität von interlagen-gekoppelten dünnen Filmen behandelt und die Bedingungen für einen temperaturgetriebenen magnetischen Reorientierungsübergang werden diskutiert. / This thesis is concerned with the ferromagnetic Kondo lattice (s-d, s-f) model for film geometry. The spin-fermion interaction of this model refers to materials in which localized spins interact with mobile charge carriers like in (dilute) magnetic semiconductors, manganites, or rare-earth compounds. The carrier-mediated, indirect interaction between the localized spins comprises the long-range, oscillatory RKKY exchange interaction in the weak-coupling case and the short-range double-exchange interaction for strong spin-fermion coupling. Both limits are recovered in this work by mapping the problem onto an effective Heisenberg model. The influence of reduced translational symmetry on the effective exchange interaction and on the magnetic properties of the ferromagnetic Kondo lattice model is investigated. Curie temperatures are obtained for different parameter constellations. The consequences of charge transfer and of lattice relaxation on the magnetic stability at the surface are considered. Since the effective exchange integrals are closely related to the electronic structure in terms of the density of states and of the kinetic energy, the discussion is based on the modifications of these quantities in the dimensionally-reduced case. The important role of spin waves for thin film and surface magnetism is demonstrated. Interlayer exchange coupling represents a particularly interesting and important manifestation of the indirect interaction among localized magnetic moments. The coupling between monatomic layers in thin films is studied in the framework of an RKKY approach. It is decisively determined by the type of in-plane and perpendicular dispersion of the charge carriers and is strongly suppressed above a critical value of the Fermi energy. Finally, the temperature-dependent magnetic stability of thin interlayer-coupled films is addressed and the conditions for a temperature-driven magnetic reorientation transition are discussed.

Neste trabalho é calculada a contribuição de duas impurezas magnéticas ao calor específico e à entropia de um metal através do grupo de renormalização numérico. Tal sistema físico foi descrito pelo modelo Kondo de duas impurezas, onde cada impureza é simplesmente um momento magnético associado a um spin S=1/2, e representa um elétron ocupando um orbital de uma impureza magnética adicionada ao metal não magnético.Para tornar possível o cálculo com malhas de discretização grossas, foi introduzida uma correção no processo de discretização, levando a novas expressões para as energias da banda de condução discretizada e permitindo um melhor tratamento da assimetria partícula-buraco do modelo. Tal assimetria decorre da dependência com a energia do acoplamento entre as impurezas e os elétrons de condução do metal. A utilização de malhas grossas é extremamente desejável para a diminuição do esforço computacional envolvido. / In this work the contribution of two magnetic impurities to the specific heat and the entropy of a metal through the group of numerical renormalization is calculated. Such physical system was described for the Kondo model of two impurities, where each impurity is simply an associated magnetic moment to one spin S=1/2, and represents an electron occupying a orbital one of a magnetic impurity added to the magnetic metal. To not become possible the calculation with thick meshes of discretization, was introduced a correction in the discretization process, having led the new expressions for the energies of the band of discredited conduction and allowing to one better treatment of the asymmetry particle-hole of the model. Such asymmetry elapses of the dependence with the energy of the coupling between the impurities and electrons of conduction of the metal. The use of thick meshes is extremely desirable for the reduction of the involved computational effort.

[pt] Nesta tese investigamos os efeitos das interações elétron- elétron nas propriedades de transporte nanosistemas. Em particular, estudamos sistemas constituídos por dois pontos quânticos conectados a dois contatos, em diferentes topologias. O principal interesse é estudar os efeitos do regime Kondo e da fase eletrônica na condutância. Na configuração onde os dois pontos são inseridos em cada braço de um anel atravessado por um fluxo magnético, denotada por PPL, calculamos as fases das correntes que circulam através de cada braço do anel. Estas fases são determinadas pelo efeito Aharonov-Bohm combinado com a inflência da interação de muitos corpos das cargas nos pontos. Este sistema apresenta ressonância Kondo para um número par de elétrons em concordância com os resultados experimentais1. Outro aspecto interessante da configuração PPL é que, mesmo na ausência de fluxo magnético, pode existir circulação de corrente no anel, dependendo dos parâmetros escolhidos. Consideramos outras duas topologias que envolvem dois pontos quânticos acoplados através de interação de tunelamento. Em uma delas, denotada PAL, os dois pontos estão alinhados com os contatos, e na outra, a configuração PPD, um ponto está inserido nos contatos entanto que o outro interage só com o primeiro. No limite de acoplamento fraco, estas duas configurações apresentam características bem distintas, no só na dependência da condutância com o potencial de porta mas também na correlação de spin dos pontos quânticos. Ambas configurações apresentam ressonância Kondo para um número par de elétrons de diferente natureza. Quando cada ponto está carregado com um elétron, no caso da configuração PAL, os spins dos pontos quânticos estão descorrelacionados enquanto que, na configuração PPD, os spins estão correlacionados ferromagneticamente. No limite do acoplamento forte as propriedades de transporte das dois configurações são similares. Os sistemas discutidos acima são representados por o Hamiltoniano de Anderson de duas impurezas acopladas, o qual é resolvido diagonalizando exatamente um aglomerado que é embebido no resto do sistema. Desta forma obtemos as propriedades de transporte a T = 0. Para estudar a dependência com a temperatura utilizamos o método da equação de movimento (EOM) no limite da repulsão Coulombiana infinita. Aplicamos este método ao caso da topologia PPD, obteniendo resultados para baixas temperaturas consistente com os obtidos com o método do aglomerado. / [en] In this thesis we investigate the effects of the eletron- eletron interaction on the transport properties of nanosystems. In particular, we study systems constituted by two quantum dots conected to leads, in different topologies. Our main interest is to study the effects of the Kondo regime and the electronic phase on the conductance. In the configuration where the two dots are inserted in each arm of a ring threaded by a magnetic flux, denoted by PPL, we calculate the phases of the currents going along each arm of the ring. These phases are determined by the Aharonov-Bohm effect combined with the dots many body charging effects. This system presents the Kondo phenomenon for an even number (two) of electrons in the dots, in agreement with experimental results1. An interesting aspect of PPL configuration is that, even in the absence of magnetic flux there can be a circulating current around the ring, depending on the system parameters. In the two other topologies we consider the two quantum dots coupled through tunneling interaction. In one of them, denoted by PAL, the two dots are aligned with the leads, and in the other, the PPD configuration, one dot is inserted into the leads while the other interacts only with the first. In the weak coupling limit these two configurations present quite different features, not only on the dependence of the conductance on the gate potencials applied to the dots, but also on the dots spin correlation. Both configurations present Kondo resonance for an even number electrons. In the PAL configuration the spins of the charged dots are uncorrelated, while in the PPD configuration they are ferromagnetically correlated. In the strong tunneling coupling limit the transport properties of two interacting dot configurations are very similar. The systems discussed above are represented by an Anderson two- impurity first-neighbor tight-binding Hamiltonian, that is solved by exactly diagonalizing a cluster that is embebed into the rest of the system. In this way we obtain only the properties of the system at T = 0. In order to study temperature dependence phenomena we use the equation of motion method (EOM) in the limit of infinite Coulomb repulsion. We apply it to the dots in the PPD topology. The results for low temperatures are consistent with hose obtained with the cluster method.

L’étude présentée dans ce manuscrit s’inscrit dans le domaine du magnétisme de surface, qui a connu de grands développements ces dernières années grâce au microscope à effet tunnel (STM). Elle a pour but de montrer qu’une molécule simple, le nickelocène [Ni(C5H5)2], peut être attachée au sommet d’une pointe STM afin de produire une pointe-sonde magnétique, qui, dans le cadre de l’imagerie magnétique, présente des avantages indéniables comparés à des pointes conventionnelles. À la différence d’autres systèmes moléculaires étudiés avec le STM, nous montrons que les propriétés magnétiques du nickelocène en phase gazeuse sont préservées en présence d’un métal, même lorsque la molécule est attachée au sommet d’une pointe STM. Nous présentons trois résultats marquants avec cette pointe-sonde moléculaire: 1) Nous montrons que l’on peut contrôler le spin du nickelocène, activant à souhait un effet Kondo ; 2) Nous produisons à l’aide du courant tunnel des excitations entre les états de spin du nickelocène, que nous pouvons aisément identifier au travers de la conductance moléculaire. Ces états sont sensibles à toute perturbation magnétique extérieure au nickelocène; 3) Au travers de ces excitations, nous sondons alors le magnétisme de surface. Nous montrons qu’en couplant magnétiquement la pointe-sonde moléculaire avec des atomes, soit isolés soit dans une surface ferromagnétique, nous pouvons mesurer leur polarisation de spin, ainsi que le couplage d’échange nickelocène-atome. Ce dernier permet d’obtenir un contraste magnétique en imagerie STM à l’échelle atomique. / The study presented in this manuscript is part of the field of surface magnetism, which has undergone major developments in recent years thanks to the scanning tunneling microscope (STM). It aims to show that a single molecule, nickelocene [Ni(C5H5)2], can be attached to the tip of a STM to produce a magnetic probe-tip, which, in the context of magnetic imaging, has undeniable advantages compared to conventional tips. Unlike other molecular systems studied with STM, we show that the magnetic properties of nickelocene in the gas phase are preserved in the presence of a metal, even when the molecule is attached to the tip of a STM. We present three remarkable results with this molecular probe-tip: 1) We show that we can control the spin of nickelocene, activating at will a Kondo effect; 2) We monitor the spin states of nickelocene by producing electrically-driven excitations, which we can easily identify through the molecular conductance. These states are sensitive to the magnetic environment surrounding nickelocene; 3) We use these states to probe surface magnetism. We show that by magnetically coupling the molecular probe tip with single atoms, either isolated or in a ferromagnetic surface, we can measure their spin polarization, as well as the nickelocene-atom exchange coupling. By monitoring this coupling it is possible to obtain a magnetic contrast in the STM images with atomic-scale resolution.

Das magnetische Verhalten zahlreicher Materialien lässt sich auf eine indirekte Wechselwirkung lokalisierter magnetischer Momente, vermittelt durch die Elektronen eines Leitungsbandes, zurückführen. Das Kondo-Gitter-Modell hat sich als elegante Möglichkeit bewährt, diesen Prozess quantenmechanisch zu beschreiben. Es reduziert die Physik auf eine intraatomare Wechselwirkung der Spins von lokalisierten und itineranten Elektronen. Die vorliegende Arbeit ist den analytischen Eigenschaften dieses Modells gewidmet. Die besondere Herausforderung des Kondo-Gitter-Modells besteht dabei im Zusammenwirken zweier verschiedener Teilchensorten, beschrieben durch Fermi-Operatoren sowie quantenmechanische Spins. Bisherige Untersuchungen haben sich in der Regel nur auf eine der beiden Teilchensorten konzentriert. Mit der Projektions-Operator-Methode stellen wir eine Möglichkeit vor, beide Teilsysteme in gleicher Qualität zu behandeln. Die Auswertung des Teilsystems der itineranten Elektronen führt auf einen Ausdruck für die Selbstenergie, der lineare und quadratische Effekte in der Wechselwirkung exakt beschreibt. Die resultierenden Zustandsdichten weisen starke Korrelationseffekte auf. Deren Untersuchung dient sowohl der Bestätigung von Ergebnissen weniger systematischer Zugänge als auch dem Aufzeigen neuer Vielteilchen-Phänomene. Die Anwendung der Projektions-Operator-Methode auf das System der lokalisierten Momente führt zu einer Analyse der bereits bekannten RPA (random phase approximation). Zu diesem Zweck werden die Magnonenspektren und die Curie-Temperaturen systematisch untersucht. Dabei treten bisher unbekannte Schwachpunkte der RPA zu Tage, die auch die Kombination mit Theorien für das itinerante Teilsystem verhindern. Verbesserungen und Alternativen zur RPA werden diskutiert. / The magnetic behaviour of various materials is due to an indirect interaction of localized magnetic moments, which is based on itinerant electrons in a conduction band. The Kondo-lattice model is an elegant approach for a quantum-mechanical description of this process. It reduces the relevant physics to an intra-atomic exchange interaction of the localized and the itinerant electrons. The aim of the present work is a detailed investigation of analytic properties of this model. Here, the interplay of two distinct types of particles, described by Fermi operators and quantum-mechanical spin operators respectively, is a major challenge of the considered model. Previous studies have focused on one of these subsystems only. Using the projection-operator method, we suggest an efficient way to describe both subsystems on the same level of approximation. An evaluation of the subsystem of itinerant electrons yields an expression for the self-energy, which describes linear and quadratic interaction effects exactly. The densities of states derived with this theory show strong correlation effects. We were able to assess results obtained with less systematic approaches and to predict new many-particle effects. The application of the projection-operator method to the subsystem of localized magnetic moments results in a detailed analysis of the RPA (random phase approximation). The dependence of magnon spectra and Curie temperatures on model parameters are investigated systematically. Previously unknown drawbacks of the RPA are revealed, which prevent the combination of these results with theories for the itinerant subsystem. Improvements beyond RPA and alternative approximations are discussed.