Neste trabalho, calculam-se o calor específico e a entropia do Modelo de Anderson simétrico de uma impureza usando o Grupo de Renormalização Numérico (GRN). O método é baseado na discretização logarítmica da banda de condução do metal hospedeiro a qual a impureza está acoplada. Porém, esta discretização introduz oscilações nas propriedades termodinâmicas. Esta inconveniência, inerente ao método, é contornável para a suscetibilidade magnética, mas é crítica para o calor específico, restringindo o alcance do GRN. Para sobrepor essa dificuldade, é usado o novo procedimento denominado intercalado que foi desenvolvido para o cálculo da suscetibilidade magnética de modelos de duas impurezas. Para reduzir as matrizes e o tempo computacional, é usado, também, o operador carga axial, recentemente definido no contexto do Modelo de Kondo de duas impurezas, e que é conservado pelo Hamiltoniano de Anderson simétrico. As curvas obtidas são comparadas com resultados exatos obtidos por ansatz de Bethe e pelo Modelo de Nível Ressonante. / The specific heat and the entropy of the one-impurity symmetric Anderson Model are calculated using the Numerical Renormalization Group (NRG). The heart of the method is the logarithmic discretization of the metal conduction band where the impurity is coupled. However, this discretization, inherent in the method, introduces oscillations in the thermodynamical properties. For the susceptibility it is not so critical but for the specific heat the usual calculation is prohibitive. To overcome this difficulty, we use the new procedure called interleaved that was developed to calculate the susceptibility of two-impurity models. In order to reduce the matrices and computation time, use is made of the axial charge operator recently defined in the two-impurity Kondo Model context and that is conserved by the symmetric Anderson Hamiltonian. The curves obtained are compared with exacts results of Bethe ansatz and Resonant Level Model.

Neste trabalho é apresentado o cálculo, pelo grupo de renormalização numérico, da condutância AC através de uma nanoestrutura acoplada a gases eletrônicos, a baixa temperatura e no regime de resposta linear. Este sistema apresenta a competição entre dois efeitos: blo¬queio Coulombiano e efeito Kondo. Nosso modelo considera gases eletrônicos unidimensionais que são unidos pelas extremidades para formar um anel, no qual a corrente é induzida por um fluxo magnético oscilante com freqüência . Nós partimos de um modelo tight-binding de vizinhos mais próximos para os gases eletrônicos e, deste modo, o potencial vetor é facilmente incorporado ao Hamiltoniano por condições de contorno torsionais. Uma barreira de potencial entre os gases eletrônicos e a nanoestrutura é simulada em termos de uma taxa de tunelamento entre a nanoestrutura e os sítios adjacentes menor que aquela entre entre sítios vizinhos no anel. A capacitância da nanoestrutura é pequena, o que implica que nós podemos considerar mudanças no número de elétrons dentro da mesma por apenas uma unidade. Como conseqüência, o Hamiltoniano é mapeado no Hamiltoniano de Anderson com correlação U entre os elétrons. Uma voltagem de gate controla a energia da impureza (da nanoestrutura), 0. Plotada como função de , a condutância mostra dois picos característicos do bloqueio Coulombiano, em freqüências correspondentes às energias para adicionar um elétron à nanoestrutura e para remover um elétron da nanoestrutura respectivamente. No regime Kondo, 0 > 0 > -U (ou seja, para voltagens de gate tais que a nanoestrutura isolada teria estado fundamental com degenerescência de spin), um pico (Kondo) adicional aparece próximo à = 0. Plotada como função de Vg, a condutância DC mostra um largo pico no regime Kondo, caindo rapidamente a zero para voltagens resultando em um estado fundamental não degenerado para a nanoestrutura isolada. Uma relação entre a condutância e a densidade espectral do nível da impureza é obtida e utilizada para interpretar os resultados numéricos. / In this work a renormalization-group calculation of the low-temperature AC conductance in the linear response regime through a nanostructure coupled to metallic leads is presented. This system shows a competition between two effects: the Coulomb blockade and the Kon¬do effect. Our model considers one-dimensional leads which are connected to form a ring, in which a current is induced by a magnetic flux oscillating at the frequency . We start from a nearest-neighbor tight-binding model for the leads and in this way the potential vector is easily incorporated in the model Hamiltonian by twisting boundary conditions. A potential barrier between the leads and the nanostructure is simulated in terms of a tunneling rate between the nanostructure and the adjacent sites in the leads, which is smaller than the one between neighbors sites in the leads. The capacity of the nanostructure is small, which implies that substantial energy changes are associated with each electron transfered to the nanostructure. As a consequence, the model Hamiltonian maps onto the spin-degenerate Anderson Hamiltoni¬an with correlation U between the electrons. A gate voltage Vg controls the impurity (i.e., nanostructure) energy 0. Plotted as a function of , the conductivity shows two Coulomb-blockade peaks, at the energy needed to add an electron to and to remove an electron from the nanostructure, respectively. In the Kondo regime 0 > 0 > -U (i.e., for gate voltages such that the isolated nanostructure would have a spin-degeneration ground state), an addition (Kondo) peak appears near = 0. Plotted as functions of Vg, the static conductivity shows a broad peak in the Kondo regime and drops rapidly to zero for voltages resulting in a non-degenerate nanostructure ground state. A relation between the conductance and the spectral density of the impurity is obtained and used to interpret the numerical results.

Nozières e Blandin generalizaram o Modelo Kondo através da inclusão de mais graus de liberdade. Eles investigaram um sistema formado de uma impureza magnética em um metal hospedeiro, considerando a estrutura orbital da impureza, campo cristalino e interações spin-órbita. Este sistema é representado pelo Hamiltoniano de Kondo Multicanal: a interação entre a impureza local e a banda de condução é feita via canais (cada canal representa um conjunto de números quânticos bem definidos). Nozières e Blandin mostraram o aparecimento de um ponto fixo anômalo no regime de acoplamento finito. Esse ponto fixo anômalo pode explicar o comportamento não-líquido de Fermi de compostos de terras-raras e actinídeos. Cox e colaboradores usaram o Hamiltoniano Kondo Quadrupolar para representar sistemas de férmions pesados em urânio e óxidos supercondutores de alta temperatura, os quais podem ser mapeados em um Modelo Kondo de dois canais. Como o Modelo Kondo tradicional (um canal) é o limite de baixa temperatura do Modelo Anderson, é interessante também generalizar este último para incluir mais canais. Nesta tese nós mostramos que o mesmo procedimento trivial, o qual generaliza o Hamiltoniano Kondo, não funciona para o Modelo de Anderson. Nós usamos um Hamiltoniano proposto por Cox para representar o Modelo de Anderson de dois canais. Usando a transformação de Schrieffer-Wolff nós demonstramos que este Hamiltoniano é equivalente ao Hamiltoniano Kondo de dois canais em baixas temperaturas. E finalmente, nós aplicamos o Grupo de Renormalização Numérico para investigar os níveis de mais baixa energia, a suscetibilidade magnética e o calor específico. / Nozières and Blandin generalized the Kondo Model by including more degrees of freedom. They investigated a system made of magnetic impurity in a metal host, considering impurity orbital structure, crystalline field and spin-orbit interactions. This system is represented by multichannel Kondo Hamiltonian: the interaction between local impurity and conduction band is done via channels (each channel represents a set of well defined quantum numbers). They showed that anomalous fixed point appears at finite coupling. The anomalous fixed point can explain the non-Fermi Liquid behaviour of rare earths and actinides compounds. Cox et al used a quadrupolar Kondo Hamiltonian for uranium heavy-fermion materials and high-temperature superconducting oxides, which can be mapped to a two-channel Kondo Model. Since Kondo Model is a low temperature limit of Anderson Model, would be interesting to generalize this last one including many channels. In this thesis we show that the same trivial procedure, which generalizes the Kondo Hamiltonian, does not work with the Anderson Model. We use a model Hamiltonian proposed by Cox to represent the two-channel Anderson Model. Using the Schrieffer-Wolf transformation we prove this Hamiltonian is equivalent to the two-channel Kondo Hamiltonian. And finally, we have applied Numerical Renormalization Group calculations to investigate the lowest energy levels, susceptibility and specific heat.

A microscopia de varredura por tunelamento (MVT) é uma nova maneira de se observar experimentalmente o efeito Kondo. Quando uma concentração de átomos é adicionada a um meio metálico (metal hospedeiro), a corrente de tunelamento passa a depender de fatores de origem não geométrica. O rearranjo das cargas dentro do volume metálico (oscilações de Friedel) e o espalhamento de spins eletrônicos (efeito Kondo), devido a introdução de impurezas, mudam o valor da corrente e influenciam o levantamento da topografia do espécime examinado. Esses fatores devem ser considerados para que a topografia gerada seja condizente com a topografia verdadeira. Utilizamos como modelo teórico para descrição desse sistema, o modelo de Anderson de uma impureza para simular o espécime examinado e uma banda de condução livre para representar os elétrons da agulha metálica do microscópio. Nossa abordagem usa a fórmula de Kubo para o cálculo da corrente de tunelamento, supondo Hamiltoniano de tunelamento como perturbação e o potencial elétrico no regime linear. Apresentamos inicialmente um estudo para o Modelo do Nível Ressonante, isto é, o modelo de Anderson sem correlação, com o objetivo de demonstrar a precisão do método do Grupo de Renormalização Numérico. Em seguida, analisamos o Modelo de Anderson correlacionado. Os resultados tanto para a condutância em função da distância entre ponta e impureza a temperatura fixa, como para condutância em função da temperatura e distância fixa, permitem interpretação física transparente desde que levem em conta a ressonância de Kondo na densidade espectral. / The scanning tunneling microscopy (STM) is a new way to observe experimentally the Kondo effect. When a concentration of atoms id added to a sample (host metal), the tunneling current begins to depend on other non-geometric factors. The rearrangement of charges in the metallic bulk (Friedel oscillations) and the electronic spin scattering (Kondo effect), due to the presence of impurities, change the current value and affect the sample´s topography. These factors must be considered in order to make a correspondence between the generated topography with the true one. As a theoretical description of the system, we use the single impurity Anderson model to simulate the examined sample and a free conduction band to represent the electrons of the microscope metallic tip. Our treatment uses the Kubo formula to calculate the tunneling current, assuming the tunneling Hamiltonian as a perturbation and the electric potential in the linear regime. We initially present a study of the Resonant Level Model, i.e, the Anderson model without correlaction, to show the accuary of the Numerical Renormalization Group procedure. In the next step, we analyse the correlated Anderson model. The dependence of the conductance on tip-impurity distance, at constant temperature, and its dependence on temperature for constant tip-impurity distance, allow a clear physical interpretation after taking into account the Kondo resonance in the spectral density.

La recherche actuelle sur les composants électroniques à l'échelle nano s'oriente vers les matériaux organométalliques. Dans ce contexte, le travail présenté ici s'est focalisé sur la molécule de TbPc2 qui a été étudiée sur différents substrats, afin de déterminer l'effet de ses propriétés géométriques, électroniques et magnétiques en fonction de son environnement. Ainsi, il a été observé qu'au-dessus du substrat d'Au (111) la TbPc2 contient un électron excédentaire délocalisé sur le ligand supérieur qui, en intéragissant avec les électrons de surface, produit une résonance Kondo. Lorsqu'il s'agit de domaines moléculaires, une manipulation moléculaire montre qu'une localisation de spin est générée aux intersections produisant une résonance magnétique. Pour aller plus loin dans la détermination de l'effet de voisinage, un second lanthanide (cérium) a été déposé au-dessus de la molécule de TbPc2, la réponse géométrique, électronique et magnétique du nouveau complexe a été examinée sur différents substrats. / Today's research on the best electronic components at the nanoscale has focused on organometallic materials. In this context, the research presented in this thesis has been performed on TbPc2 molecules that were investigated on various substrates, in order to highlight the environment effect on both geometric, electronic and magnetic properties. It has been observed that on Au (111), the TbPc2 has an excedentary electron delocalized over the upper ligand. This electron interacts with the surface electron sea creating a Kondo resonance.When it comes to a molecular domain, it has been demonstrated throughout a molecular manipulation that a spin localization is made at the molecular intersection regions creating also a magnetic resonance. In order to further investigate the environmental modification, a second lanthanide (cerium) has been deposited over the TbPc2 molecule. The properties of the new complex were deeply investigated on various substrates.

La combinaison de la spintronique et de I' électronique organique est censée conduire à une nouvelle gamme d'applications en la domaine de spintronique organique. Ce travail se concentre sur la physique des molécules organiques adsorbées sur des surfaces métalliques, en mettant I' accent sur les changements de leurs structures électroniques en raison de I' effet important du substrat métallique. Nous avons étudié le complexe Ni2 adsorbé sur le Cu qui montre un effet Kondo à basses températures. Nous avons ensuite étudié des chaînes d'oligoacènes (anneaux de benzène fusionnè) qui présentent une propriété prédite: une oscillation de la bande interdite d' énergies en fonction de la longueur de la molécule. Cette propriété peut survivre même lorsque la molécule est adsorbée sur une surface, comme I' Au ou le Si02. Pour terminer, nous avons étudié des petites molécules, telles que l'éthane ou I'éthylène, adsorbées sur un subtrat de Cu et de Co. La différence d' énergie entre I' orbitale vide la plus basse (LUMO) et I' orbitale moléculaire occupée la plus élevée (HOMO) est étudiée dans les approximations de la théorie de la fonctionnelle de la densité (DFT) et la méthode GW. / The combination of spintronics and organic electronics, is believed to lead to a new generation of spin based devices, which would likely open a new broad range of applications in the field of organic spintronics. ln this context, this work focuses on organic molecules adsorbed on metallic surfaces and their electronic structure changes due to the important screening of the metallic environment. We have studied different systems, starting with a Ni2 complex adsorbed on Cu (001), where Kondo effect sets in. This study is followed by oligoacene chains (fused benzene rings) where an extraordinary property is seen: an oscillation of the energy band gap with respect to the molecular length. This property is proved to survive under the screening of surfaces such as Au(111) and Si02. We finally focused on small molecules, like ethane and ethylene, adsorbed on Cu and Co. The difference of energy between the lowest unoccupied molecular orbital (LUMO) and the highest occupied molecular orbital (HOMO) is studied using density functional theory (DFT)and GW methodologies.

M. Sc. / The substitution series CeCu5−xAlx where x 2 {1.0, 1.5, 2.0, 2.1, 2.2, 2.3, 2.4} was synthesized and characterized via x-ray diffraction and scanning electron microscope analysis. All the compounds formed single phase in the P6/mmm hexagonal crystal structure, which pushed the solubility limit of Al within this structure from CeCu3Al2 to CeCu2.6Al2.4. The ascast samples were annealed, but the annealing process had no visible effect on the crystalline nature nor on the physical properties of the samples. The electric, magnetic and thermal properties were measured on Quantum Design’s Physical Properties Measurement System and Magnetic Properties Measurement System. The electrical resistivity showed single-ion Kondo scattering at intermediate temperatures with no signs of coherence for x 2 {1.0, 1.5, 2.0, 2.1, 2.2, 2.3} CeCu2.6Al2.4 on the other hand showed a weak maximum at 2 K, which was the onset of antiferromagnetic ordering confirmed by other measurements. The magnetoresistance was fitted by the Beth´e ansatz spin-1/2 model and the obtained Kondo temperatures had a maximum at CeCu3Al2, with linear dependencies on Al concentration on either side of this point. The Kondo moments followed an exponential dependence on the Al concentration, but these effective moments were far lower than the free-ion value, due to the Kondo interaction. The thermal conductivity in this series was phonon dominated with the magnitude of the electronic component being inversely proportional to the Kondo temperature, showing the effect that the Kondo scattering mechanism has on the availability of the conduction electrons to participate in heat transport. The magnitude of the peak in the thermoelectric power S(T) was strongly dependent on the Al concentration, having a maximum at CeCu2.8Al2.2. Below the peak there were two temperature dependencies: S(T) / T for x 2 {1.0, 1.5, 2.4} which is metallic and for x 2 {2.0, 2.1, 2.2, 2.3} S(T)/T /−ln(T) which is characteristic of a quantum critical point. The data were also fitted with a phenomenological model and the obtained Kondo temperatures were quantitatively similar to those obtained from the Beth´e ansatz. The heat capacity Cp(T) data confirmed these compounds to be heavy fermions and also showed Cp(T)/T /−ln(T) below 10 K, which is the hallmark for a magnetically tuned quantum critical point. The magnetic susceptibility showed a Curie-Weiss temperature dependence at temperatures above 100 K, with magnetic moments close to the free-ion value, indicating the presence of localized magnetic moments. The low temperature data found (T) /−ln(T) for Al concentrations near CeCu3Al2 and the ordering present in CeCu2.6Al2.4 was suppressed by 0.3 K in going from 0.01 T to 2 T, suggesting that the ground state is antiferromagnetic in this compound.

Cette thèse est consacrée au transport quantique à travers une impureté Kondo, formée dans une boîte quantique réalisée dans un nanotube de carbone. L’effet Kondo est ainsi sondé à travers deux situations : en compétition avec l’effet Josephson induit dans le nanotube par des contacts supraconducteurs et à travers son émission haute fréquence. Dans une première série d’expériences, nous avons introduit un nanotube dans un SQUID, afin de mesurer la relation entre son supercourant et la différence de phase supraconductrice à ses bornes. Nous avons mesuré cette relation lorsque les corrélations Kondo et supraconductrices sont du même ordre de grandeur et montré que l’état du système, singulet ou doublet (correspondant respectivement à une jonction 0 ou π) peut alors être contrôlé par la phase supraconductrice. Nous avons également montré que, si un deuxième niveau d’énergie participe au transport des paires de Cooper, la transition 0-π n’est plus une transition du premier ordre comme c’est le cas quand un seul niveau est impliqué. Dans la deuxième partie de la thèse, le nanotube de carbone est couplé, aux fréquences déterminées par un résonateur, à une jonction tunnel supraconductrice servant de détecteur on-chip de bruit haute fréquence. Ceci nous a permis de mesurer le bruit en émission de la boîte quantique dans le régime Kondo avec des couplages aux réservoirs plus ou moins symétriques. Nos mesures posent le problème de l’asymétrie spatiale du bruit mesuré et semblent montrer que, plus le couplage aux réservoirs est symétrique, plus la résonance Kondo est affaiblie dans une situation hors équilibre. Enfin, ce dispositif a été utilisé afin de mesurer l’émission Josephson AC d’un nanotube avec des électrodes supraconductrices, afin de voir ce que devient la compétition entre l’effet Kondo et la supraconductivité à haute fréquence. Ces mesures révèlent une diminution de l’émission Josephson alors que l’on a un maximum de supercourant. / This thesis is dedicated to quantum transport through a Kondo impurity, formed in a carbon nanotube quantum dot. We probe the Kondo effect in two situations: in competition with the Josephson effect induced in the nanotube by superconducting contacts and through its high frequency emission. In a first experiment, we have introduced a nanotube in a SQUID in order to measure its supercurrent as a function of the superconducting phase across it. We have measured this quantity in the regime where the Kondo and superconducting correlations are of the same order of magnitude and shown that the ground state of the system, singlet or doublet (corresponding respectively to 0 and π junctions), is then controlled by the superconducting phase. We have also demonstrated that, if a second energy level participates in the transport of Cooper pairs, the 0-π transition is not anymore a first order one as it is the case when only one level is involved. In the second part of the thesis, the carbon nanotube is coupled, at some frequencies determined by a resonator, to a tunnel superconducting junction which is used as an on-chip high-frequency noise detector. This enables the measurement of the emission noise of the quantum dot in the Kondo regime, with reservoirs coupled either symmetrically or not to the dot. Our measurements raise the problem of the spatial asymmetry of the measured noise and seem to show that, the more symmetric is the coupling of the reservoirs to the dot, the more the Kondo resonance is weaken in an out-of-equilibrium situation. Finally, this setup has been used in order to measure the AC Josephson emission of a nanotube contacted with superconducting electrodes, in order to extend our investigation of the competition between the Kondo effect and superconductivity at high frequency. These measurements reveal a decrease of the Josephson emission observed together with a maximum of supercurrent.

Cette thèse explore plusieurs sujets fondamentaux pour les circuits mésoscopiques qui incorporent un faible nombre de canaux de conduction électroniques. Les premières expériences concernent le caractère quantifié (discret) de la charge dans les circuits. Nous démontrons le critère de quantification de la charge, nous observons la loi d’échelle prédite pour cette quantification ainsi qu’une transition vers comportement universel à mesure que la température augmente. Le second ensemble d’expériences concerne la physique critique quantique non-conventionnelle qui émerge du modèle Kondo à multi-canaux. Par l’implémentation d’une impureté Kondo avec un pseudo-spin de valeur ½ constitué de deux états de charge dégénérés d’un circuit, nous explorons la physique Kondo à deux- et trois-canaux. Au point critique quantique symétrique, nous observons les points fixes Kondo universels prédits, des exposants universels de lois d’échelle et nous validons les courbes complètes obtenues par le groupe de renormalisation numérique. En s’écartant du point critique quantique, nous explorons la transition depuis la zone critique quantique : par une visualisation directe du development d’une transition de phase quantique, par l’espace des paramètres de la zone critique quantique ainsi que par les comportements d’universalité et d’échelle. / This thesis explores several fundamental topics in mesoscopic circuitry that incorporates few electronic conduction channels. The first experiments address the quantized character (the discreteness) of charge in circuits. We demonstrate the charge quantization criterion, observe the predicted charge quantization scaling and demonstrate a crossover toward a universal behavior as temperature is increased. The second set of experiments addresses the unconventional quantum critical physics that arises in the multichannel Kondo model. By implementing a Kondo impurity with a pseudo-spin of ½ constituted by two degenerate charge states of a circuit, we explore the two- and three-channel Kondo physics. At the symmetric quantum critical point, we observe the predicted universal Kondo fixed points, scaling exponents and validate the full numerical renormalization group scaling curves. Away from the quantum critical point, we explore the crossover from quantum criticality: direct visualization of the development of a quantum phase transition, the parameter space for quantum criticality, as well as universality and scaling behaviors.

Au cours de cette thèse, nous nous sommes intéressés à l'effet Kondo moléculaire au sein de réseaux supramoléculaires bidimensionnels en contact avec des surfaces métalliques monocristallines. Les techniques mises en oeuvre sont la diffraction d'électrons lents (LEED) et la microscopie à effet tunnel (STM) pour l'étude de la croissance ainsi que la spectroscopie à effet tunnel (STS) et la photoémission pour l'étude des propriétés électroniques. Les molécules employées dans le cadre de ce travail sont composées de macrocycles de phtalocyanine et tétraphénylporphyrine. Elles ont été choisies sur la base de l'orbitale contenant le spin moléculaire. Dans un premier cas, une phtalocyanine non métallée 2HPc a été déposée sur une surface monocristalline d'Ag(111). Un transfert de charge du métal vers la molécule conduit à l'apparition d'un effet Kondo à base température observé par STS sur des molécules individuelles ainsi que sur des auto-assemblages. Dans le deuxième cas, nous avons choisi un composé hôte à double plateaux contenant un ion cérium de type 4f. Nous avons mis en évidence l'influence du substrat sur l'effet Kondo. En effet, tandis que nous observons par STS, l'apparition d'une résonance Kondo lorsque la molécule est auto-assemblée sur Ag(111), aucun effet n'est observé sur Cu(111). Les résultats sont discutés en terme d'interactions molécule-molécule et molécule-substrat / In this work, we investigated molecular Kondo effect in two-dimensional supramolecular lattices adsorbed on metallic single crystalline surfaces by means of low-energy electron diffraction (LEED), scanning tunneling microscopy/spectroscopy (STM/STS) and photoemission (PES). The molecular compounds used in this PhD thesis have been chosen in regards to their spin orbital. The first molecule under investigation is a metal free phthalocyanine adsorbed on Ag(111). A Kondo effect has been evidenced by STS for single molecules as well as for self-assembly up to one monolayer coverage at low temperature. In that case, the spin originates from charge transfer from the Ag surface to the molecule. The second molecular compound is a double-decker molecule hosting a cerium 4f-ion. In that case, a Kondo resonance is evidenced by STS when it is self-assembled on Ag(111) whereas it is absent on Cu(111). These results are discussed in terms of intermolecular and molecule-metal interactions