In der vorliegenden Arbeit wurde der elektrische Transport im Schwere-Fermionen-System YbRh2Si2 sowohl in seiner stöchiometrischen Form als auch mit teilweiser isoelektronischer Substitution von Ir oder Co auf dem Rh-Platz untersucht. In YbRh2Si2 liegt ein quantenkritischer Punkt vor, der zugänglich ist, indem der antiferromagnetische Phasenübergang mittels eines kleinen Magnetfelds zum absoluten Nullpunkt der Temperatur unterdrückt wird. Die zentralen Messungen des Hallkoeffizienten zeigen einen Übergang der in der Extrapolation zu T=0 zu einer Diskontinuität wird und somit auf eine Rekonstruktion der Fermifläche am quantenkritischen Punkt schließen lässt. Dies belegt die unkonventionelle Natur der Quantenkritikalität in YbRh2Si2. Unterstützt wird dies auf fundamentale Weise durch verknüpfungen mit unkonventionellem Skalierungsverhalten. In den Proben mit teilweiser Substitution wird der Einfluss einer Veränderung der Gitterparameter auf die Quantenkritikalität mit Hilfe von Widerstandsmessungen untersucht. Dabei zeigt sich, dass der magnetische Übergang von der Fermiflächenrekonstruktion separiert wird. Für Proben mit teilweiser Ir-Substitution, welche negativen Drücken entspricht, scheint im Zwischenbereich eine neuartige metallische Spinflüssigkeit hervorzutreten. / This work investigates the electrical transport of the heavy-fermion compound YbRh2Si2 in its stoichiometric form as well as with slight isoelectronic substitution of Ir or Co on the Rh site. A quantum critical point is present in YbRh2Si2 which is accessed by tuning the transition temperature of the antiferromagnetic order to absolute zero via the application of a small magnetic field. The central measurements of the Hall coefficient reveal a crossover which sharpens to a discontinuity in the extrapolation to zero temperature implying a reconstruction of the Fermi surface at the quantum critical point. This allows to rule out conventional descriptions of the quantum criticality in YbRh2Si2. A scaling analysis corroborates this on a fundamental basis. In the samples with partial substitution the effect of unit cell volume change on the quantum criticality was investigated by means of resistivity measurements. Surprisingly, the magnetic transition is separated from the Fermi surface reconstruction. For samples with Ir substitution corresponding to negative chemical pressure, a new metallic spin liquid seems to emerge in the intermediate regime.

Cette thèse a comme sujet général l’étude théorique de deux aspects de la physique des systèmes d’électrons 4f. La première partie est consacrée aux systèmes intermétalliques de lanthanides à valence intermédiaire ou possédant une transition de valence. Dans ce but, nous étudions une version étendue du modèle d’Anderson périodique, auquel est ajoutée une interaction coulombienne entre les électrons de conduction et les électrons f localisés (intéraction de Falico-Kimball). Si cette interaction est plus forte qu’une valeur critique, le changement de valence n’est plus continu, mais devient discontinu. Le modèle est traité par un ensemble de approximations appropriées aux échelles d’énergie du problème : Hubbard I et champ moyen.Le diagramme de phases du modèle à température nulle et l’évolution de la valence avec les paramètres du modèle sont déterminés. En plus, les effets d’un champ magnétique extérieur et des interactions ferromagnétiques entre les électrons localisés sont examinés. Nos résultats sont comparés à quelques composés à base de Yb et Eu, comme YbCu2Si2, YbMn6Ge6-xSnx and EuRh2Ir2.Dans la deuxième partie nous étudions des systèmes de lanthanides dans lesquels le nombre d’atomes magnétiques localisés peut être modifié par substitution par des atomes non-magnétiques (Alliages Kondo). Dans ces systèmes il est possible de passer du régime d’impureté Kondo au régime de réseau Kondo ; à basse température ces deux régimes sont des liquides de Fermi dont les caractéristiques sont différentes. Le modèle d’alliage Kondo est étudié dans la théorie du champ moyen dynamique statistique, qui traite différents aspects du désordre et qui est formellement exacte dans un arbre de Bethe avec un nombre de coordination quelconque.Les distributions des paramètres de champ moyen, des densité d’états locales et d’autres quantités locales sont présentées en fonction des paramètres du modèle, en particulier la concentration de moments magnétiques x, le nombre d’électrons de conduction par site nc, et la valeur de l’interaction Kondo JK. Nos résultats montrent une différence nette entre les régimes d’impureté et de réseau pour une interaction Kondo forte. Pour des concentrations intermédiaires (proches de la concentration des électrons de conduction), le système est dominé par le désordre et des indications d’un comportement non-liquide de Fermi et d’une localisation des états électroniques sont observés. Ces caractéristiques disparaissent quand l’interaction Kondo est faible. Nous discutons aussi la question d’une basse dimensionnalité et la relation avec le problème de percolation dans ces systèmes. / The topics of the thesis concerns two theoretical aspects of the physics of 4f electron systems.In the first part the topic of intermediate valence and valence transitions in lanthanide systems is explored. For that purpose, we study an extended version of the Periodic Anderson Model which includes the Coulomb interaction between conduction electrons and the localized f electrons (Falicov-Kimball interaction). If it is larger than a critical value, this interaction can transform a smooth valence change into a discontinuous valence transition. The model is treated in a combination of Hubbard-I and mean-field approximations, suitable for the energy scales of the problem.The zero temperature phase diagram of the model is established. It shows the evolution of the valence with respect to the model parameters. Moreover, the effects of an external magnetic field and ferromagnetic interactions on the valence transitions are investigated. Our results are compared to selected Yb- and Eu-based compounds, such as YbCu2Si2, YbMn6Ge6-xSnx and EuRh2Ir2.In the second part of the thesis, we study lanthanide systems in which the number of local magnetic atoms is tuned by substitution of non-magnetic atoms, also known as Kondo Alloys. In such systems it is possible to go from the single Kondo impurity to the Kondo lattice regime, both characterized by different type of Fermi liquids. The Kondo Alloy model is studied within the Statistical Dynamical Mean-Field Theory, which treats different aspects of disorder and is formally exact in a Bethe lattice of any coordination number.The distributions of the mean-field parameters, the local density of states and other local quantities are presented as a function of model parameters, in particular the concentration of magnetic moments x, the number of conduction electrons per site nc and the Kondo interaction strength JK. Our results show a clear distinction between the impurity (x<<1) and the lattice (x≈1) regimes for a strong Kondo interaction. For intermediate concentrations (x≈nc), the system is dominated by disorder effects and indications of Non-Fermi liquid behavior and localization of electronic states are observed. These features disappear if the Kondo interaction is weak. We further discuss the issue of low dimensionality and its relation to the percolation problem in such systems.

La manipulation de la matière au niveau nanométrique a ouvert depuis une quinzaine d'années de nouveaux champs fondamentaux et applicatifs pour les scientifiques et les industriels. Dans ce nouveau paradigme, la nanoélectronique quantique se propose de fonder une nouvelle électronique basée sur les phénomènes quantiques de la matière et plus particulièrement sur la nature quantique des électrons. Ce projet de thèse s'articule autour d'un système électronique quantique hybride supraconducteur/nanotube de carbone (CNT) dénommé nano-SQUID. Ce dispositif présente une boucle supraconductrice contenant deux jonctions CNT en parallèle. Il couple de façon unique les propriétés d'un interféromètre supraconducteur SQUID avec celles de jonctions Josephson à boîte quantique moléculaire. A travers des expériences de transport réalisées, à des températures de quelques dizaines de milli-Kelvins, dans un cryostat à dilution inversé, nous avons étudié les interactions électroniques entre une boîte quantique nanotube et des électrodes supraconductrices. Nous nous sommes particulièrement focalisés sur l'influence de l'état de spin du nanotube sur le courant supraconducteur, qui peut, dans certaines conditions, conduire à la réalisation d'un jonction-. Par un contrôle électrostatique des paramètres microscopiques du dispositif nous avons ainsi pu définir un diagramme de phase expérimental des transitions 0- d'une jonction Josephson à boîte quantique. La dernière partie de cette thèse a porté sur l'utilisation du nano-SQUID comme magnétomètre. En effet, en couplant un aimant moléculaire au CNT composant le SQUID, il a été montré théoriquement qu'il est possible de détecter le retournement d'aimantation d'un spin unique. Nous avons ainsi couplé au nano-SQUID l'aimant moléculaire Double Decker Holmium et réalisé les premières mesures de détections magnétiques aux résultats prometteurs. / The manipulation of matter at the nano-scale has opened, since fifteen years, new fundamental and application avenues for science and industry. In this new paradigm, quantum nano-electronics propose to start a new electronics based on quantum effects of matter and more particularly on the quantum nature of electrons. This thesis project deals with an electronic hybrid superconductor/carbon nanotube (CNT) system called nano-SQUID. This device has a superconducting loop containing two CNT junctions in parallel. This unique system couples the properties of a superconducting interferometer (SQUID) with those of molecular quantum dot (QD) Josephson junctions (CNT junction). Through transport experiments performed in a reversed dilution cryostat at temperatures of several tens of milli-Kelvin, we studied the electronic interactions between a nanotube quantum dot and superconducting electrodes. We specifically focused on the influence of the magnetic state of the nanotube on the superconducting current flowing through. Depending on the QD spin state, the CNT Josephson junction can behave as a -junction. Finally a complete electrostatic control allowed us to define an experimental 0- phase diagram of a QD Josephson junction.

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.

Orientadores: Roberto Eugenio Lagos Monaco, Guillermo Gerardo Cabrera Oyarzun / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin / Made available in DSpace on 2018-08-04T08:16:12Z (GMT). No. of bitstreams: 1 ChavesNeto_AntonioMaiadeJesus_D.pdf: 1164069 bytes, checksum: a0ef564c6eb492fa671d7430fad4221a (MD5) Previous issue date: 2004 / Resumo: O Hamiltoniano do modelo de Anderson para duas impurezas é estudado via um desacoplamento das funções de Green. Neste caso resulta ser equivalente a aproximação de potencial coerente (CPA) que também, neste caso, coincide com a aproximação Hubbard-I. Consideram-se todos os termos de interação impureza-impureza, tanto os denominados termos de um corpo como os de dois corpos. Os parâmetros associados às interações mencionadas acima incluem: repulsão coulombiana intra e intersítio, hopping direto, hopping correlacionado e o termo de troca (exchange). Todos estes são modelados via orbitais atômicos de Slater, e neste caso se considera o modelo mais simples, o caso não degenerado, ou seja, um nível por impureza. Nesta modelagem, incluindo o metal hospedeiro, os parâmetros independentes resultam ser: a constante de hibridização eletrônica impureza-metal, o número de portadores do metal hospedeiro, o vetor de onda de Fermi associado ao mesmo, a largura dos orbitais atômicos das impurezas e a distância impureza-impureza. Para o caso particular de temperatura nula e no regime denominado de banda semicheia (a metade dos níveis das impurezas são preenchidos considerando os valores esperados) são calculadas as densidades espectrais (densidade de estados) associadas às impurezas, as funções de correlações de spin e carga, suscetibilidades magnéticas e de carga, e a energia de correlação associada as impurezas. Os resultados são discutidos no contexto dos modelos já a existentes na literatura, assim como os casos limites para os quais existem resultados exatos. Os resultados encontrados estão de acordo com os casos limites conhecidos e são interessantes. Mostram também a importância de se considerar todas as interações impureza-impureza, fato negligenciado até agora na literatura / Abstract: We study the two impurity Anderson Model Hamiltonian via a Greens function decoupling scheme. This case turns out to be equivalent to the Coherent Potential Approximation (CPA) and furthermore equivalent to the Hubbard-I approximation. We consider all one and two body impurity-impurity interactions. The parameters associated to the latter include: the intra and intersite Coulomb repulsion, direct (band) hopping, correlated hopping and the exchange term. All of the above are modeled via Slater atomic orbitals, and here we consider the simplest model, non degenerate single impurity level. Including the host metal the resulting independent parameters are: The impurity-metal hybridization constant, the metal host carrier density, the associated Fermi wavevector, the atomic orbital width and the impurity-impurity distance. For the zero temperature case and in the so called band half called regime (impurities levels half called, in the mean) we compute the impurities spectral densities (density of states), spin and charge correlation functions, their respective susceptibilities and the correlation energy. We discuss our results considering the existing literature as well as the exact results for particular limiting cases. Our results agree with the latter and also yield interesting consequences, among others: the importance of including all impurity-impurity interactions, hitherto not considered. / Doutorado / Física da Matéria Condensada / Mestre em Física

Cette thèse est consacrée à l'étude théorique des propriétés de transportd'un nanodispositif comme par exemple une boîte quantique. A faible dimensionnalité,les propriétés de transport sont fortement liées à la densité d'étatsélectroniques du système, il est donc important d'utiliser une approche capablede calculer cette dernière correctement notamment en tenant comptedu confinement électronique.En utilisant le modèle d'Anderson et l'approximation de non croisementafin de calculer la densité d'états, on a pu observer et caractériser les transfertsde poids spectral pour des orbitales simplement, doublement ou triplementdégénérées. Ces transferts de poids spectral sont typiques des systèmescorrélés, mais lorsqu'une différence de potentiel est appliquée, on a pu remarquerque ces transferts se faisaient en deux temps.Dans un second temps, on a analysé les signatures du couplage de Hundincluant le terme de saut de paires dans les diagrammes de stabilité. Ces deuxtermes, provenant de l'interaction Coulombienne, modifient sensiblement lastructure des diamants de Coulomb et doivent donc être considérés lorsqu'ondéduit les paramètres microscopiques à partir du diagramme de stabilitéexpérimental.Enfin, on s'est placé dans le régime de générateur thermoélectrique, et ona utilisé le pic de Kondo comme canal de transport. Cependant l'optimisationà la fois du rendement et de la puissance en utilisant les bandes de Hubbardcomme canaux de transport est impossible. Or les particularités et les grandeurscaractérisant le pic de Kondo permettent d'une part de s'affranchirpartiellement de ce compromis mais cela permet également de générer uneplus grande puissance. / This thesis is devoted to the theoretical study of a nanodevice transportproperties, such as a quantum dot. At low dimensionality, transport propertiesare strongly related to the local density of state, it is important to use anapproach able to compute the latter properly especially tanking into accountthe electronic containment.Using the Anderson model and the non-crossing approximation to computedensity of states, we observed and characterize spectral weight transfersfor simply, doubly and triply degenerated orbitals. These spectral weighttransfers are typical of correlated systems, but when potential bias is applied,we note that these transfers occur in two stages.In a second step, we analyze Hund coupling footprint including pair hoppingin stability diagrams. These two terms, from the Coulomb interaction,substantially alter the Coulomb diamonds structure and must be considerwhen microscopic parameters are derived from experimental stability diagrams.Finally, we placed in the thermoelectric generator regime, and we usedKondo peak as transport channel. However, optimization of both efficiencyand power output using Hubbard bands as transport channel is impossible.But the features and scales characterizing Kondo peak serve on the one handto overcome this compromise and on the other hand to generate a greaterpower output.

Eine Vielzahl von interessanten Phänomenen entsteht durch die quantenmechanischeWechselwirkung einer großen Zahl von Teilchen. In den meisten Fällen ist die Beschreibung der relevanten physikalischen Eigenschaften extrem schwierig, da die Komplexität des Systems exponentiell mit der Anzahl der wechselwirkenden Teilchen anwächst und das Lösen der zugrunde liegenden Schrödingergleichung unmöglich macht. Trotzdem gab es in der Geschichte der Festkörperphysik eine Reihe von bahnbrechenden Entdeckungen, die unser Verständnis von komplexen Phänomenen deutlich voran gebracht haben. Dazu zählt die Entwicklung der Landau’schen Theorie der Fermiflüssigkeit, der BCS-Theorie der Supraleitung, der Theorie der Supraflüssigkeit und der Theorie des fraktionalen Quanten-Hall-Effekts. In all diesen Fällen ist ein theoretisches Verständnis mithilfe sogenannter Quasiteilchen gelungen. Anstatt ein komplexes Phänomen durch das Verhalten von fundamentalen Teilchen wie der Elektronen zu erklären, ist es möglich, die entsprechenden Eigenschaften durch das simple Verhalten von Quasiteilchen zu beschreiben, die allein auf Grund der komplexen kollektiven Wechselwirkung entstehen. Eines der seltenen Beispiele, bei dem ein stark korreliertes quantenmagnetisches Problem analytisch lösbar ist, ist das Kitaev Modell. Es beschreibt wechselwirkende Spins auf einem Sechseck-Gitter und zeichnet sich durch einen Spinflüssigkeits-Grundzustand aus. Auch hier gelang die Lösung mittels spezieller Quasiteilchen, den Majorana Fermionen. Experimentell ist es jedoch noch nicht gelungen eine Spinflüssigkeit eindeutig nachzuweisen, da diese sich gerade durch das Fehlen jeglicher klassischer Ordnung und üblicher experimenteller Kenngrößen auszeichnet. Dagegen kann die Beobachtung von Quasiteilchenanregungen einen Hinweis auf den zugrunde liegenden Zustand liefern. Aber auch der definitive Nachweis von Majorana Fermionen in jeglicher Art System, bleibt ein ausstehendes Ziel in der modernen Festkörperphysik. Diese Arbeit befasst sich daher mit der Frage, wie solche Quasiteilchen experimentell sichtbar gemacht werden könnten. Dazu untersuchen wir den Einfluss von Unordnung auf die Zustände und Messgrößen des Kitaev Modells. Dies ist in zweierlei Hinsicht relevant. Einerseits ist Unordnung in der Natur allgegenwärtig, andererseits kann sie auch strategisch herbeigeführt werden, um die Reaktion eines System gezielt zu testen. Das zentrale Ergebnis dieser Arbeit ist, dass den Majorana Fermionen dabei in der Tat eine physikalische, messbare Bedeutung zukommt. Die Arbeit beginnt mit einer Einführung in frustrierte quantenmagnetische Systeme und Spinflüssigkeiten und diskutiert einige Effekte, die durch Gitterverzerrungen oder Verunreinigungen entstehen können. Anschließend zeigen wir, wie sich durch die frustrierte Wechselwirkung im Kitaev Modell ein Spinflüssigkeits-Grundzustand herausbildet. Die analytische Lösung des Modells gelingt mit Hilfe von Majorana Fermionen, jedoch verdoppelt sich der Hilbertraum pro Spin durch die Einführung dieser Quasiteilchen. Ein zentraler Aspekt dieser Arbeit ist daher die richtige Auswahl der „physikalischen“ Zustände, also solcher, die einem Zustand im ursprünglichen Spin Modell entsprechen. Dabei unterscheiden wir zwischen offenen und periodischen Randbedingungen. Wir konnten beweisen, dass sich, in der Phase ohne Bandlücke und für periodische Systeme, stets ein angeregtes Fermion befindet. Dies führt zu großen Effekten in endlichen Systemen, wie wir anhand der Suszeptibilität und der Anregungslücke für magnetische Flüsse zeigen. Außerdem berechnen wir numerisch die statische und dynamische Suszeptibilität abhängig von der Unordnung in der Wechselwirkungsstärke. Diese Art der Unordnung entsteht beispielsweise durch unregelmäßige Gitterstrukturen oder chemische Verunreinigungen auf den nicht-magnetischen Gitterplätzen. Insbesondere ergibt die Verteilung der lokalen Suszeptibilitäten das Linienspektrum, welches sich in Kernspinresonanz Experimenten messen lässt. Für große Unordnung postulieren wir einen Übergang zu einem Zustand mit einer zufälligen Verteilung magnetischer Flüsse. Ein weiterer Kern der Dissertation ist die Untersuchung eines magnetischen Defekts im Kitaev Modell. Diese Situation beschreibt den ungewöhnlichen Fall eines Kondoeffekts in einer Spinflüssigkeit. In der Majorana Fermionen Darstellung gelingt es uns, das Problem in eine Form zu bringen, die mit Hilfe von Wilson’s numerischer Renormalisierungsgruppe untersucht werden kann. Es zeigt sich, dass dadurch eine Nullpunktsentropie des Defekts entsteht, die durch lokalisierte Majorana Fermionen erklärt werden kann. Durch die Darstellung des Kitaev Modells mithilfe von Quasiteilchen ist es möglich eine elegante Beschreibung eines komplexen, stark wechselwirkenden Systems zu finden. Die Ergebnisse dieser Arbeit zeigen, dass den Majorana Fermionen dabei durchaus eine physikalische Bedeutung zukommt. Gelingt es sie z.B. durch magnetische Störstellen zu lokalisieren, wäre ein direkter experimenteller Nachweis möglich. / Many interesting phenomena in quantum physics arise through the quantum mechanical interaction of a large number of particles. In most cases describing the relevant physical properties is extremely difficult, because the complexity of the system increases exponentially with the number of interacting particles and solving the underlying Schrödinger equation becomes impossible. Nevertheless, our understanding of complex phenomena has progressed through some groundbreaking discoveries in the history of condensed matter physics. Examples include the development of Landau’s theory of Fermi liquids, the BCStheory of superconductivity, the theory of superfluidity and the theory of the fractional quantum Hall effect. In all these cases a theoretical understanding was achieved with so-called quasi-particles. Instead of explaining a phenomenon through the behavior of fundamental particles, such as electrons, the corresponding properties can be described by the simple behavior of quasi-particles, which are themselves a result of the complex collective interaction. One of the rare examples, where a strongly correlated quantum mechanical problem can be solved analytical, is the Kitaev model. It describes interacting spins on a honeycomb lattice and exhibits a spin liquid ground state. Here the solution was achieved by means of certain quasi-particles, called Majorana fermions. However, it has not been possible to clearly identify such a spin liquid experimentally, because its defining feature is the absence of any conventional order, in particular magnetic order. In contrast, the observation of quasiparticle excitations may hint at the nature of the ground state. But also a definite detection of Majorana fermions in any kind of system remains one of the outstanding issues in modern condensed matter physics. Therefore this thesis is devoted to the question how such quasiparticles may be found experimentally. For this reason we study the influence of disorder on the states and observables of the Kitaev model. This is relevant in two respects: Firstly, disorder is ubiquitous in nature and secondly, it may be used strategically to probe the response of a system. The central result of this work is that Majorana fermions hereby indeed obtain a true physical and observable significance. The thesis starts with an introduction of frustrated quantum mechanical systems and spin liquids, and discusses some of the effects that arise through lattice distortions or impurities. Afterwards we show how the frustrated interactions in the Kitaev model lead to a spin liquid ground state. The analytical solution of the model is achieved through the introduction of Majorana fermions. However, resulting from the introduction of these quasi-particles the Hilbert space per spin doubles. A central aspect of this thesis is therefore the right selection of the “physical” states, which correspond to a state of the original spin Hamiltonian. To do this, we distinguish between periodic and open boundary conditions explicitly. We were able to prove that there is always one excited fermion in the gapless phase of the periodic system. This leads to large finite-size effects, as we will illustrate for the susceptibility and the magnetic flux gap. Moreover we compute the static and dynamic spin susceptibilities for finite-size systems subject to disorder in the exchange couplings. In a possible experimental realization, this kind of disorder arises from lattice distortions or chemical disorder on nonmagnetic sites. Specifically, we calculate the distribution of local susceptibilities and extract the lineshape, which can be measured in nuclear-magnetic-resonance experiments. Further, for increasing disorder we predict a transition to a random-flux state. Another core of this dissertation is the investigation of a magnetic impurity in the Kitaev model. This setup represents the unusual case of a Kondo effect in a quantum spin liquid. Utilizing the Majorana representation we are able to formulate the problem in a way that can be analyzed using Wilson’s numerical renormalization group. The numerics reveal an impurity entropy which can be explained by localized Majorana fermions. Through the representation of the Kitaev model in terms of quasi-particles an elegant description of a complex, strongly correlated system is possible. The results of this thesis indicate that these Majorana acquire a relevant physical meaning. If one can localize them, for example with the help of magnetic impurities, a direct experimental observation would be feasible.

Ziel dieser Arbeit war es, Beziehungen zwischen den kristallchemischen Eigenschaften und dem beobachteten anomalen Verhalten im spezifischen elektrischen Widerstand (nicht-magnetischer Kondo-Effekt) aufzuzeigen und zusammenhängend zu interpretieren. Verbindungen, an denen dieser Effekt beobachtet wurde, werden aus einem Übergangs-, oder Actinidmetall mit je einem Vertreter der 15. (Pniktogene) und 16. Gruppe (Chalkogene) des Periodensystems gebildet und kristallisieren im PbFCl-Strukturtyp. Da zu ternären Actinidmetall-Pniktid-Chalkogeniden (z.B. ThAsSe, UPS) nur sehr wenige chemische und kristallographische Informationen existieren, wurden in dieser Arbeit umfassende Untersuchungen zur Kristallchemie ternärer Phasen aus den Systemen M-Pn-Q (M = Zr, Hf, La-Ce; Pn = As, Sb; Q = Se, Te durchgeführt. Der Schwerpunkt lag dabei auf der strukturellen Lokalisierung der beobachteten Widerstandsanomalie und der Erarbeitung chemisch-physikalischer Eigenschaftsbeziehungen. Die Darstellung der untersuchten ternären Phasen in Form von Einkristallen gelang über exothermen Chemischen Transport mit Jod. Da die erhaltenen Kristalle bis zu mehreren Millimetern groß sind, konnten an ein und demselben Kristallindividuum sowohl die stoffliche Charakterisierung (EDXS, WDXS, ICP-OES, LA-ICP-MS, CIC) und die strukturelle Charakterisierung, als auch die Messung der physikalischen Eigenschaften erfolgen. Es konnte u.a. gezeigt werden, dass ZrAs1,4Se0,5 und HfAs1,7Se0,2 ein ähnlich ungewöhnliches Verhalten im temperaturabhängigen elektrischen Widerstand zeigen, welches bereits an Thorium-Arsenid-Seleniden und Uran-Phosphid-Sulfiden beobachtet wurde. Desweiteren gelang es den beobachteten Verlauf im elektrischen Widerstand, mit seinem Minium bei etwa T = 15 K, auf intrinsische strukturelle Merkmale in der anionischen Arsen-Teilstruktur zurückzuführen. / The aim of this work was, to evaluate and interpret a relationship between the crystal-chemical properties and the observed unusual behavior in the electrical resistivity (non-magnetic Kondo-effect). Compounds, which show such an effect, are formed by a transition- or actinide-metal with both a group 15 element and a group 16 element of the periodic table. All these compounds crystallizing in the PbFCl type of structure. Because of less crystallographic and chemical information about actinide-metal-pnictide-chalcogenides (i.e. ThAsSe, UPS), intensive investigation were made concerning the crystal-chemistry of ternary phases of the systems M-Pn-Q (M = Zr, Hf, La-Ce; Pn = As, Sb; Q = Se, Te. Our studies were focused on the structurally localization of the observed anomaly in the electrical resistivity and the evaluation of chemical-physical relations of properties. The synthesis of the investigated ternary phases was realized by exothermically Chemical Transport with iodine as transport agent. The dimension of the synthesized crystals allowed a chemical (EDXS, WDXS, ICP-OES, LA-ICP-MS, CIC) and structurally characterization, as well as a determination of the physical properties on one large single crystal. It could be shown, that ZrAs1,4Se0,5 and HfAs1,7Se0,2 reveal a similar unusual behavior in the temperature dependent electrical resistivity, as it was observed in thorium-arsenide-selenides and uranium-phosphide-sulphides. In conclusion, the non-magnetic Kondo-effect, which was found in the low-temperature range (about 15 K), arises from structurally features of the anionic sublattice with arsenic.

Cette thèse présente les résultats de mesures expérimentales effectués à basse température par les techniques de microscopie tunnel à balayage et de spectroscopie par tunnel à balayage (STS) sur les métaux de transitions phthalocyanines déposées sur les surfaces de métaux nobles. Les mesures STM/STS ont été effectuées pour les molécules MnPc et CuPc adsorbées sur les surfaces Ag (111) et Au (111) à la température expérimentale de travail de 4,5 K. Ces deux types de molécules présentent une différence substantielle de configurations d'adsorption, des comportements électroniques et magnétiques et des structures vibratoires moléculaire. Les études STM/STS ont principalement porté sur les propriétés magnétiques de ces molécules à travers l’effet Kondo et une attention particulière a été accordée à la molécule de MnPc en raison de son comportement magnétique plus intéressant issu de l'atome Mn central. Particulièrement, nous avons étudié l'évolution spectrale des structures électroniques et magnétiques du MnPc partant d'une molécule unique jusqu'à la structure bicouche ordonnée sur la surface Ag (111). En outre, les études STM/STS ont montré une preuve de couplage magnétique entre les moments magnétiques de l'atome de Co et de la molécule de MnPc ainsi que sa forte dépendance vis-à-vis du site d'adsorption de l'atome de Co. Ces études STM/STS sur ce système nous ont permis de comprendre l'effet des interactions molécule-substrat, molécule-molécule et molécules-atome sur les propriétés électroniques et magnétiques des molécules de MnPc. / This thesis presents the results of low-temperature scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS) studies on transition-metal phthalocyanines molecules on the noble metal surfaces. The STM/STS measurements have been performed for MnPc and CuPc molecules adsorbed on Ag(111) and Au(111) surfaces at the experimental working temperature of 4.5 K. These two types of molecules exhibit substantially different adsorption configurations, the electronic and magnetic behaviors and the molecule vibrational structures. The STM/STS studies have focused mainly on the magnetic properties of these molecules by means of Kondo effect, and special attention has been paid to MnPc molecule due to its more interesting magnetic behavior arising from the central Mn atom. Particularly we investigated the spectral evolution of electronic and magnetic structures of MnPc starting from a single molecule up to the ordered bilayer structures on Ag(111) surface. In addition, the STM/STS investigations showed an evidence of magnetic coupling between the magnetic moments of the Co atom and MnPc molecule and its strong dependence on the adsorption site of Co atom. These STM/STS investigations on this system allowed us to understand the effect of molecule-substrate, molecule-molecule and molecule-atom interactions on the electronic and magnetic properties of MnPc molecules.

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