A plasmônica tem chamado atenção nos últimos anos como um candidato viável para substituir a indústria eletrônica, assim como interação dos plásmons com a matéria devido a suas propriedades exóticas. O confinamento destes plásmons de superfície em nanoestruturas metálicas fabricadas com técnicas de litografia óptica, eletrônica e de íons cada vez mais avançadas, abriu a possibilidade de desenvolver vários modelos de dispositivos ópticos que trabalham na região do visível. Além disso, o estudo da interação de plásmons poláritons de superfície com emissores quânticos nas proximidades de nanoestruturas metálicas permite manipular as propriedades tanto dos plásmons como dos emissores quânticos. Tanto a preparação como a análise de amostras em plasmônica necessitam de técnicas capazes de investigar sistemas em nanoescala. Neste trabalho, investigamos a interação de plásmon poláritons confinados numa superfície de ouro com átomos artificiais, i.e. os emissores quânticos são pontos quânticos numa matriz de InAs/GaAs. Para isso, empregamos a análise da interação dos plásmons confinados numa grade metálica, com dimensões características abaixo do comprimento de onda da luz utilizada, assim como um sistema simples composto por uma na camada de ouro capaz de confinar plásmons em duas dimensões. A análise da interação com os estados de energia dos éxcitons nos pontos quânticos foi feita empregando medidas de micro-fotoluminescência a 77K e medidas de tempo de vida. Nos sistemas compostos pelas grades metálicas, observamos que é possível manipular a relação do espectro de luminescência correspondente a cada estado de energia do éxciton. Já no sistema composto pelo filme metálico simples, foi possível modificar o tempo de vida do estado fundamental do éxciton apenas modificando o cap layer da camada de pontos quânticos. / Plasmonics has drawn attention in recent years as a viable candidate to replace the electronics industry, as well as the interaction of plasmons with matter due to its exotic properties. The confinement of these surface plasmons in metal nanostructures made of increasingly advanced optical, electronic and ionic lithography techniques, opened the possibility of developing various models of optical devices working in the visible spectrum. Moreover, the study of interaction of surface plasmon polaritons with quantum emitters nearby metallic nanostructures opens a path to manipulate the properties of both plasmons and the quantum emitters. Both the preparation and analysis of samples in plasmonics require techniques capable of investigating nanoscale systems. In this thesis, we investigate the interaction of plasmon polaritons confined to a golden metallic surface with artificial atoms, i.e. quantum emitters consisting of quantum dots in a matrix of InAs/GaAs. For this, we used the analysis of the interaction of plasmons confined in a metallic grating with characteristic dimensions below the wavelength of light used, as well as a simple system composed of a thin gold layer which can confine plasmons in two dimensions. The analysis of the interaction with the exciton energy states in quantum dots was made using micro-photoluminescence measurements at 77 K and lifetime measurements. In systems composed by metal gratings, we note that it is possible to manipulate the relationship of the corresponding luminescence spectrum for each exciton energy state. In the system composed of the simple metal lm, it was possible to modify the ground state lifetime of the exciton only modifying the cap layer of the quantum dot layer.

A plasmônica tem chamado atenção nos últimos anos como um candidato viável para substituir a indústria eletrônica, assim como interação dos plásmons com a matéria devido a suas propriedades exóticas. O confinamento destes plásmons de superfície em nanoestruturas metálicas fabricadas com técnicas de litografia óptica, eletrônica e de íons cada vez mais avançadas, abriu a possibilidade de desenvolver vários modelos de dispositivos ópticos que trabalham na região do visível. Além disso, o estudo da interação de plásmons poláritons de superfície com emissores quânticos nas proximidades de nanoestruturas metálicas permite manipular as propriedades tanto dos plásmons como dos emissores quânticos. Tanto a preparação como a análise de amostras em plasmônica necessitam de técnicas capazes de investigar sistemas em nanoescala. Neste trabalho, investigamos a interação de plásmon poláritons confinados numa superfície de ouro com átomos artificiais, i.e. os emissores quânticos são pontos quânticos numa matriz de InAs/GaAs. Para isso, empregamos a análise da interação dos plásmons confinados numa grade metálica, com dimensões características abaixo do comprimento de onda da luz utilizada, assim como um sistema simples composto por uma na camada de ouro capaz de confinar plásmons em duas dimensões. A análise da interação com os estados de energia dos éxcitons nos pontos quânticos foi feita empregando medidas de micro-fotoluminescência a 77K e medidas de tempo de vida. Nos sistemas compostos pelas grades metálicas, observamos que é possível manipular a relação do espectro de luminescência correspondente a cada estado de energia do éxciton. Já no sistema composto pelo filme metálico simples, foi possível modificar o tempo de vida do estado fundamental do éxciton apenas modificando o cap layer da camada de pontos quânticos. / Plasmonics has drawn attention in recent years as a viable candidate to replace the electronics industry, as well as the interaction of plasmons with matter due to its exotic properties. The confinement of these surface plasmons in metal nanostructures made of increasingly advanced optical, electronic and ionic lithography techniques, opened the possibility of developing various models of optical devices working in the visible spectrum. Moreover, the study of interaction of surface plasmon polaritons with quantum emitters nearby metallic nanostructures opens a path to manipulate the properties of both plasmons and the quantum emitters. Both the preparation and analysis of samples in plasmonics require techniques capable of investigating nanoscale systems. In this thesis, we investigate the interaction of plasmon polaritons confined to a golden metallic surface with artificial atoms, i.e. quantum emitters consisting of quantum dots in a matrix of InAs/GaAs. For this, we used the analysis of the interaction of plasmons confined in a metallic grating with characteristic dimensions below the wavelength of light used, as well as a simple system composed of a thin gold layer which can confine plasmons in two dimensions. The analysis of the interaction with the exciton energy states in quantum dots was made using micro-photoluminescence measurements at 77 K and lifetime measurements. In systems composed by metal gratings, we note that it is possible to manipulate the relationship of the corresponding luminescence spectrum for each exciton energy state. In the system composed of the simple metal lm, it was possible to modify the ground state lifetime of the exciton only modifying the cap layer of the quantum dot layer.

Almost a century after its discovery, superconductivity (SC) is still the most challenging and fascinating topic in condensed matter physics. Organic superconductors show exotic phases and phase transitions with a change in temperature or pressure. In this dissertation, we studied the phases and phase-transitions in one-dimensional (1D) and two-dimensional (2D) organic materials. This dissertation itself is a group of three sub-projects. In project (i), we studied the properties of a novel state “paired electron crystal” (PEC) in the quarterfilled Hubbard model to understand the phases and properties of 2D organic materials. We also studied the effects of charge and spin frustration on the 2D strongly correlated quarterfilled band. Our conclusions are based on exact diagonalization (ED) studies that include electron-electron and adiabatic electron-phonon interactions. For moderate to strong frustration, the dominant phase is a novel spin-singlet PEC. We discuss the implications of the PEC concept for understanding several classes of quarterilled band materials that display unconventional superconductivity. In project (ii), we studied the thermodynamics of a zigzag ladder model, applicable to quasi-1D organic materials. Using the quantum Monte Carlo (QMC) method, we studied the thermodynamics of charge ordering in quarterilled quasi-1D organic charge transfer solids (CTS). Previous theoretical studies on these CTS have focused on ground state properties or purely 1D systems. In the zigzag ladder, no separate high-temperature ordering is expected; instead the ladder is metallic at high temperature, and as temperature decreases, a single transition to the PEC state with a spin-gap takes place. In project (iii), we studied superconducting pairing correlation and metal-insulator transitions in the halfilled Hubbard model. We employed the Hubbard model and used the path integral renormalization group (PIRG) method for this study. Antiferromagneticmediated SC was suggested for small to large frustration in anisotropic triangular lattices. Previous work on the halfilled Hubbard model using the ED method was successful in showing the absence of d-wave SC on a small anisotropic triangular lattice. We extended this study to larger lattices to investigate the existence of long-range order of superconducting pair-pair correlations. We also show the absence of d-wave SC in this model on larger lattices.

Cette thèse aborde deux problèmes ayant trait à la physique des gaz quantiques de basse dimensionnalité. Le premier système étudié est un mélange unidimensionnel de bosons et de fermions sans spin soumis à un potentiel aléatoire. Nous commençons par écrire un Hamiltonien de basse énergie et abordons la question de la localisation du point de vue de l'accrochage des ondes de densité par un désordre faible. En utilisant le Groupe de Renormalisation et une méthode variationnelle dans l'espace des répliques, le diagramme de phase peut être tracé en fonctions de deux paramètres : la force des interactions Bose-Bose et Bose-Fermi. La position et les propriétés des phases dépendent d'un paramètre additionnel, le rapport des vitesses du son de chaque composante du gaz. Quelque soit la valeur de ce rapport nous trouvons trois phases, (i) une phase totalement délocalisée, le liquide de Luttinger à deux composantes, (ii) une phase totalement localisée où les deux composantes sont accrochées par le désordre et (iii) une phase intermédiaire où seuls les fermions sont localisés. Le deuxième système est un gaz de bosons de cœur dur sur un réseau en échelle. Trois paramètres en contrôlent la physique : les amplitudes de saut transverse et longitudinale, et le remplissage. En utilisant plusieurs méthodes analytiques (théorie des perturbations, bosonisation et RG) nous proposons une interprétation de résultats numériques nouveaux obtenus par nos collaborateurs, notamment sur le paramètre de Luttinger du mode symétrique. Nous en déduisons un diagramme de phase en présence de désordre faible. / In this thesis we study two distinct problems related to the physics of quantum gases in one dimension. After writing a low-energy Hamiltonian, we address the question of localization by considering the pinning of density waves by weak disorder. Using the Renormalization Group and a variationnal method in replica space, we find that the phase diagram is adequately plotted as a function of two parameters: the strength of Bose-Bose and Bose-Fermi interactions. The position and properties of the various phases depend on an additional third parameter, the ratio of the phonon velocities of each component of the gas. Whatever the value of this ratio, we identify -- using the Renormalization Group and a variational calculation -- three types of phases, (i) a fully delocalized phase, that is a two-component Luttinger, (ii) a fully localized phase where both components are pinned by disorder and (iii) an intermediate phase where fermions are localized and bosons are superfluid. The second system is a two-leg ladder lattice of hardcore bosons. Three parameters control the physics: transverse and longitudinal tunneling and the filling. Using several analytical methods (perturbation theory, bosonization, RG) we give an interpretation of new numerical results obtained by our collaborators, namely on the Luttinger parameter of the symmetric mode. We deduce a phase diagram for weak disorder.

Este trabalho estuda o modelo de Falicov e Kimball com duas impurezas. O modelo consiste de um metal com duas impurezas separadas por uma distância R, cada uma das quais é representada por um único nível eletrônico. Um acoplamento V permite transferência de carga entre cada impureza e a banda de condução do metal. Além disso, cada impureza introduz um potencial espalhador G cuja intensidade depende da ocupação do seu nível, assim simulando a interação eletrostática entre um buraco na impureza e os elétrons de condução. Esta dissertação diagonaliza o Hamiltoniano do modelo pelo método do grupo de renormalização numérico. Dá-se atenção à possível equivalência entre este modelo (desprovido de spin) e o modelo de Kondo para duas impurezas. Discute-se em particular essa equivalência para R=0 e para R= INFINITO. Para R finito, apenas um primeiro passo na direção de se estabelecer a equivalência é dado: obtém-se uma expressão analítica para a taxa de transição eletrônica entre os níveis das impurezas e a banda de condução. / In this work, the two-impurity Falicov-Kimball model is studied. The model consists of a metal containing two impurities separated by a distance R, each represented by a single electronic level. A coupling V allows charge transfer between each impurity and the conduction band. In addition, each impurity scatters the conduction electrons with a localized potential G whose intensity depends on the occupancy of the impurity level; this mimics the Coulomb attraction between na impurity hole and the conduction band. This dissertation diagonalizes the model Hamiltonian with the numerical renormalization group method. In two special limits, R=0 and R=INFINITO, the equivalence between the (spinless) Falicov-Kimball model and the two-impurity Kondo model is discussed. For other impurity separations, only a first step torwards establishing that equivalence is taken: na analytical expression for the electronic transition rate between the impurity levels and the conduction states is obtained.

Este trabalho estuda o modelo de Falicov e Kimball com duas impurezas. O modelo consiste de um metal com duas impurezas separadas por uma distância R, cada uma das quais é representada por um único nível eletrônico. Um acoplamento V permite transferência de carga entre cada impureza e a banda de condução do metal. Além disso, cada impureza introduz um potencial espalhador G cuja intensidade depende da ocupação do seu nível, assim simulando a interação eletrostática entre um buraco na impureza e os elétrons de condução. Esta dissertação diagonaliza o Hamiltoniano do modelo pelo método do grupo de renormalização numérico. Dá-se atenção à possível equivalência entre este modelo (desprovido de spin) e o modelo de Kondo para duas impurezas. Discute-se em particular essa equivalência para R=0 e para R= INFINITO. Para R finito, apenas um primeiro passo na direção de se estabelecer a equivalência é dado: obtém-se uma expressão analítica para a taxa de transição eletrônica entre os níveis das impurezas e a banda de condução. / In this work, the two-impurity Falicov-Kimball model is studied. The model consists of a metal containing two impurities separated by a distance R, each represented by a single electronic level. A coupling V allows charge transfer between each impurity and the conduction band. In addition, each impurity scatters the conduction electrons with a localized potential G whose intensity depends on the occupancy of the impurity level; this mimics the Coulomb attraction between na impurity hole and the conduction band. This dissertation diagonalizes the model Hamiltonian with the numerical renormalization group method. In two special limits, R=0 and R=INFINITO, the equivalence between the (spinless) Falicov-Kimball model and the two-impurity Kondo model is discussed. For other impurity separations, only a first step torwards establishing that equivalence is taken: na analytical expression for the electronic transition rate between the impurity levels and the conduction states is obtained.

Title: U in metastable systems: structure, magnetism, and superconductivity Author: Volodymyr Buturlim Department / Institute: Department of Condensed Matter Physics, Faculty of Mathematics and Physics, Charles University Supervisor of the doctoral thesis: Doc. RNDr. Ladislav Havela, CSc., Department of Condensed Matter Physics, Faculty of Mathematics and Physics, Charles University, Prague, The Czech Republic Abstract: This thesis presents studies of U-Nb and U-Ti alloys and hydrides synthesized via different technological paths. Investigation of the microstructure of the alloys with different concentrations of Ti (Nb) allowed to find the optimum setting for stabilization of the metastable bcc U allotrope. Ultra-fast cooling accompanied by alloying leads to retention of materials with high degree of atomic disorder apparent from the studies of their transport properties. The alloys exhibit a weakly paramagnetic ground state and low-temperature superconductivity, the critical temperature of which has only moderate variations with Ti (Nb) concentrations and which has very high upper critical fields. Interaction with hydrogen allows to stabilize two distinctive forms of hydride: β-UH3 and UTi2Hx. β-UH3 alloyed by Ti (Nb) orders ferromagnetically with transition temperatures exceeding 170 K, weakly influenced...

In dieser Arbeit wurden mit Hilfe von Transportmessungen – vor allem mit thermischem Transport bei sehr tiefen Temperaturen – intermetallische Seltenerdverbindungen untersucht. Diese Materialien sind oft durch starke elektronische Korrelationen gekennzeichnet, die zu neuartigen Eigenschaften führen. Um die Wechselwirkungen in den untersuchten Systemen zu beeinflussen, führten wir ein Magnetfeld als zusätzlichen Parameter ein. Damit untersuchten wir drei Fragestellungen. Im ersten Teil überprüften wir die Gültigkeit des Wiedemann-Franz-Gesetzes in YbRh2Si2. Dieses Material zeigt einen durch ein kleines Magnetfeld induzierten quantenkritischen Punkt, für dessen unkonventionelle Eigenschaften es noch keine allgemein etablierte mikroskopische Theorie gibt. Mit Hilfe des Wiedemann-Franz-Gesetzes haben wir untersucht, ob eine solche Theorie im Rahmen des Quasiteilchenbildes formuliert werden kann. Während wir eine Bestätigung für Magnetfelder abseits des quantenkritischen Punktes zeigen, ergibt unsere Analyse direkt am quantenkritischen Punkt eine Verletzung des Weidemann-Franz-Gesetzes. Dies hat weitreichende physikalische Folgen, da eine Verletzung den Zusammenbruch des Konzeptes von Quasiteilchen impliziert. In der zweiten Studie untersuchten wir die Kondogittersysteme YbRh2Si2 und CeRu2Si2 in Magnetfeldern mit Energien von der Größenordnung der Kondotemperatur. Beide Systeme zeigen bislang ungeklärte feldinduzierte Übergänge mit sehr unterschiedlichen Signaturen jedoch den selben Vorschlägen für deren Ursache: ein abrupter Zusammenbruch des Kondoeffekts oder ein Lifshitzübergang. Mit Thermokraft- und Widerstandsmessungen konnten wir für CeRu2Si2 zeigen, dass auch der thermische Transport kompatibel mit einem Lifshitzübergang ist. Ein globales Modell, das thermodynamische Größen mit einschließt, ist jedoch weiterhin nicht vorhanden. In YbRh2Si2 detektierten wir anstatt eines einzelnen, insgesamt drei Übergänge in höheren Magnetfeldern. Mithilfe einer sehr guten Übereinstimmung von renormalisierten Bandstrukturrechnungen mit unseren und früheren Experimenten, können wir die Entwicklung von YbRh2Si2 im Magnetfeld als Superposition von einer stetigen Unterdrückung des Kondoeffekts und drei Lifshitzübergängen beschreiben. Im dritten Projekt untersuchten wir den supraleitenden Ordnungsparameter von LaPt4Ge12. Während frühere Experimente auf konventionelle Supraleitung hindeuten, wird für das eng verwandte PrPt4Ge12 unkonventionelle und/oder Multiband-Supraleitung diskutiert. Resultate an der Substitutionsreihe LaxPr1-xPt4Ge12 suggerieren jedoch kompatible Ordnungsparameter für beide Verbindungen. Unsere Ergebnisse der spezifischen Wärme und der temperatur- und feldabhängigen Wärmeleitfähigkeit an LaPt4Ge12 sind kompatibel mit dem Modell konventioneller Supraleitung ohne Nullstellen im der supraleitenden Bandlücke. Die Abhängigkeit der Wärmeleitfähigkeit vom Feldwinkel zeigt unerwartet umfangreiche Oszillationsmuster. Während solche Oszillationen oft als Zeichen von Nullstellen in der Bandlücke interpretiert werden, konnten wir die meisten Frequenzen anderen Ursachen zuordnen. Eine sehr genaue Analyse von winkelabhängigen Messungen ist daher unabdingbar, um daraus Schlussfolgerungen für den Ordnungsparameter ziehen zu können.

Strongly correlated systems on geometrically frustrated lattices can stabilize a large number of interesting phases that includes a wide array of novel Mott insulators in both bosonic and electronic systems. Charge fluctuations in a Mott insulator are suppressed due to strong mutual interaction among the particles. The presence of frustration is of particular importance as the physics it offers is often rich, unexpectedly complicated, and continues to raise many open questions. The thesis elucidates some of these issues on a kagome lattice where strong interactions among the particles in the Mott phase impose non-trivial local constraints depending on the filling fraction on the lattice. These Mott insulators, in addition to featuring unusual magnetic and/or charge ordering, can also harbor topologically ordered states of quantum matter, e.g., resonating valence bond liquids realized in certain quantum dimer models on non-bipartite lattices. The dimer models can be regarded as low-energy effective theories for different types of bosonic models in the strong-coupling limit. Exploring this connection is a central theme of this thesis with the aim of realizing novel strongly correlated ground states. Past studies of these models have revealed the existence of various ordered and disordered phases with distinct signatures. Among these low-energy phases, the presence of a stable topological liquid at a particular point, known as Rokhsar-Kivelson point, in the phase diagram is notable. The classical versions of the dimer model are also known to have garnered a vast interest in various fields ranging from problems of pure mathematical origin to ones in physical chemistry as well as statistical physics. Pioneered by Kasteleyn, several analytical works came forward to exactly calculate the partition function of the problem from which other physical observables can be derived. Classical numerical methods are extensively applied to these models to verify the analytical predictions. We introduce a new classical algorithm here to compute the correlation functions of a classical dimer model on a square (bipartite) and a triangular (non-bipartite) lattice based on a tensor network construction. The method, called tensor network renormalization group, turns out to be a powerful tool for simulating short-ranged gapped systems as inferred from our results benchmarked against the classical Monte-Carlo technique and compared with past analytical studies. One should note that the quantum dimer model at the Rokhsar-Kivelson point can also be described as an infinite temperature canonical ensemble of classical dimers because of the particular structure of the ground state which is an equal weight superposition in the configuration manifold. The geometry of the lattice plays a pivotal role in deciding the nature of the phases that arise in the dimer models. Many physical properties of the dimer liquid phase can be extracted in the simple classical setting which certainly allows for a deep understanding of the classical models to be developed. The liquid phase is gapped on non-bipartite lattices and gapless on bipartite lattices, which is reflected in the decay of correlation functions with spatial distances. In general on non-bipartite lattices, the topological nature of the dimer liquid is characterized by a Z2 topological order which survives even when the model is perturbed away from the Rokhsar-Kivelson point. Stability of this liquid phase not only depends on the lattice geometries but notably on dimer concentrations also. In this context, we focus on a particular variant of the dimer model on a triangular lattice which is known as the quantum fully packed loop model. The model is composed of nonintersecting closed loops made of dimers and governed by the same Hamiltonian as the quantum dimer model. The loop model provides an effective low-energy description of a strongly correlated bosonic system at 1/3 filling on the kagome lattice. The corresponding Bose-Hubbard Hamiltonian consists of nearest-neighbor hopping and all possible repulsive interactions within a hexagonal plaquette. Conspicuous features of the zero-temperature phase diagram for this model include (i) presence of a stable Z2 liquid even without any Rokhsar-Kivelson potential term (in distinction to the standard quantum dimer model), and (ii) an unconventional phase transition from the liquid phase to a novel crystalline phase that has nematic order (dubbed lattice nematic). For a deeper understanding of the physics, a mapping to an Ising gauge theory is presented. The gauge theoretic description provides a useful way to predict the nature of the quantum phase transition to lie in the O(3) universality class. Finally a fermionic model at the same 1/3 filling is considered in which the ground state exhibits a number of exotic local orderings resulting from the spin-charge interplay of electrons. The Hamiltonian comprises nearest-neighbor hopping, strong on-site Coulomb interaction, and repulsive interaction terms only between nearest-neighbors. In the strong correlation limit, this fermionic problem maps to a two-color fully packed loop model – a model in which the loop segments carry an additional quantum number as color on a honeycomb lattice. The effective theory is governed by coherent three-particle ring exchanges and nearest-neighbor antiferromagnetic spin exchanges. The competition between these two leads to a phase diagram composed of a novel plaquette ordered state (known as the plaquette phase) that undergoes phase transition to a new kind of charge ordered state which we call a short loop phase. From our numerical analysis, we conclude that the plaquette phase features an unusual antiferromagnetic order with gapless spin excitations while the charge-ordered state is subjugated by spin fluctuations of localized electrons arranged in small hexagonal loops on the kagome lattice.

In this thesis, we summarize the material-specific theories of strongly correlated systems and apply them to selected materials. We describe and apply the corre- lated band theory methods: the local density approximation plus Coulomb U, and the density functional theory plus exact diagonalization of single impurity An- derson model. First, we investigate the systems containing impurity atoms: cobalt impurity located in the bulk copper and samarium, and neodymium adatoms on the surface of graphene. We present the spectral densities and study the magnetism of those compounds. Afterwards, we analyze three Np-based compounds: NpPt2In7, Np2Ni17 and NpBC. For all three compounds we analyze the spin, orbital and to- tal magnetic moments and the total density of states, as well as its projections for selected orbitals and spins. Moreover, for NpPt2In7 and NpBC we perform the to- tal energy analysis between different magnetic moment arrangements on the Np atoms.