Fermi surface, the locus in momentum space of gapless low-energy excitations, is a concept of fundamental importance in solid state physics. Electronic properties of a material are determined by the long-lived low-energy excitations near the Fermi surface. Conventionally, Fermi surface is understood as a property exclusive to a metallic state, contoured by electronic bands crossed by the Fermi level, although there has been a continuing effort in searching for Fermi surface outside the conventional description. In this thesis, techniques developed to prepare high-quality single crystals of SmB$_6$ and YBa$_2$Cu$_3$O$_{6+x}$ (abbreviated as YBCO$_{6+x}$ hereinafter) are described. By utilising measurement techniques of exceptional sensitivity and exploring a wide range of temperatures, magnetic fields, and electrical currents, we found signatures of unconventional Fermi surfaces beyond the traditional description in these strongly correlated electronic systems. SmB$_6$ is a classic example of Kondo insulators whose insulating behaviour arises due to strong correlation between the itinerant $d$-electrons and localised $f$-electrons. The peculiar resistivity plateau onsets below 4 K has been a decades-long puzzle whose origin has been recently proposed as the manifestation of topological conducting surface states. We found that the insulating behaviour in electrical transport is robust against magnetic fields up to 45 T, while prominent quantum oscillations in magnetisation are observed above 10 T. Angular dependence of the quantum oscillations revealed a three-dimensional characteristics with an absolute amplitude consistent with a bulk origin, and temperature dependence showed a surprising departure from the conventional Lifshitz-Kosevich formalism. Complementary thermodynamic measurements showed results consistent with a Fermi surface originating from neutral itinerant low-energy excitations at low temperatures. Theoretical proposals of the unconventional ground state uncovered by our measurements in SmB$_6$ are discussed. YBCO$_{6+x}$ is a high-temperature superconductor with a maximum $T_{\rm c}$ of 93.5 K and the cleanest member in the family of copper-oxide, or {\it cuprate}, superconductors. The correct description of electronic ground state in the enigmatic pseudogap regime, where the antinodal density of states are suppressed below a characteristic temperature $T^*$ above $T_{\rm c}$, has been a subject of active debates. While the quantum oscillations observed in underdoped YBCO$_{6+x}$ have been predominately interpreted as a property of the normal state where the superconducting parameter is completely suppressed at $\approx$ 23 T, we made the discovery that YBCO$_{6.55}$ exhibits zero resistivity up to 45 T when a low electrical current is used, consistent with the observation of a hysteresis loop in magnetisation. Quantum oscillations in the underdoped YBCO$_{6+x}$ are thus seen to coexist with $d$-wave superconductivity. Characteristics of the quantum oscillations are consistent with an isolated Fermi pocket reconstructed by a charge density wave order parameter and unaccompanied by significant background density of states, suggesting the antinodal density of states is completely gapped out by a strong order parameter involving pairing correlations, potentially in addition to the other order parameters. Transport measurements performed over a wide doping range show signatures consistent with pairing correlations that persist up to the pseudogap temperature $T^*$. The surprising observation of quantum oscillations in insulating SmB$_6$ and superconducting YBCO$_{6+x}$ demonstrates a possible new paradigm of a Fermi surface without a conventional Fermi liquid. A new theoretical framework outside the realm of Fermi liquid theory may be needed to discuss the physics in these strongly correlated materials with enticing electronic properties.

In this dissertation, we used a combination of synchrotron-based x-ray spectroscopic techniques such as angle-resolved photoelectron spectroscopy (ARPES), soft x-ray ARPES, hard x-ray photoelectron spectroscopy (HAXPES), and soft x-ray absorption spectroscopy (XAS) to investigate momentum-resolved and angle-integrated electronic structure of advanced three- and two-dimensional materials and interfaces. The results from the experiments were compared to several types of state-of-the-art first-principles theoretical calculations. In the first part of this dissertation we investigated the effects of spin excitons on the surface states of samarium hexaboride (SmB6), which has gained a lot of interest since it was proposed to be a candidate topological Kondo insulator. Here, we utilized high-resolution (overall resolution of approximately 3 meV) angle-resolved and angle-integrated valence-band photoemission measurements at cryogenic temperatures (1.2 K and 20 K) to show evidence for a V-shap / Physics

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