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Thesis advisor: Ziqiang Wang / One of the most unconventional electronic states in high transition temperature cuprate superconductors is the pseudogap state. In the temperature versus doping phase diagram, the pseudogap state straddles across the antiferromagnetic (AF) state near half filling and the superconducting (SC) dome on the hole doped side above the transition temperature Tc. The relationship between the pseudogap state and these two well known states - the AF state and the SC state is believed to be very important for understanding superconductivity and the emergent quantum electronic matter in doped Mott insulators. The pseudogap is characterized by the emergence of a soft gap in the single-particle excitation spectrum in the normal state in the temperature range between Tc and a characteristic temperature T*, i.e. Tc < T < T*. The most puzzling feature of the pseudogap is the nodal-antinodal dichotomy. Observed by ARPES in momentum space, the Fermi surface is gapped out in the antinodal region leaving a Fermi arc of gapless excitations near the nodes. Whether the pseudogap is an incoherent superconducting gap (onegap scenario) or it is a different gap governed by other mechanisms, other than superconductivity, (two-gap scenario) is still under debate. In this thesis I study the particle-particle channel and the particle-hole channel of the valence bond fluctuations away from half filling. Based on a strong-coupling analysis of the t-J model, I argue that the superexchange interaction J induced incommensurate bond centered density wave order is the driving mechanism for the pseudogap state. Low energy density of states (DOS) are eliminated by multiple incommensurate scatterings in the antinodal region at the Fermi level. I show that the interplay between the incommensurate bond centered d-wave density wave instability and the intrinsic electronic inhomogeneity in real cuprate materials is responsible for the observed pseudogap phenomena. Utilizing the spatially unrestricted Gutzwiller approximation, I show that the off-stoichiometric doping induced electrostatic disorder pins the low-energy d-wave bond density fluctuations, resulting in a VBG phase. The antinodal Fermi surface (FS) sections are gapped out, giving rise to a genuine normal state Fermi arc. The length of the Fermi arc shrinks with underdoping below the temperature T* determined by thermal filling of the antinodal pseudogap. Below Tc, the d-wave superconducting gap due to singlet pairing coexists and competes with the VBG pseudogap. The spatial, momentum, temperature and doping dependence of these two gaps are consistent with recent ARPES and STM observations in underdoped and chemically substituted cuprates. The temperature versus doping phase diagram captures the salient properties of the pseudogap phenomena and provides theoretical support for the two-gap scenario. In addition to resolving the complexities of the quantum electronic states in hole-doped cuprates, my unified theory elucidates the important role of the interplay between the strong electronic correlation and the intrinsic electronic disorder in doped transition metal oxides. / Thesis (PhD) — Boston College, 2011. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

Thesis advisor: Vidya Madhavan / <p>It has been more than two decades since the first high temperature superconductor was discovered. In this time there has been tremendous progress in understanding these materials both theoretically and experimentally. Some important questions however remain to be answered; one of them is the temperature dependence of the superconducting gap which is in turn tied to question of the origin of the pseudogap and its connection with superconductivity.</p> <p> In this thesis, we present detailed Scanning Tunneling Microscopy (STM) spectroscopic studies of an electron doped superconductor, Pr<subscript>0.88</subscript>LaCe<subscript>0.12</subscript>CuO<subscript>4-&#948;</subscript> (PLCCO). The electron doped compounds form an interesting venue for STM studies for many reasons. In the hole-doped materials, especially in the underdoped side of the phase diagram, there is mounting evidence of a second gap that survives to high temperatures (high temperature pseudogap) that may have a different origin from superconductivity. This complicates studies of the temperature dependence of the superconducting gap in these materials. In PLCCO however, there is little evidence for a high temperature pseudogap potentially allowing us to address the question of the temperature evolution of the superconducting gap without the complication of a second gap. Secondly, the low T<subscript>c</subscript> of the optimally doped materials makes it easily accessible to temperature dependent STM studies. Finally, while hole-doped materials have been extensively studied by scanning tunneling microscopy (STM), there have been no detailed STM spectroscopic studies on the electron doped compounds. </p> <p> In the first part of the thesis, we investigate the effect of temperature on the superconducting gap of optimally doped PLCCO with T<subscript>c</subscript> = 24K. STM spectroscopy data is analyzed to obtain the gap as a function of temperature from 5K to 35K. The gap is parameterized with a d-wave form and the STM spectra are fit at each temperature to extract the gap value. A plot of this gap value as a function of temperature shows clear deviations from what is expected from BCS theory. We find that similar to the hole-doped superconductors a fraction of the surface still shows a gap above T<subscript>c</subscript>. The implications of our finding to the pseudogap phase are discussed.</p> <p> In the second part of the thesis, STM spectra are analyzed to determine the effect of impurities or vacancies on the local density of states. Electron doped superconductors require a post-annealing process to induce superconductivity. It is claimed that Cu vacancies in the CuO<subscript>2</subscript> planes which suppress superconductivity are healed by this process. This implies that for the same doping, a sample with higher T<subscript>c</subscript> should have fewer impurities compared to a sample with lower T<subscript>c</subscript>. We studied two PLCCO samples with 12% Ce doping; one with higher T<subscript>c</subscript> (24K) and the other with lower T<subscript>c</subscript> (21K). Through quasiparticle scattering study we find that there are more impurities in 21K samples than 24K sample, consistent with the picture of Cu vacancies in as grown samples. Finally, we present a discussion of the bosonic modes observed in the STM spectra and their connection to the spin excitations measured by neutron scattering.</p> / Thesis (PhD) — Boston College, 2009. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

Os supercondutores de alta temperatura crítica apresentam propriedades diferentes dos supercondutores convencionais, uma destas propriedades importantes é a simetria não isotrópica do parâmetro de ordem. Neste trabalho se apresenta um modelo que mostra a presença de simetria d-wave em uma classe de supercondutores de alta Tc, assim como a condição para a existência de ondas de densidade nos estados de equilíbrio. Se analisa primeiro um sistema de três corpos, um bipolaron e dois elétrons, com o objetivo de estudar o efeito da repulsão coulombiana local e não local sobre a simetria do parâmetro de ordem para o caso exato e também o limite de acoplamento forte. Se mostra também a construção de um Hamiltoniano efetivo que desacopla a interação el etron-bipolaron com o fim de abordar o problema coletivo de infinitos corpos e vemos como o modelo proposto prediz a formação de ondas de densidade para uma região especifica dos parâmetros físicos do Hamiltoniano estudado. / High-temperature superconductors have different properties than conventional superconductors, one of these important properties is non-isotropic symmetry of the order parameter. In this work we present a model that shows the presence of symmetry d-wave in a class of superconductors of high Tc , as well as the condition for the existence of density waves in the states of equilibrium. We first analyze a three-body system, a bipolaron and two electrons, in order to study the effect of local and non-local Coulomb repulsion on the symmetry of the order parameter for the exact case and also the strong coupling limit. It is also shown the construction of an effective Hamiltonian that decouples the electron-bipolaron interaction in order to approach the collective problem of infinite bodies and we see how the proposed model predicts the formation of density waves for a specific region of the physical parameters of the studied Hamiltonian.

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.

We carried out systematic neutron scattering experiments to investigate the magnetic properties and their relationship to the high-$T_c$ superconductivity, when the materials are tuned from their antiferromagnetic (AF) parent compounds to the superconducting regime. We observed resonance mode in the electron doped cuprate Nd$_{1.85}$Ce$_{0.15}$CuO$_4$, demonstrating that the resonance is a general phenomenon in cuprate superconductors regardless of hole- or electron-doping. In Pr$_{0.88}$LaCe$_{0.12}$CuO$_4$, the local susceptibility displays two distinct energy scales that are broadly consistent with the bosonic modes revealed by scanning tunneling microscopy experiments. These results indicate the presence of very strong electron spin excitations couplings in electron doped cuprates. Shortly after the discovery of high-$T_c$ superconductivity in the Fe pnictides, we discovered that the magnetic phase diagram of CeFeAsO$_{1-x}$F$_x$ is remarkably similar to that of the cuprates. Besides CeFeAsO, similar magnetic and lattice structures are also observed in PrFeAsO and SrFe$_2$As$_2$ systems. Neutron scattering measurements show that in SrFe$_2$As$_2$, the spectrum of magnetic excitations consists of a Bragg peak at the elastic position, a spin gap, and sharp spin-wave excitations at higher energies. Based on the observed dispersion relation, we estimated the effective magnetic exchange coupling using a Heisenberg model. In order to study the nature of the exchange interactions in the parent compound of Fe pnictides, we studied the high energy spin-wave excitations in CaFe$_2$As$_2$. Although the spin waves in the entire Brillouin zone can be described by an effective three-dimensional anisotropic Heisenberg Hamiltonian, the magnetism in this system is neither purely local nor purely itinerant; rather it is a complicated mix of the two. When the Fe pnictide is tuned into superconducting regime with doping, the low energy spin fluctuation is dominated by a resonance mode. In the optimally electron doped BaFe$_{1.9}$Ni$_{0.1}$As$_2$, application of a magnetic field that suppresses the superconductivity and superconducting gap energy also reduces the intensity and energy of the resonance. These results suggest that the energy of the resonance is proportional to the electron pairing energy, and thus indicate that spin fluctuations are intimately related to the mechanism of high $T_c$ superconductivity.

The stoichiometry of the Nd_1+xBa_2-xCu₃O_7-δ solid solution has been investigated using XRD and EPMA. At 980°C in air, an essentially continuous solid solution forms with limiting compositions x_min = 0.03(1) and x_max = 0.92(2). The solid solution limits are independent of temperature over the range 300 to 1050°C, i.e. stoichiometric Nd123 does not form. Preliminary studies show that annealing in an Ar atmosphere does not affect x_min. Three structurally distinct polymorphs of Nd123ss exist - tetragonal Nd123ss, orthorhombic Nd123ss and orthorhombic Nd123ss. The stability range of each in air has been determined. Quenched samples with 0.03 ≤ x ≤ 0.6 have the tetragonal Nd123ss structure. On oxygenation, samples with 0.03 ≤ x <˜0.2 are orthorhombic. The orthorhombic-tetragonal phase transition is second order, both with increasing temperature and increasing x. Samples with 0.7-0.9 have the orthorhombic Nd213ss structure at all oxygen contents. Tetragonal Nd123ss is isostructural with tetragonal Y123 and orthorhombic Nd123ss is isostructural with orthorhombic Y123. Orthorhombic Nd213ss has the ideal stoichiometry Nd₂BaCu₃O_7-δ and is based on a 2a x b x 2c superstructure of the Nd123ss structure. The supercell is due to ordering of the Nd and Ba atoms, which leads to ordering of the oxygen atoms. Melting temperatures decrease with x. Two distinct regions of melting behaviour are observed; the first for 0.03 ≤ x ≤ 0.6 with a thermal minimum at x˜0.4, and the second for 0.7 ≤ x ≤ 0.9. Oxygen contents increase with x. Samples with larger x values have a smaller range of oxygen contents. High pressure oxygen annealing results in a constant Cu valence state of ˜2.35 for all values of x. Average copper valence states <2 are only obtained readily for x ≤ 0.3. T_c decreases with x and samples become non-superconducting at x˜0.5. For samples annealed in 1 bar O₂, 'double plateau' behaviour is observed.

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