Over the past 20 years a great deal of progress has been made towards understanding the physics of the high-temperature (high-Tc) cuprate superconductors. Much of the low- energy physics of these materials appears to be captured by two-dimensional Hubbard or t-J models which have provided significant insight into a number of properties such as the pseudogap, antiferromagnetism and superconductivity itself. However, intrinsically planar models are unable to account for the large variations in Tc observed across materials nor do they capture the electron-phonon (el-ph) interaction, the importance of which a number of experimental probes now indicate. This thesis examines the el-ph interaction in cuprates using a combination of analytical and numerical techniques. Starting from the microscopic mechanism for coupling to in-plane and c-axis polarized oxygen phonons, the theory of el-ph coupling is presented. The el-ph self-energy is derived in the context of Migdal-Eliashberg theory and then applied to understanding the detailed temperature and doping dependence of the renormalizations observed by Angle-resolved photoemission spectroscopy. The qualitative signatures of el- boson coupling in the density of states of a d-wave superconductor are also examined on general grounds and a model calculation is presented for el-ph coupling signatures in the density of states. Following this, the theory is extended to include the effects of screening and the consequences of this theory are explored. Due to the quasi-2D nature of the cuprates, screening is found to anomalously enhance the el-ph contribution to d-wave pairing. This result is then considered in light of the material and doping dependence of Tc and a framework for understanding the materials variations in Tc is presented. From these studies, a detailed picture of the role of the el-ph interaction in the doped cuprates emerges where the interaction, working in conjunction with a dominant pairing interaction, provides much of the materials variations in Tc observed across the cuprate families. Turning towards numerical techniques, small cluster calculations are presented which examine the effects of a local oxygen dopant in an otherwise ideal Bi2Sr2CaCu2O8+δ crystal. Here, it is demonstrated that the dopant locally enhances electronic properties such as the antiferromagnetic exchange energy J via local el-ph coupling to planar local oxygen vibrations. Finally, in an effort to extend the scope of this work to the underdoped region of the phase diagram, an examination of the properties of the single-band Hubbard and Hubbard-Holstein model is carried out using Determinant Quantum Monte Carlo. Here focus is placed on the spectral properties of the model as well as the competition between the the antiferromagnetic and charge-density-wave orders. As with the small cluster calculations, a strong interplay between the magnetic and lattice properties is observed.

Diese Arbeit befasst sich mit der Charakterisierung einer verhältnismäßig wenig beforschten Untergruppe der hochtemperatur-supraleitenden Kuprate (HTSCs-high-temperature superconducting cuprates), den elektronendotierten HTSCs, vermittels kernmagnetischer Resonanz (NMR-nuclear magnetic resonance). Die Untersuchungen umfassen 63Cu und 17O NMR an ausgerichteten Pulverproben und Einkristallen von Pr2−xCexCuO4 (x = 0, 0.05, 0.10, 0.15, 0.20) sowie auch Nd2−xCexCuO4 (x = 0, 0.13) in externen Magnetfeldern von 2.35 bis 17.6 T und Temperaturen zwischen 8 und 400 K. Durch eine Vielzahl von Experimenten wird die erste eindeutige spektrale Analyse für beide Nuklide vorgenommen. Es wird gezeigt, dass die indirekte, homonukleare Kopplung, wie sie beim Hahn-Echo-Zerfall von planarem 63,65Cu in lochdotierten HTSCs und auch im undotierten Pr2CuO4 gefunden wird, durch Elektronendotierung weitestgehend unterdrückt wird. Eine Analyse der Quadrupolaufspaltungen zeigt, dass nicht nur die lokale Verteilung der dotierten Elektronen und Löcher in den CuO2-Schichten quantitativ gemessen werden kann, sondern, dass auch Unterschiede in den 63Cu und 17O Aufspaltungen verschiedener undotierter Kuprate auf eine variable Ladungsverteilung zurückzuführen sind. Somit ist eine quantitative Messung der lokalen Ladungsverteilung in der CuO2 -Schicht der HTSCs möglich, welche ein neues, differenziertes Bild der unterschiedlichen Materialien ergibt.

High-quality platelet single crystals of Tl₂Ba₂CuO₆±δ (Tl-2201) have been grown using a novel time-varying encapsulation scheme, minimizing the thallium oxide loss that has plagued other attempts and reducing cation substitution. This encapsulation scheme allows the melt to be decanted from the crystals, a step previously impossible, and the remaining cation substitution is homogenized via a high-temperature anneal. Oxygen annealing schemes were developed to produce sharp superconducting transitions from 5 to 85 K without damaging the crystals. The crystals' high homogeneity and high degree of crystalline perfection are further evidenced by narrow rocking curves; the crystals are comparable to YSZ-grown YBa₂Cu₃O₆₊δ by both metrics. Electron probe microanalysis (EPMA) ascertained the crystals' composition to be Tl₁.₉₂₀₍₂₎Ba₁.₉₆₍₂₎Cu₁.₀₈₀₍₂₎O₆₊δ; X-ray diffraction found the composition of a Tc = 75 K crystal to be Tl₁.₉₁₄₍₁₄₎Ba₂Cu₁.₀₈₆₍₁₄₎O₆.₀₇₍₅₎, in excellent agreement. X-ray refinement of the crystal structure found the crystals orthorhombic at most dopings, and their structure to be in general agreement with previous powder data. Cation-substituted Tl-2201 can be orthorhombic, orthorhombic crystals can be prepared, and these superconduct, all new results. X-ray diffraction also found evidence of an as yet unidentified commensurate superlattice modulation. The Tl-2201 crystals' electronic structure were studied by X-ray absorption and emission spectroscopies (XAS/XES). The Zhang-Rice singlet band gains less intensity on overdoping than expected, suggesting a breakdown of the Zhang-Rice singlet approximation, and one thallium oxide band does not disperse as expected. The spectra correspond very closely with LDA band structure calculations, and do not exhibit the upper Hubbard bands arising from strong correlations seen in other cuprates. The spectra are noteworthy for their unprecedented (in the high-Tc cuprates) simplicity. The startling degree to which the electronic structure can be explained bodes well for future research in the cuprates. The overdoped cuprates, and Tl-2201 in particular, may offer a unique opportunity for understanding in an otherwise highly confusing family of materials.

High-quality platelet single crystals of Tl₂Ba₂CuO₆±δ (Tl-2201) have been grown using a novel time-varying encapsulation scheme, minimizing the thallium oxide loss that has plagued other attempts and reducing cation substitution. This encapsulation scheme allows the melt to be decanted from the crystals, a step previously impossible, and the remaining cation substitution is homogenized via a high-temperature anneal. Oxygen annealing schemes were developed to produce sharp superconducting transitions from 5 to 85 K without damaging the crystals. The crystals' high homogeneity and high degree of crystalline perfection are further evidenced by narrow rocking curves; the crystals are comparable to YSZ-grown YBa₂Cu₃O₆₊δ by both metrics. Electron probe microanalysis (EPMA) ascertained the crystals' composition to be Tl₁.₉₂₀₍₂₎Ba₁.₉₆₍₂₎Cu₁.₀₈₀₍₂₎O₆₊δ; X-ray diffraction found the composition of a Tc = 75 K crystal to be Tl₁.₉₁₄₍₁₄₎Ba₂Cu₁.₀₈₆₍₁₄₎O₆.₀₇₍₅₎, in excellent agreement. X-ray refinement of the crystal structure found the crystals orthorhombic at most dopings, and their structure to be in general agreement with previous powder data. Cation-substituted Tl-2201 can be orthorhombic, orthorhombic crystals can be prepared, and these superconduct, all new results. X-ray diffraction also found evidence of an as yet unidentified commensurate superlattice modulation. The Tl-2201 crystals' electronic structure were studied by X-ray absorption and emission spectroscopies (XAS/XES). The Zhang-Rice singlet band gains less intensity on overdoping than expected, suggesting a breakdown of the Zhang-Rice singlet approximation, and one thallium oxide band does not disperse as expected. The spectra correspond very closely with LDA band structure calculations, and do not exhibit the upper Hubbard bands arising from strong correlations seen in other cuprates. The spectra are noteworthy for their unprecedented (in the high-Tc cuprates) simplicity. The startling degree to which the electronic structure can be explained bodes well for future research in the cuprates. The overdoped cuprates, and Tl-2201 in particular, may offer a unique opportunity for understanding in an otherwise highly confusing family of materials. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

Diese Arbeit befasst sich mit der Charakterisierung einer verhältnismäßig wenig beforschten Untergruppe der hochtemperatur-supraleitenden Kuprate (HTSCs-high-temperature superconducting cuprates), den elektronendotierten HTSCs, vermittels kernmagnetischer Resonanz (NMR-nuclear magnetic resonance). Die Untersuchungen umfassen 63Cu und 17O NMR an ausgerichteten Pulverproben und Einkristallen von Pr2−xCexCuO4 (x = 0, 0.05, 0.10, 0.15, 0.20) sowie auch Nd2−xCexCuO4 (x = 0, 0.13) in externen Magnetfeldern von 2.35 bis 17.6 T und Temperaturen zwischen 8 und 400 K. Durch eine Vielzahl von Experimenten wird die erste eindeutige spektrale Analyse für beide Nuklide vorgenommen. Es wird gezeigt, dass die indirekte, homonukleare Kopplung, wie sie beim Hahn-Echo-Zerfall von planarem 63,65Cu in lochdotierten HTSCs und auch im undotierten Pr2CuO4 gefunden wird, durch Elektronendotierung weitestgehend unterdrückt wird. Eine Analyse der Quadrupolaufspaltungen zeigt, dass nicht nur die lokale Verteilung der dotierten Elektronen und Löcher in den CuO2-Schichten quantitativ gemessen werden kann, sondern, dass auch Unterschiede in den 63Cu und 17O Aufspaltungen verschiedener undotierter Kuprate auf eine variable Ladungsverteilung zurückzuführen sind. Somit ist eine quantitative Messung der lokalen Ladungsverteilung in der CuO2 -Schicht der HTSCs möglich, welche ein neues, differenziertes Bild der unterschiedlichen Materialien ergibt.

Diese Arbeit befasst sich mit der Charakterisierung der Ladungssymmetrie in der CuO2 Ebene in den hochtemperatur-supraleitenden Kupraten (HTSCs - high-temperature superconducting cuprates). Hierfür wurden Experimente mit kernmagnetischer Resonance (NMR - nuclear magnetic resonance) an Einkristallen von YBa2Cu3O7 und YBa2Cu3O6.9 sowie an Pulverproben von YBa2Cu4O8 durchgeführt. Der Fokus der Arbeit lag auf der Untersuchung des elektrischen Feldgradientens (EFG) der CuO2 Ebene unter hohem Druck und unterschiedlichen Temperaturen. Neben dem Cu Kern wurde für die Hochdruck-NMR-Untersuchung zum ersten Mal auch der O Kern der CuO2 Ebene verwendet und für beide Kerne die Druckabhängigkeit des vollständigen EFG Tensors bestimmt. Zusätzlich wurde die Magnetfeldabhängigkeit des EFG untersucht. Ein Schwerpunkt der Arbeit lag in der Vorbereitung der NMR Druckzelle für Einkristallmessungen sowie deren Ausrichtung im Magnetfeld. Es konnte gezeigt werden, dass die örtliche Variation des Cu EFG Tensors in allen untersuchten HTSCs stark mit Druck zunimmt und ähnlich groß ist, wie die Variation des EFG durch chemisch induzierte Unordnung. Durch die Analyse der Cu und O NMR Spektren in YBa2Cu3O6.9 konnte gezeigt werden, dass der EFG der CuO2 Ebene nicht direkt durch die orthorhombische Kristallstruktur beeinflusst wird - so wie lange angenommen wurde - sondern durch eine geordnete Ladungsvariation am O erklärt werden muss. Druck und tiefe Temperaturen erhöhen die Ladungsordnung. Es konnte eine eindeutige, lokale Ladungssymmetrie und Amplitude bei 18 kbar und 100 K bestimmt werden, die quantitativ mit den Cu und O Spektren übereinstimmt. Die NMR Daten sind mit einer langreichweitigen Ladungsdichtewelle konsistent. Zusätzlich wurde herausgefunden, dass das Magnetfeld sowohl die Variation als auch die Orientierung des planaren Cu EFG beeinflusst. Mit der Arbeit konnte gezeigt werden, dass Ladungsordnung in Y-basierten HTSCs nahe der Dotierung mit der höchsten kritischen Temperatur (Tc) existiert und sie durch Druck, Variation der Temperatur sowie Magnetfelder beeinflusst werden kann.

In spite of the failures to find an ultimate theory of unconventional superconductivity, after many years of research the scientific community possesses a considerable store of theoretical knowledge about the problem. Over time, the focus is gradually shifted from finding a theoretical description of an experimentally observed phenomenon to distinguishing between multiple models that offer comparably reasonable descriptions. From the point of view of an experimentalist, this means that any qualitative under-standing of an experimental observation would no longer suffice. Instead, the empha-sis in the experimental research should be shifted to accurate quantification of obser-vations, which becomes possible only if the results available from all the available ex-perimental methods are connected together by the theoretical glue. Among the meth-ods that are to be unified, ARPES plays a central role. The reason for this is that it gives access to the single-particle excitation spectrum of the material as a function of both momentum and energy with very high resolution. Other experimental techniques, such as inelastic neutron scattering (INS), Raman spectroscopy, or the newly estab-lished Fourier-transform scanning tunneling spectroscopy (FT-STS) probe more com-plicated two-particle spectra of the electrons and up to now can not achieve the mo-mentum resolution comparable with that of ARPES. Such reasoning serves as the mo-tivation for the present work, in which some steps are done towards understanding the anomalous effects observed in the single-particle excitation spectra of cuprates and relating the ARPES technique to other experimental methods. First, the electronic properties of BSCCO are considered — the superconducting cuprate most studied by surface-sensitive methods. The recent progress in un-derstanding the electronic structure of this material is reported, focusing mainly on the many-body effects (renormalization) and their manifestation in the ARPES spectra. The main result of this part of the work is a model of the Green’s function that is later used for calculating the two-particle excitation spectrum. Then, the matrix element effects in the photoemission spectra of cuprates are discussed. After a general introduction to the problem, the thesis focuses on the recently discovered anomalous behavior of the ARPES spectra that partially originates from the momentum-dependent photoemission matrix element. The momentum- and excitation energy dependence of the anomalous high-energy dispersion, termed “waterfalls”, is covered in full detail. Understanding the role of the matrix element effects in this phenomenon proves crucial, as they obstruct the view of the underlying excitation spectrum that is of indisputable interest. Finally, the work describes the relation of ARPES with other experimental methods, with the special focus on the INS spectroscopy. For the optimally doped bilayer Bi-based cuprate, the renormalized two-particle correlation function in the superconducting state is calculated from ARPES data within an itinerant model based on the random phase approximation (RPA). The results are compared with the experimental INS data on BSCCO and YBCO. The calculation is based on numerical models for the normal and anomalous Green’s functions fitted to the experimental single-particle spectra. The renormalization is taken into account both in the single-particle Green’s function by means of the self-energy, and in the two-particle correlation function by RPA. Additionally, two other applications of the same approach are briefly sketched: the relation of ARPES to FT-STS, and the nesting properties of Fermi surfaces in two-dimensional charge density wave systems.

No description available.

<p>In this thesis, we investigate the properties of a model of an anti-phase modulated d-wave superconductor, particularly in the presence of a magnetic field. This so-called model of $\pi$-striped superconductor has been proposed to describe the decoupling between Cu-O planes in $1/8$ doped La$_{2-x}$Ba$_{x}$CuO$_{4}$. The d-wave superconducting order parameter in a $\pi$-striped superconductor oscillates spatially with period 8 and zero average value. Unlike a uniform d-wave superconductor, this model has non-zero density of states at zero energy and exhibits an extended Fermi surface. Within Bogoliubov-de Gennes theory, we study the mixed state of this model and compare it to the case of a uniform d-wave superconductor. We find a periodic structure of the low-energy density of states, with a period that is proportional to $B$, corresponding to Landau levels that are a coherent mixture of particles and holes. These results are also discussed in the context of experiments which observe quantum oscillations in the cuprates.</p> <p>Furthermore, within Bogoliubov-de Gennes theory, a semiclassical approximation is used to study quantum oscillations and to determine the Fermi surface area associated with these oscillations in this model. The Fermi surface is reconstructed via Andreev-Bragg scattering, and the semiclassical motion is along these Fermi surface sections as well as between them via magnetic breakdown. Oscillations periodic in 1/B are found in both the positions and widths of the lowest Landau levels. The area corresponding to these quantum oscillations for intermediate pairing interaction is similar to that reported for experimental measurements in the cuprates. A comparison is made of this theory to data for quantum oscillations in the specific heat measured by Riggs et al.</p> / Doctor of Philosophy (PhD)

Ce mémoire traite des propriétés du La2CuO4 dopé en trous, le premier supraconducteur à haute température critique ayant été découvert. Les différentes phases électroniques du cristal y seront présentées, ainsi que le diagramme de phases en dopage de ce matériau. Les trois structures dans lesquelles on peut retrouver ce cristal seront décrites en détail, et leurs liens présumés avec les phases électroniques seront présentés. Il s’en suivra une étude utilisant la théorie de la fonctionnelle de la densité combinée au modèle de Hubbard (DFT+U) des différentes phases structurales, en plus des phases antiferromagnétiques et paramagnétiques. L’effet de la corrélation électronique sur la structure cristalline sera également étudié par l’intermédiaire du paramètre de Hubbard. Le but sera de vérifier si la DFT+U reproduit bien le diagramme de phases expérimentales, et sous quelles conditions. Une étude des effets de l’inclinaison des octaèdres d’oxygène sur la structure électronique sera également présentée. / Presented here is a study on the hole doped La2CuO4, the first discovered high-­‐Tc superconductor of the cuprate family. The different electronic phases of this crystal are briefly reviewed. The three crystal structures present in this material are described, and the link between those phases and the electronic structure are discussed. The relationship of those structural phases with the magnetic phases is investigated with the help of calculations based on the density functional theory where an additional Hubbard term has been added (DFT+U). With the help of the Hubbard parameter, the effect of the electronic correlation’s strength on the structural parameters of the crystal is also studied. The idea here is to verify how well the DFT+U is able to reproduce the experimental phase diagram of this material. The effect of the tilting of the oxygen octahedras on the electronic structure is also addressed.