This work focuses principally on two compounds, CeCu_1-xOS and LiFeAs, which have related layered structures but exhibit radically different physical properties. The nature of the air sensitivity of the ZrCuSiAs-type oxysulfide CeCu_1-xOS has been investigated by neutron diffraction and magnetometry. It was found that this compound can be made fully stoichiometric, with structural and magnetic properties that are consistent with other LnCuOS compounds, indicating that this is a bona-fide Ce³⁺ compound. Upon air exposure, Cu ions are extruded from the sulfide layer to leave a Cu-deficient phase with contracted unit cell parameters and a diminished paramagnetic moment consistent with mixed-valence Ce^3+/4+.The extruded Cu forms CuO and can be re-inserted into the sulfide layer by heating under a reducing atmosphere. This explains the anomalous behaviour of CeCuOS reported throughout the literature and has implications for the behaviour of other layered Cu-sulfides with oxidisable cations. At low temperatures Cu-deficient CeCu_0.8OS was found to exhibit structural ordering of Cu⁺ ions and vacancies, resulting in a √5a x √5a basal expansion of the high-temperature unit cell. The layered iron arsenide LiFeAs was synthesised and found to be superconducting below 17 K. Joint XRD/NPD measurements showed unambiguously that the compound adopts the anti-PbFCl structure with Li ions in a square-pyramidal LiAs5 environment. No evidence was found for an orthorhombic structural distortion at low temperatures. Further diffraction experiments showed that the compound can be made with non-stoichiometric compositions Li_1-yFe_1-y for small values of y (<0.05), as Fe can be accommodated on the Li site. This type of non-stoichiometry was found to strongly inhibit superconductivity (which was quenched entirely when y>0.02). Three series of compounds of type LiFe_1-xM_xAs (M = Mn, Co, Ni) were synthesised and characterised struturally bu high-resolution XRD and/or NPD. Substitution by Co and Ni was found to cause a monotonic decrease in T_c, and Ni was found to be twice as effective at suppressing T_c as Co. MuSR measurements showed the penetration depth increasing with Co and Ni substitution, consisitent with the superconducting state becoming less robust. Substitution by Mn was found to strongly inhibit superconductivity, and this behaviour is reminiscent of the non-stoichiometric Li_1-yFe_1-yAs materials. The structures and superconducting properties of LiFeAs and NaFeAs were studied under high pressures. Equations of state were obtained for each compound. Hydrostatic pressure was found to distort of the FeAs₄ away from ideal tetrahedral geometry in both compounds. These changes caused a monotonic decrease in T_c in LiFeAs, but has a smaller and more complex effect on the T_c of NaFeAs. Furthermore, NaFeAs was found to undergo a structural transition above P = 22 GPa, but the high-pressure structure could not be solved and this will become a target for future work.

In this thesis, intrinsic Josephson junctions, naturally formed in the strongly anisotropic high-temperature superconductor Bi2Sr2CaCu2O8 (Bi-2212), are studied experimentally. For this purpose, small mesa structures are fabricated on the surface of single crystals using micro- and nano-fabrication tools, focused ion beam is used to reduce the area of the mesa-structures down to ≈ 1 × 1 μm2. The properties of charge transport across copper-oxide layers inside the mesas are studied by intrinsic tunneling spectroscopy. Temperature, bias and magnetic field dependences of current-voltage characteristics are examined. In the main part of the thesis, the behavior of intrinsic Josephson junctions in magnetic fields B parallel to the copper-oxide planes is studied. Parallel magnetic fields penetrate the junctions in the form of Josephson vortices (fluxons). At high magnetic fields, fluxons are arranged in a regular lattice and are accelerated by a sufficient high transport current. As the fluxon lattice is moving through the mesa, it emits electromagnetic waves in the important THz frequency range. Properties of Bi-2212 mesas in this flux-flow regime are studied in this thesis. The following new observations were made during the course of this work: a crossover from thermal activation above Tc to quantum tunneling below Tc is seen in the interlayer transport-mechanism, the Fraunhofer pattern of Ic(B) is observed clearly in Bi-2212, superluminal electromagnetic cavity resonances and phonon-polaritons are observed in Bi-2212. It is argued that the employed technique for miniaturization of mesas and the obtained results can be useful for a better understanding of fundamental properties of high-temperature superconductors and for the realizations of coherent flux-flow oscillators and coherent phonon-polariton generators in the important THz frequency range. / At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 6: Manuscript.

Thesis (Ph. D.)--University of Washington, 1998. / Vita. Includes bibliographical references (p. [225]-236).

No description available.

<p>In this thesis, we present the results for the finite frequency response of a variety of materials. These materials all share the common theme that their low energy excitations are Dirac-like. This coincidence was not by design, and highlights the now-ubiquitous nature of Dirac-quasiparticles in condensed matter physics. We present results for graphene, the high temperature superconducting cuprates, and Weyl semi metals. For graphene, our calculations revolve around a new experimental technique: Near field infrared spectroscopy. Conventionally it is ok to use the $\vec{q}\rightarrow 0$ limit when calculating the low energy optical response. This new technique is able to directly probe the finite $\vec{q}$ response by using an atomic force microscope tip as an antenna. We computed the optical conductivity of graphene at finite wavevector and studied how the quasiparticle peak is altered by disorder and the electron-phonon interaction. The calculations on the high $T_c$ cuprates use a model of the pseudogap phase known as the Yang, Rice and Zhang (YRZ) model. We employed the model to study the resistivity in the pseudogap regime, both in-plane and along the c-axis. We used a coherent tunneling matrix element to describe transport along the c-axis. We found that the model was able to reproduce the metaliclike behavior in the plane while being resistive out of plane. We then extended the model to the finite frequency response, as well as the superconducting phase. We found a pseduogap feature at finite frequency that was previously explained through an interlayer collective mode. We also found that microwave spectroscopy puts strong limits on the form of the scattering rate. Finally, we computed the optical response of Weyl semimetals subjected to an applied magnetic field. Weyl semimetals are a topological phase of matter that have yet to be observed. The form of the conductivity contains a series of asymmetric peaks, whose spacing is a signature of the underlying relativistic dispersion. These peaks remain robust, even with moderate disorder.</p> / Doctor of Philosophy (PhD)

Condensed matter physics is a rapidly evolving field of research enriched with the synthesis of new materials exhibiting a bewildering variety of phenomena and advances in experimental techniques. Over the years, discoveries and innovations in electronic systems have emphasized the crucial role played by correlations among electrons behind many of the observed unusual properties and have posed serious challenges to the physics community by exposing the lack of well-controlled theoretical methods to study the class of materials known as strongly correlated electronic systems. In these systems, known theoretical techniques typically fail to capture the essential features of the many-body ground state and finite temperature properties of the systems as typical electronic interaction energies are of order of or larger than the kinetic energies. The study of strongly correlated electronic systems went through a revolution in the 1980s and 1990s after the discovery of superconductivity inorganic compounds, in heavy fermion systems and ultimately in copper oxides, referred to as cuprates, by Bednorz and Muller. In particular, the pursuit of understanding the mysterious origin of superconductivity in the cuprates and other associated strange phenomena has fascinated the condensed matter community over last two and half decades leading to most of the important unsolved, and probably interconnected, problems of quantum condensed matter physics such as the metal-insulator transition in low dimensions breakdown of Fermi liquid theory, the origin and behavior of unconventional superconductivity, quantum critical points, electronic in homogeneities and localization in interacting systems. This thesis is devoted to the study of some of the aspects of high-temperature superconductivity and associated phenomena in cuprates. In what follows, I give an overview of the organization of the thesis in to different chapters and their contents. For setting up the stage, in Chapter 1, I give a brief account of some of the remarkable phenomena and properties observed in strongly correlated electronic matter and their salient features, that continue to draw much attention and excitement in current times. The peculiarity of the state of affairs in these systems is emphasized and motivated in the background of the paradigmatic Landau Fermi liquid theory and Hubbard model, the minimal model that is expected to capture the quintessence of electronic strong correlation. In Chapter 2, starting with a brief historical account of the discovery of superconductivity in cuprates, the crystal structure of these materials, their chemical realities and basic electronic details are reviewed. This is followed by a survey of the phase diagram of cuprates, doped with, say, x number of holes per copper site, and a plethora of experimental findings that constitute the high-c puzzle. Characteristics of various observed phases, such as the superconducting, pseudo gap and strange metal phases, are discussed on the basis off acts accumulated through various experimental probes, e.g. nuclear magnetic resonance(NMR), neutron scattering, specific heat, transport and optical conductivity measurements as well as photo emission, tunnelling and Raman spectroscopies. As elucidated, these experiments point toward the need for an unconventional mechanism of superconductivity in cuprates and, more so, for the description of the rather abnormal high-temperature normal state that is realized above the superconducting transition temperature c. Keeping in mind the fact that there is no consensus even about the minimal microscopic electronic model, I review two models, namely the three band model and the t - J model; various approximate treatments of these models have dominated the theoretical developments in this field. A large number of theoretical pictures have been proposed based on different microscopic, semi-microscopic and phenomenological approaches in the past two decades for explaining the genesis of the observed strange phenomena in high-c cuprates. I include brief discussions on only a few of them while citing relevant references. As mentioned above, a variety of approximate microscopic theories, based on both strong and weak coupling approaches, as well as numerical techniques have been tried to understand the cuprate phase diagram and capture the aspects of strong correlations in-built in Hubbard and t -J models. On the other hand, in conventional superconductors and, in general, for the study of phase transitions, phenomenological Ginzburg-Landau(GL) functionals written down from very general symmetry grounds have provided useful description for a variety of systems. Specially, Ginzburg-Landau theory has been proven to be complementary to the BCS theory for attacking a plethora of situations in superconductors, e.g., in homogeneities, structures of an isolated vortex and the vortex lattice etc. The GL functional has found wide applicability for the study of vortex matter in high-c superconductors as well. Inspired by the success of this type of phenomenological route, we propose and develop in Chapter 3 an approach, analogous in spirit to that of Ginzburg and Landau, for the superconducting and pseudogap phases of cuprates. We encompass a large number of well known phenomenologies of cuprate superconductivity in the form of a low-energy effective lattice functional of complex spin-singlet pair amplitudes with magnitude Δm and phase m, i.e. m =Δm exp(i m), that resides on the Cu-Cubonds(indexed by m)of the CuO2 planes of cuprates. The functional respects general symmetry requirements, e.g. the -wave symmetry of the superconducting order parameter as found in experiments. The assumptions and the specific physical picture behind such an approach as well as the key empirical inputs that go into it are discussed in this chapter. We calculate the superconducting transition temperature c and the average magnitude of the local pair amplitude, Δ= (Δm), using single-site mean-field theory for the model. We show that this approximation leads to general features of the doping-temperature(x - T )phase diagram in agreement with experiment. In particular, we find a phase coherent superconducting state with d-wave symmetry below a parabolic Tc (x) dome and a phase incoherent state with a perceptible local gap that persists up to a temperature around which can be thought of as a measure of the pseudogap temperature scale T* . Further, effects of thermal fluctuations beyond the mean-field level are captured via Monte Carlo(MC) simulations of the model for a finite two-dimensional (2D) lattice. We exhibit results for Tc obtained from MC simulations as well as that estimated in a cluster mean field approximation. Based on our picture we remark on contrasting scenarios proposed for the doping dependence of the pseudogap temperature. Chapter 4 describes fluctuation phenomena related to pairing degrees of freedom and manifestations of these effects in various quantities of interest, e.g. superfluid density, specific heat etc., at finite temperature. Fluctuation effects have been studied in detail in superconductors over the years and pursued mainly using either the conventional GL functional or the BCS-framework at a microscopic level. However, the picture, in which the pseudogap phase is viewed as one consisting of bond-pairs with a d-wave symmetry correlation length growing as T approaches Tc, implies fluctuation phenomena of quite a different kind, as we discuss here. The contribution of the bond-pair degrees of freedom to thermal properties is obtained here from the lattice free-energy functional using MC simulation, as mentioned in the preceding paragraph. The results for the superfluid density or superfluid stiffness ps, a quantity measured e.g. via the penetration depth, are discussed. As shown, its doping and temperature dependence compare well with experimental results. In this chapter, I also report the calculation of the fluctuation specific heat Cv(T) and find that there are two peaks in its temperature dependence, a sharp one connected with Tc (ordering of the phase of m)and a relatively broad one(hump)connected to T* (rapid growth of the magnitude of Δm). The former is specially sensitive to the presence of a magnetic field, as we find in agreement with experiment. Vortices are relevant excitations in a superconductor and, in particular, in 2D orquasi-2D systems vortices influence the finite temperature properties in a major way. The results for the temperature dependence of vortex density obtained in the MC simulation of the GL-like model are also mentioned in Chapter 4. I report an estimate of the correlation length as well. These results might have relevance for the large Nernst signal observed over a broad temperature range above c in cuprates, as pointed out there. Properties of an isolated vortex and collective effects arising due to interaction between vortices are of much significance for understanding mixed state of type-II superconductors and thus of cuprates. The superconducting order is destroyed in the core region around the centre of a vortex and the vortex core carries signatures of the normal state in a temperature regime where it is generally unattainable due to occurrence of superconductivity. As mentioned in Chapter 5, vortex properties(e.g. electronic excitation spectrum at the vortex core) in BCS superconductors have been explored theoretically, at a microscopic level through the Bogoliubov-deGennes(BdG) theory as well as using the Ginzburg-Landau functional. However, properties of vortices in cuprate superconductors have been found to be much more unusual than could possibly be captured by straightforward extensions of BCS theory to a -wave symmetry case. Chapter 5 briefly reviews the experimental findings on vortices in the superconducting state of cuprates, mainly as probed by Scanning Tunnelling Microscopy(STM) as well as from other probes such as NMR, neutron scattering, SR etc. I discuss some of the consequences of our GL-like functional regarding vortex properties, namely that of the vortex core and the region around it. We use our model to find Δm and m at different sites m for a 2π vortex whose core is at the midpoint of a square plaquette of Cu lattice sites. The vortex is found to change character from being primarily a phase or Josephson vortex for small x to a more BCS-like or Abrikosov vortex with a large diminution in the magnitude Δm as one approaches the vortex core, for large . Here I do not make any direct comparison with experimental data but discuss implications of our results in the background of existing experimental facts. Unravelling the mysteries of high-Tc cuprates should necessarily involve the understanding of electronic excitations over a broad regime of doping and temperature encompassing the pseudo gap, superconducting and strange metal states. A phenomenological theory which aims to describe the pseudo gap phase as one consisting of preformed bond-pairs, is required to include both unpaired electrons and Cooper pairs of the same electrons coexisting and necessarily coupled with each other. In our Ginzburg Landau approach only the latter are explicit, while the former are integrated out. However, effects connected with the pair degrees of freedom are often investigated via their coupling to electrons, one very prominent examples being Angle Resolved Photoemmision Spectroscopy(ARPES),in which the momentum and energy spectrum of electrons ejected from the metal impinged by photons is investigated. In Chapter 6, we develop a unified theory of electronic excitations in the superconducting and pseudo gap phases using a model of electrons quantum mechanically coupled to spatially and temporally fluctuating Cooper pairs(the nearest neighbour singlet bond pairs). We discuss the theory and a number of its predictions which seem to be in good agreement with high resolution ARPES measurements, which have uncovered a number of unusual spectral properties of electrons near the Fermi energy with definite in-plane momenta. We show here that the spectral function of electrons with momentum ranging over the putative Fermi surface(recovered at high temperatures above the pseudogap temperature scale) is strongly affected by their coupling to Cooper pairs. On approaching Tc i.e. the temperature at which the Cooper pair phase stiffness becomes nonzero, the inevitable coupling of electrons with long-wavelength(d-wave symmetry) phase fluctuations leads to the observed characteristic low-energy behavior as reported in Chapter 6. Collective d-wave symmetry superconducting correlations develop among the pairs with a characteristic correlation length ξ which diverges on approaching the continuous transition temperature Tc from above. These correlations have a generic form for distances much larger than the lattice spacing. As we show here, the effect of these correlations on the electrons leads, for example, to a pseudogap in electronic density of states for T > T c persisting till T* , temperature-dependent Fermi arcs i.e. regions on the Fermi surface where the quasiparticle spectral density is non zero for a zero energy excitation and to the filling of the antinodal pseudogap in the manner observed. Further, the observed long-range order(LRO) below c leads to a sharp antinodal spectral feature related to the non zero superfluid density, and thermal pair fluctuations cause a deviation(‘bending’) of the inferred ‘gap’ as a function of k from the expected d-wave form (cos kxa - cos kya). The bending, being of thermal origin, decreases with decreasing temperature, in agreement with recent ARPES measurements. I conclude in Chapter 7 by mentioning some natural directions in which the functional and the approach used here could be taken forward. The phenomenological theory proposed and developed in this thesis reconciles and ties together a range of cuprate superconductivity phenomena qualitatively and confronts them quantitatively with experiment. The results, and their agreement with a large body of experimental findings, strongly support the mechanism based on nearest neighbor Cooper pairs, and emergence of long-range -wave symmetry order as a collective effect arising from short range interaction between these pairs. This probably points to the way in which high-c superconductivity will be understood.

This thesis describes the fabrication and characterization of ex situ magnesium diboride (MgB<sub>2<) bulk material to study its sintering behaviour. Since the discovery of superconductivity in magnesium diboride in 2001, many research studies have identified the attractive properties of this easy-to-fabricate, low cost superconductor which can attain high critical current density even without heat-treatment. However there is little consensus in the literature on the processing requirements to produce high quality MgB<sub>2< material with low impurity content and high density. In this work, the key parameters in the production of dense ex situ MgB<sub>2< produced from Alfa Aesar MgB<sub>2< powder are established by examining the effect of modifying the characteristics of the starting material and the processing parameters during pressureless and pressure assisted heat-treatment. The particle size distribution, impurity content and particle morphology of Alfa Aesar MgB<sub>2< powder were determined using laser dffraction, X-ray diffraction, X-ray photoelectron spectroscopy, electron dispersive spectroscopy, scanning electron microscopy and transmission electron microscopy. This powder was also modified by separation (sieving and sedimentation) and milling (ball milling and attrition milling), with changes made to the powder determined by the same techniques. A pressureless heat-treatment method using a magnesium diboride powder bed was developed. This minimised MgO formation in samples produced from as-purchased MgB<sub>2< powder to less than 8 wt.% for heat-treatment at 1100°C. MgO content was determined by X-ray diffraction using calibrated standards. MgB<sub>2< bulk material was produced from as-purchased and modified powders by pressureless heat-treatment under Ar gas, and characterized using Archimedes' density method, X-ray diffraction, Vickers hardness testing, scanning electron microscopy, and magnetization measurements. Very limited densification was observed for all samples prepared by pressureless heat-treatment, with only limited increases in connectivity observed for some samples heat-treated at 1100°C. Pressure-assisted bulk samples were prepared from as-purchased MgB<sub>2< and selected modified powders using resistive sintering, spark plasma sintering, and hot pressing. These were characterized using the same techniques, which indicated much more extensive densification with similar levels of impurity formation as for pressureless heat-treatment at 1100°C. The results indicate that densification and applied pressure are strongly correlated, while the effect of temperature is less significant. The optimum processing environment (inert gas or vacuum) was dependent on the technique used. These results indicate that pressure-assisted heat-treatment is required in order to produce dense bulk MgB<sub>2<.

The work described in this thesis uses oxygen NMR to probe the electronic system of rare earth co-doped La_{2-x}Sr_xCuO_4, the prototypical high temperature superconducting cuprate (HTSC). Oxygen NMR turns out to be a powerful tool for this purpose. The nucleus is located directly inside the CuO_2 planes. It has a spin of 5/2 and a quadrupole moment and therefore can probe both, interactions with the magnetic hyperfine field as well as interactions through the electric field gradient of the crystal. Furthermore, the spin lattice relaxation time T_1 and the spin spin relaxation time T_2 contain information about the dynamics of these interactions. Such a link between the spin and charge structures in high temperature superconductors has been elusive until today. Instead, there are magnetic probes such as neutron scattering and muSR that provide evidence for a modulation of the spin structure and static magnetic moments, respectively, and charge probes like STM that reveal inhomogeneous doping distributions in the CuO_2 planes. In either case, inhomogeneities in the spin and charge system seem to be typical for HTSCs. Whereas the spin and charge modulations are believed to be dynamic in the superconducting compounds, they become static at low temperatures in Eu doped La_{2-x}Sr_xCuO_4, where superconductivity is suppressed. As could be demonstrated here, evidence for such a spin and charge separation, that often revealed stunning similarities to the spin ladder compounds, is apparent in almost all measured NMR parameters. / In dieser Arbeit werden Sauerstoff NMR Untersuchungen der elektronischen Struktur von Selten-Erd dotiertem La_{2-x}Sr_xCuO_4, dem prototypischen Hochtemperatursupraleiter (HTSL), vorgestellt. Sauerstoff NMR ist zu diesem Zweck besonders gut geeignet. Der Kern befindet sich innerhalb der Kupferoxid-Ebenen. Er hat einen Spin von 5/2 und ein Quadrupolmoment. Damit lassen sich Wechselwirkungen mit dem magnetischen Hyperfeinfeld der Cu-Atome sowie Wechselwirkungen mit dem elektrischen Feldgradienten des Kristalls untersuchen. Des Weiteren geben die Spin-Gitter-Relaxationszeit T_1 sowie die Spin-Spin-Relaxationszeit T_2 Aufschluss über die Dynamik dieser beiden Wechselwirkungen. Eine Verbindung zwischen der Spin- und Ladungsordnung gibt es in den HTSL bisher nicht. Statt dessen haben magnetische Messmethoden wie Neutronenstreuung oder muSR Aussagen über die magnetische Ordnung geliefert. Unabhängig davon liefern Messmethoden wie STM nur Informationen über eine Ladungsordnung oder inhomogene Ladungsverteilungen. Inhomogenitäten der Spins und Ladungen scheinen aber typisch für die HTSL zu sein. Man vermutet, dass diese Inhomogenitäten dynamisch in den supraleitenden Verbindungen sind, während sie in Eu dotiertem La_{2-x}Sr_xCuO_4 bei tiefen Temperaturen statisch werden und die Supraleitung unterdrücken. In dieser Arbeit wird gezeigt, dass sich diese Ladungs- und Spininhomogenitäten in vielen Parametern der NMR Spektren bemerkbar machen.

In this thesis, the tunneling between individual atomic layers in structures of Bi2Sr2CaCu2O8+x based high-temperature superconductors are experimentally studied employing the intrinsic Josephson effect. A special attention is paid to the fabrication of small mesa structures using micro and nanofabrication techniques. In the first part of the thesis, the periodic Fraunhofer-like modulation of the critical current of the junctions as a function of in-plane magnetic field is investigated. A transition from a modulation with a half flux quantum to a flux quantum periodicity is demonstrated with increasing field and decreasing junction length. It is interpreted in terms of the transformation of the static fluxon lattice of stacked, strongly coupled intrinsic Josephson junctions and compared with theoretical predictions. A fluxon phase diagram is constructed.Numerical simulations have been carried out to complement the experimental data. In the second part of the thesis, different resonant phenomena are studied in the dynamic flux-flow state at high magnetic fields, including Eck-resonances and Fiske steps. Different resonant modes and their velocities, including superluminal modes, are identified. In the third part, different experiments attempting to detect radiation from small mesa structures using different setups based on hot-electron bolometer mixers and calorimeters are described. No distinct radiation with emission powers higher than about 500pW could be detected. Furthermore, the interaction with external GHz-radiation is studied. Resonances attributed to an induced flux-flow are observed, and the reflectivity of the sample can be tuned by switching mesas between the superconducting and quasiparticle state. In the last part, the resistive switching of mesas at high bias is studied. It is attributed to a persistent electrical doping of the crystal. Superconducting properties such as the critical current and temperature and the tunneling spectra are analyzed at different doping states of the same sample. The dynamics of the doping is studied, and attributed to two mechanisms; a charge-transfer effect and oxygen reordering

The study of cuprate high-temperature superconductors has undergone a recent resurgence due to the discovery of charge order in several families of cuprate materials. While its existence is now well established, little is known about its microscopic origins or its relationship to high-temperature superconductivity and the pseudogap. The aim of the research presented in this thesis is to address these questions. In this thesis I will report on the use of spectroscopic-imaging scanning tunnelling microscopy (SI-STM) to visualise the short-ranged charge density wave (CDW) in Bi₂Sr₂CaCu₂O₈₊ₓ and NaxCa₂₋ₓCuO₂Cl₂. Building on previous measurements of the intra unit-cell electronic structure of cuprates, I introduce sub-lattice segregated SISTM to individually address the atomic sub-lattices in the CuO₂ plane with spatial phase sensitivity. Using this technique I establish that the CDW in Bi₂Sr₂CaCu₂O₈+x and NaxCa₂₋ₓCuO₂Cl₂ has a previously unobserved d-symmetry form factor, where a breaking of rotational symmetry within the unit cell is modulated periodically in space. Towards identifying a mechanism of CDW formation, I establish that the amplitude of CDW modulations in the electronic structure are maximal at the pseudogap energy-scale and that these modulations exhibit a spatial phase difference of π between filled and empty states. Together with the doping evolution of the CDW wave-vector this highlights the role of the low-energy electronic structure of the pseudogap regime in CDW formation. To elucidate the relationship between the CDW and the superconducting condensate I will introduce nanometer resolution scanned Josephson tunnelling microscopy (SJTM). In this approach the Cooper pair (Josephson) tunnelling current between a Bi₂Sr₂CaCu₂O₈₊ₓ sample and a scan-able Bi₂Sr₂CaCu₂O₈₊ₓ nano-flake STM tip is used to directly visualise the superconducting condensate. I will report the observation of a periodic modulation in the Cooper pair condensate at the same wave-vector as the CDW, the first direct detection of a periodically modulating condensate in any superconductor.