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Hole-doped cuprate high temperature superconductors have ushered in the modern era of high temperature superconductivity (HTS) and have continued to be at center stage in the field. Extensive studies have been made, many compounds discovered, voluminous data compiled, numerous models proposed, many review articles written, and various prototype devices made and tested with better performance than their nonsuperconducting counterparts. The field is indeed vast. We have therefore decided to focus on the major cuprate materials systems that have laid the foundation of HTS science and technology and present several simple scaling laws that show the systematic and universal simplicity amid the complexity of these material systems, while referring readers interested in the HTS physics and devices to the review articles. Developments in the field are mostly presented in chronological order, sometimes with anecdotes, in an attempt to share some of the moments of excitement and despair in the history of HTS with readers, especially the younger ones.
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We have computed alpha^2Fs for the hole-doped cuprates within the framework of the one-band Hubbard model, where the full magnetic response of the system is treated properly. The d-wave pairing weight alpha^2F_d is found to contain not only a low energy peak due to excitations near (pi,pi) expected from neutron scattering data, but to also display substantial spectral weight at higher energies due to contributions from other parts of the Brillouin zone as well as pairbreaking ferromagnetic excitations at low energies. The resulting solutions of the Eliashberg equations yield transition temperatures and gaps comparable to the experimentally observed values, suggesting that magnetic excitations of both high and low energies play an important role in providing the pairing glue in the cuprates.
The spectral energy gap is an important signature that defines states of quantum matter: insulators, density waves, and superconductors have very different gap structures. The momentum resolved nature of angle-resolved photoemission spectroscopy (ARPES) makes it a powerful tool to characterize spectral gaps. ARPES has been instrumental in establishing the anisotropic d-wave structure of the superconducting gap in high-transition temperature (Tc) cuprates, which is different from the conventional isotropic s-wave superconducting gap. Shortly afterwards, ARPES demonstrated that an anomalous gap above Tc, often termed the pseudogap, follows a similar anisotropy. The nature of this poorly understood pseudogap and its relationship with superconductivity has since become the focal point of research in the field. To address this issue, the momentum, temperature, doping, and materials dependence of spectral gaps have been extensively examined with significantly improved instrumentation and carefully matched experiments in recent years. This article overviews the current understanding and unresolved issues of the basic phenomenology of gap hierarchy. We show how ARPES has been sensitive to phase transitions, has distinguished between orders having distinct broken electronic symmetries, and has uncovered rich momentum and temperature dependent fingerprints reflecting an intertwined & competing relationship between the ordered states and superconductivity that results in multiple phenomenologically-distinct ground states inside the superconducting dome. These results provide us with microscopic insights into the cuprate phase diagram.
The presence of different electronic orders other than superconductivity populating the phase diagram of cuprates suggests that they might be the key to disclose the mysteries of this class of materials. In particular charge order in the form of charge density waves (CDW), i.e., the incommensurate modulation of electron density in the CuO$_2$ planes, is ubiquitous across different families and presents a clear interplay with superconductivity. Until recently, CDW had been found to be confined inside a rather small region of the phase diagram, below the pseudogap temperature and the optimal doping. This occurrence might shed doubts on the possibility that such low temperature phenomenon actually rules the properties of cuprates either in the normal or in the superconducting states. However, recent resonant X-ray scattering (RXS) experiments are overturning this paradigm. It results that very short-ranged charge modulations permeate a much wider region of the phase diagram, coexisting with CDW at lower temperatures and persisting up to temperatures well above the pseudogap opening. Here we review the characteristics of these high temperature charge modulations, which are present in several cuprate families, with similarities and differences. A particular emphasis is put on their dynamical character and on their coupling to lattice and magnetic excitations, properties that can be determined with high resolution resonant inelastic x-ray scattering (RIXS).
High-temperature superconductivity (HTSC) mysteriously emerges upon doping holes or electrons into insulating copper oxides with antiferromagnetic (AFM) order. It has been thought that the large energy scale of magnetic excitations, compared to phonon energies for example, lies at the heart of an electronically-driven superconducting phase at high temperatures. However, despite extensive studies, little information is available for comparison of high-energy magnetic excitations of hole- and electron-doped superconductors to assess a possible correlation with the respective superconducting transition temperatures. Here, we use resonant inelastic x-ray scattering (RIXS) at the Cu L3-edge to reveal high-energy collective excitations in the archetype electron-doped cuprate Nd2-xCexCuO4 (NCCO). Surprisingly, despite the fact that the spin stiffness is zero and the AFM correlations are short-ranged, magnetic excitations harden significantly across the AFM-HTSC phase boundary, in stark contrast with the hole-doped cuprates. Furthermore, we find an unexpected and highly dispersive mode in superconducting NCCO that is undetected in the hole-doped compounds, which emanates from the zone center with a characteristic energy comparable to the pseudogap, and may signal a quantum phase distinct from superconductivity. The uncovered asymmetry in the high-energy collective excitations with respect to hole and electron doping provides additional constraints for modeling the HTSC cuprates.
We investigate infrared manifestations of the pseudogap in the prototypical cuprate and pnictide superconductors: YBa2Cu3Oy and BaFe2As2 (Ba122) systems. We find remarkable similarities between the spectroscopic features attributable to the pseudogap in these two classes of superconductors. The hallmarks of the pseudogap state in both systems include a weak absorption feature at about 500 cm-1 followed by a featureless continuum between 500 and 1500 cm-1 in the conductivity data and a significant suppression in the scattering rate below 700 - 900 cm-1. The latter result allows us to identify the energy scale associated with the pseudogap $Delta_{PG}$. We find that in the Ba122-based materials the superconductivity-induced changes of the infrared spectra occur in the frequency region below 100 - 200 cm-1, which is much lower than the energy scale of the pseudogap. We performed theoretical analysis of the scattering rate data of the two compounds using the same model which accounts for the effects of the pseudogap and electron-boson coupling. We find that the scattering rate suppression in Ba122-based compounds below $Delta_{PG}$ is solely due to the pseudogap formation whereas the impact of the electron-boson coupling effects is limited to lower frequencies. The magnetic resonance modes used as inputs in our modeling are found to evolve with the development of the pseudogap, suggesting an intimate correlation between the pseudogap and magnetism.
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