Universal scaling laws can guide the understanding of new phenomena, and for cuprate high-temperature superconductivity the influential Uemura relation showed, early on, that the maximum critical temperature of superconductivity correlates with the density of the superfluid measured at low temperatures. Here we show that the charge content of the bonding orbitals of copper and oxygen in the ubiquitous CuO2 plane, measured with nuclear magnetic resonance, reproduces this scaling. The charge transfer of the nominal copper hole to planar oxygen sets the maximum critical temperature. A three-dimensional phase diagram in terms of the charge content at copper as well as oxygen is introduced, which has the different cuprate families sorted with respect to their maximum critical temperature. We suggest that the critical temperature could be raised substantially if one were able to synthesize materials that lead to an increased planar oxygen hole content at the expense of that of planar copper.

Nuclear magnetic resonance (NMR) shifts, if stripped of their uncertainties, must hold key information about the electronic fluid in the cuprates. The early shift interpretation that favored a single-fluid scenario will be reviewed, as well as recent experiments that reported its failure. Thereafter, based on literature shift data for planar Cu, a contrasting shift phenomenology for cuprate superconductors is developed, which is very different from the early view while being in agreement with all published data. For example, it will be shown that the hyperfine scenario used up to now is inadequate as a large isotropic shift component is discovered. Furthermore, the changes of the temperature dependences of the shifts above and below the superconducting transitions temperature proceed according to a few rules that were not discussed before. It appears that there can be substantial spin shift at the lowest temperature if the magnetic field is perpendicular to the CuO 2 plane, which points to a localization of spin in the 3d(x 2 − y 2 ) orbital. A simple model is presented based on the most fundamental findings. The analysis must have new consequences for theory of the cuprates.

The distribution of electrons and holes in the CuO2 plane of the high-temperature superconducting cuprates is determined with nuclear magnetic resonance through the quadrupole splittings of 17 O and 63 Cu. Based on new data for single crystals of electron-doped Pr2−xCexCuO4(x=0, 0.05, 0.10, 0.15) as well as Nd2−xCexCuO4 (x=0, 0.13) the changes in hole contents n d of Cu 3d(x 2 − y 2 ) and np of O 2pσ orbitals are determined and they account for the stoichiometrically doped charges, similar to hole-doped La2−xSrxCuO4. It emerges that while n d + 2np = 1 in all parent materials as expected, n d and np vary substantially between different groups of materials. Doping holes increases predominantly np, but also n d . To the contrary, doping electrons predominantly decreases n d and only slightly np. However, np for the electron doped systems is higher than that in hole doped La1.85Sr0.15CuO4. Cuprates with the highest maximum Tcs appear to have a comparably low n d while, at the same time, np is very high. The rather high oxygen hole content of the Pr2CuO4 and Nd2CuO4 with the low n d seems to make them ideal candidates for hole doping to obtain the highest Tc. The high-temperature superconducting cuprates (HTSCs) emerge from insulating antiferromagnetic parent materials, the essential unit of which is the CuO 2 plane. It is formed, in first approximation, by Cu 2+ (3d 9 ) and O 2− (2p 6 ), with the half-filled Cu 3d(x 2 − y 2 ) orbital hybridized with four O 2p σ orbitals, so that a near square planar arrangement of Cu and O follows. Charge neutrality is provided by layers between CuO 2 planes, the chemistry of which can be varied widely. By changing the average charge state of the layers, e.g., by doping them, electrons are added or removed from the CuO 2 plane. These additional electrons or holes destroy the Cu-based antiferromagnetism. Above a certain doping level superconductivity can emerge with a maximum critical transition temperature T c at optimal average doping, and it decreases nearly parabolically as the doping departs from the optimal value. The highest T c 's vary widely among different materials, and it is not quite clear which material parameters affect this behavior. Therefore, the knowledge of the microscopic distribution of charges in the CuO 2 plane is of great interest for a better understanding of the doping process.A local probe like nuclear magnetic resonance (NMR) can yield vital information about the doping process since a change in the hole or electron content in the Cu 3d(x 2 − y 2 ) or O 2p σ orbitals changes the electric field gradients (EFGs) experienced by the 63,65 Cu (I = 3 2) and 17 O (I = 5 2) nuclei through the electric quadrupole interaction that splits the nuclear resonances for Cu and O into 2I lines in a high magnetic field. Their frequencies are given by ν n = ν 0 ± nν Q : the central line (n = 0) is in leading order unaffected by the quadrupole interaction that causes an angular dependent quadrupole splitting ν Q for the 2I − 1 satellite transitions (n = 1 for Cu and n = 1, ...

Nuclear relaxation is an important thermodynamic probe of electronic excitations, in particular in conducting and superconducting systems. Here, an empirical phenomenology based on all available literature data for planar Cu in hole-doped cuprates is developed. It is found that most of the seemingly different relaxation rates among the systems are due to a temperature independent anisotropy that affects the mostly measured 1/T 1 , the rate with an external magnetic field along the crystal c-axis, while 1/T 1⊥ is largely independent on doping and material above the critical temperature of superconductivity (Tc). This includes very strongly overdoped systems that show Fermi liquid behavior and obey the Korringa law. Below Tc the relaxation rates are similar, as well, if plotted against the reduced temperature T /Tc. Thus, planar Cu nuclear relaxation is governed by a simple, dominant mechanism that couples the nuclei with varying anisotropy to a rather ubiquitous bath of electronic excitations that appear Fermi liquid-like irrespective of doping and family. In particular, there is no significant enhancement of the relaxation due to electronic spin fluctuations, different from earlier conclusions. Only the La2−xSrxCuO4 family appears to be an outlier as additional relaxation is present, however, the anisotropy remains temperature independent. Also systems with very low doping levels, for which there is a lack of data, may behave differently.

Cuprate superconductors still hold many open questions, and recently, the role of symmetry breaking electronic charge ordering resurfaced in underdoped cuprates as phenomenon that competes with superconductivity. Here, unambiguous NMR proof is presented for the existence of local charge ordering in nearly optimally doped YBa2Cu3O6.9, even up to room temperature. Increasing pressure and decreasing temperature leads to the highest degree of order in the sense that the two oxygen atoms of the unit cell of the CuO2 plane develop a charge difference of about 0.02 holes, and order throughout the whole crystal. At ambient conditions a slightly smaller charge difference and a decreased order is found. Evidence from literature data suggests that this charge ordering is ubiquitous to the CuO2 plane of all cuprates. Thus, the role of charge ordering in the cuprates must be reassessed.