Distribution of electrons and holes in cuprate superconductors as determined from $^{17}$O and $^{63}$Cu nuclear magnetic resonance

The distribution of electrons and holes in the CuO$_2$ 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 Pr$_{2-x}$Ce$_x$CuO$_4$(x=0, 0.05, 0.10, 0.15) as well as Nd$_{2-x}$Ce$_x$CuO$_4$ (x=0, 0.13) the changes in hole contents $n_d$ of Cu 3d$(x^2-y^2)$ and $n_p$ of O 2$p_sigma$ orbitals are determined and they account for the stoichiometrically doped charges, similar to hole-doped lsco. It emerges that while $n_d+2n_p=1$ in all parent materials as expected, $n_d$ and $n_p$ vary substantially between different groups of materials. Doping holes increases predominantly $n_p$, but also $n_d$. To the contrary, doping electrons predominantly decreases $n_d$ and only slightly $n_p$. However, $n_p$ for the electron doped systems is higher than that in hole doped La$_{1.85}$Sr$_{0.15}$CuO$_4$. Cuprates with the highest maximum $T_{rm c}$s appear to have a comparably low $n_d$ while, at the same time, $n_p$ is very high. The rather high oxygen hole content of the Pr$_2$CuO$_4$ and Nd$_2$CuO$_4$ with the low $n_d$ seems to make them ideal candidates for hole doping to obtain the highest $T_{rm c}$.

Phase diagram of hole-doped cuprates based on $^{17}$O and $^{63}$Cu NMR quadrupole splittings

The phase diagram of the superconducting cuprates is often used to show how their electronic properties change as a function of the mean doping level, i.e., the average hole content of the CuO$_2$ plane. In Nuclear Magnetic Resonance (NMR) experiments average doping, as well as the distribution of these holes between planar Cu and O reveals itself through the quadrupole splittings of the $^{63,65}$Cu and $^{17}$O NMR. Here we argue based on all published NMR data available to us in favor a new type of phase diagram that has the planar oxygen quadrupole splitting and with it the planar oxygen hole content as abscissa rather than the average hole content of the CuO$_2$ plane. In such a plot the superconducting domes of the different cuprate families are shifted horizontally according to their maximum critical temperature $T_{rm c,max}$ set by the chemistry of the parent material, which determines its oxygen hole content. The higher the O hole content the higher $T_{rm c,max}$ that can be achieved by actual doping. These findings also offer a strategy for finding cuprates with higher $T_{rm c,max}$.