High-temperature superconducting cuprates respond to doping with a dome-like dependence of their critical temperature ( T _c ). But the family-specific maximum T _c can be surpassed by application of pressure, a compelling observation known for decades. We investigate the phenomenon with high-pressure anvil cell NMR and measure the charge content at planar Cu and O, and with it the doping of the ubiquitous CuO ₂ plane with atomic-scale resolution. We find that pressure increases the overall hole doping, as widely assumed, but when it enhances T _c above what can be achieved by doping, pressure leads to a hole redistribution favoring planar O. This is similar to the observation that the family-specific maximum T _c is higher for materials where the hole content at planar O is higher at the expense of that at planar Cu. The latter reflects dependence of the maximum T _c on the Cu–O bond covalence and the charge-transfer gap. The results presented here indicate that the pressure-induced enhancement of the maximum T _c points to the same mechanism.

Recently, an analysis of all available planar oxygen shift and relaxation data for the cuprate high-temperature superconductors showed that the data can be understood with a simple spin susceptibility from a metallic density of states common to all cuprates. It carries a doping dependent but temperature independent pseudogap at the Fermi surface, which causes the deviations from normal metallic behavior, also in the specific heat. Here, a more coherent, unbiased assessment of all data, including planar Cu, is presented and consequences are discussed, since the planar Cu data were collected and analyzed prior to the O data. The main finding is that the planar Cu shifts for one direction of the external magnetic field largely follow from the same states and pseudogap. This explains the shift suppression stated more recently, which leads to the failure of the Korringa relation in contrast to an enhancement of the relaxation due to antiferromagnetic spin fluctuations originally proposed. However, there is still the need for a second spin component that appears to be associated with the Cu $3d(x^2-y^2)$ hole to explain the complex Cu shift anisotropy and family dependence. Furthermore, it is argued that the planar Cu relaxation which was reported recently to be rather ubiquitous for the cuprates, must be related to this universal density of states and the second spin component, while not being affected by the simple pseudogap. Thus, while this universal metallic density of states with a pseudogap is also found in the planar Cu data, there is still need for a more elaborate scenario that eludes planar O.

Cuprates currently hold the record for the highest temperature superconductivity at ambient pressure, but the microscopic understanding of these materials remains elusive. Here, we utilize nuclear magnetic resonance (NMR) data of planar oxygen and copper from essentially all hole-doped cuprates to provide a universal phenomenology relating the NMR spin shifts, which measure the electronic spin polarization at a given nucleus, with the superconducting dome and maximum critical temperature. There appear to be two separate contributions to the spin shift in planar copper, only one of which is seen at the oxygen site, and we associate them with two different types of carriers. Upon disentangling these two components, their relative size is shown to correlate not only with the doping dependence of the superconducting dome but also with the variation in maximum superconducting critical temperature, $T_{\mathrm{c},\max }$, between different families. One of these components is independent of family and resides in the hybridized planar orbitals of Cu and O. The second component, in contrast, is predominately isotropic and encodes the differences between the families. It is thus related to the charge transfer gap and planar hole sharing. Our findings offer universal insight which should prove useful in the continuing development of a comprehensive theory of the cuprates, as well as an indication of how it may be possible to engineer materials with higher critical temperatures.