Two-carrier description of cuprate superconductors from NMR

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. We demonstrate that there are two separate contributions to the spin shift at planar copper, only one of which is seen at oxygen, and associate them with two different carrier types. Upon disentangling these two components, their relative size is shown to determine not only the doping dependence of the superconducting dome, but also the variation in maximum superconducting critical temperature, $T_\mathrm{c}$, between different families. One of these components is independent of family and resides in the hybridized planar orbitals. The second component, in contrast, has a more three-dimensional character and encodes the differences between the families. It is thus related to the charge transfer gap and planar hole sharing. Our findings offer a key, 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.