Materials science and high technologies are the driving force of any advanced society. The phenomenon of high-temperature superconductivity, found in cuprates, is of indisputable technological importance. It also presents one of the most exciting, thoroughly investigated yet still unresolved problems in physics. A major difficulty in understanding high-Tc systems lies in the complexity of the materials and phase diagram, where the delicate balance between material specific properties, disorder and the number of electronic phases superimpose makes it hard to identify the leading interactions. Despite the complexity, we have identified a series of surprisingly simple and universal behaviors (1-7). Based on them we show that the phenomenology of cuprates across the phase diagram is fully captured by the simple charge conservation relation:
1 + p = nloc + neff
Here, p is the doping while neff is the carrier density and nloc is the density of localized charge within a CuO2 plaquette. The corresponding superfluid density is related to both components:
ρS = neff ⋅ (OS nloc).
where all terms can be experimentally determined directly. The charge nloc is responsible for all the strangeness of these compounds, which includes the pseudogap phenomenon and the superconducting glue (8,9).
The compound-dependent constant, OS, is fine-tuned by the local crystal structure. It arises from the p–d–p fluctuation by the Cu-localized holes visiting the neighboring planar–oxygen atoms and can be determined from NMR (9).