Comparison of the Hole Concentration determined by Transport Measurement for the Hole-doped Cuprate Superconductors

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We have compared the hole concentration (Ppl) determined by hole-scale based on the thermoelectric power at RT (S²⁹⁰) to the hole concentrations (P) determined by two popular hole-scales based on the superconducting critical temperature (Tc) and Hall coefficient (Rₕ). While the hole concentrations based on different hole-scales are different, we show that when the Ppl is divided by either the effective unit cell volume (Veuc) which is the unit-cell volume per one CuO₂ plane or the optimal hole concentration (Pplopt) we can find some correlation between Ppl and P. That is, the normalized Tc (Tc / Tc(Pplopt)) and the Hall number (1/eRₕ) are well scaled with Ppl / Pplopt and Ppl / Veuc, respectively. We find that the Ppl-scale can map to and reproduce the other two hole scales if proper dimensionality and normalization are taken into account but not vice versa.