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

We have compared the hole concentration ($P_{pl}$) determined by hole-scale based on the thermoelectric power at RT ($S^{290}$) to the hole concentrations ($P$) determined by two popular hole-scales based on the superconducting critical temperature ($T_c$) and Hall coefficient ($R_H$). While the hole concentrations based on different hole-scales are different, we show that when the $P_{pl}$ is divided by either the effective unit cell volume ($V_{euc}$) which is the unit-cell volume per one CuO$_2$ plane or the optimal hole concentration ($P_{pl}^{opt}$) we can find some correlation between $P_{pl}$ and $P$. That is, the normalized $T_c$ ($T_c$ / $T_c$($P_{pl}^{opt}$)) and the Hall number (1/$eR_H$) are well scaled with $P_{pl}$ / $P_{pl}^{opt}$ and $P_{pl}$ / $V_{euc}$, respectively. We find that the $P_{pl}$-scale can map to and reproduce the other two hole scales if proper dimensionality and normalization are taken into account but not vice versa.