On the quantitative determination of hole-concentration in high-temperature cuprate superconductors

We compared four hole-scales that have been used to determine the hole-concentration in high-temperature cuprate superconductors. We show that the hole-scale, $P_{pl}$-scale, based on the thermoelectric power [T. Honma $et$ $al$., Phys. Rev. B70, (2004) 214517.] is quantitatively consistent with spectroscopic probes for many different cuprate materials, while the other hole-scales, based on a well-known dome-shaped $T_c$-curve [M. R. Presland $et$ $al$., Physica C176, 95 (1991)], the $c$-axis lattice parameter [R. Liang $et$ $al$., Phys. Rev. B73, (2006) 180505(R).], and Hall coefficient [Y. Ando $et$ $al$., Phys. Rev. B61, (2000) 14956(R).], are not. We show that the quantitatively different hole-scales resulted in opposite conclusion of the same experimental observations. It can also lead to different interpretations of the electronic phase diagram when comparing different physical properties in different high-$T_c$ systems. We suggest that the $P_{pl}$-scale is the correct universal scale that works for all high-$T_c$ cuprates and it should be used for all quantitative doping dependence studies of cuprates.