Dependence of ${\mathrm{T}}_{\mathrm{c}}$ and transport properties on the Cu valence in ${\mathrm{HgBa}}_2$${\mathrm{Ca}}_{\mathrm{n}\mathrm{-}1}$${\mathrm{Cu}}_{\mathrm{n}}$${\mathrm{O}}_{2(\mathrm{n}+1\mathrm{})+\mathrm{\delta }}$ (n=2,3) superconductors

We have determined the oxygen content and the Cu valence by iodometric titiration of single-phase ${\mathrm{HgBa}}_2$ ${\mathrm{Ca}}_{\mathrm{n}\mathrm{-}1}$ ${\mathrm{Cu}}_{\mathrm{n}}$ ${\mathrm{O}}_{2(\mathrm{n}+1\mathrm{})+\mathrm{\delta }}$ (n=2,3), Hg-1212 and Hg-1223, superconductors postannealed under various conditions in either a reducing or an oxidizing atmosphere. Their lattice parameters, ${\mathrm{T}}_{\mathrm{c}}$, resistivity, and the thermoelectric power have been systematically investigated as a function of Cu valence. Hg-1212 exhibits a parabolic or ``bell-shaped'' relationship between ${\mathrm{T}}_{\mathrm{c}}$ and the Cu valence similar to that reported for ${\mathrm{HgBa}}_2$ ${\mathrm{CuO}}_{4+\mathrm{\delta }}$ (Hg-1201), while only a half of the parabola is observed for Hg-1223. The systematic variations in the resistivity and the thermoelectric power as well as the relationship between ${\mathrm{T}}_{\mathrm{c}}$ and the Cu valence confirm that the Hg-1223 sample with the highest ${\mathrm{T}}_{\mathrm{c}}$ of 135 K is almost optimally doped. Both Hg-1212 and Hg-1223 as well as Hg-1201 exhibit their maximum ${\mathrm{T}}_{\mathrm{c}}$ values at the same nominal Cu valence of approximately 2.20 which is also comparable to those for other high-${\mathrm{T}}_{\mathrm{c}}$ cuprate superconductors. This coincidence of the Cu valence for optimally doped states suggests that the simple ionic model where each excess oxygen in the Hg-${\mathrm{O}}_{\mathrm{\delta }}$ charge reservoir supplies two holes is appropriate in the present Hg-12(n-1)n samples.