Unusual hole dependence of ${\mathit{T}}_{\mathit{c}}$ in ${\mathrm{HgBa}}_2$${\mathrm{CuO}}_{4+\mathrm{\delta }}$

The anion doping effect on the superconducting transition temperature (${\mathit{T}}_{\mathit{c}}$) of ${\mathrm{HgBa}}_2$ ${\mathrm{CuO}}_{4+\mathrm{\delta }}$ has been determined with a wide ${\mathit{T}}_{\mathit{c}}$ variation. We found a parabolic variation of ${\mathit{T}}_{\mathit{c}}$ with δ over the entire range of superconductivity. Remarkably, the dependence of ${\mathit{T}}_{\mathit{c}}$ on p (the number of holes per ${\mathrm{CuO}}_2$) has richer features: for δ≤0.28, ${\mathit{T}}_{\mathit{c}}$ is parabolic in p, but with an unusual prefactor and p=0.72δ, giving significantly less than two holes per oxygen; and for δ>0.28, a drastic departure from the parabolic ${\mathit{T}}_{\mathit{c}}$(p) occurs. Implications for the occurrence of superconductivity in this material are discussed.