Approaching the Mott-Hubbard insulator in the 85-K superconductor ${\mathrm{Bi}}_2$(Sr,Ca${)}_3$${\mathrm{Cu}}_2$${\mathrm{O}}_{8+\mathrm{d}}$ by doping with Tm

As x increases in ${\mathrm{Bi}}_4$${\mathrm{Sr}}_3$${\mathrm{Ca}}_{3\mathrm{-}\mathit{x}}$${\mathrm{Tm}}_{\mathit{x}}$${\mathrm{Cu}}_4$${\mathrm{O}}_{16+\mathit{y}}$ the Hall carrier density $n_H$ decreases linearly. The variation is consistent with Mott-Hubbard behavior, but in conflict with band-structure results which ignore correlations. We find that the variation of $T_c$ vs $n_H$ is nonmonotonic. The source of the large carrier population (0.4/Cu) in the undoped (x=0) compound is discussed.