Doping dependence of the Fermi surface in $(\mathrm{B}\mathrm{i},\mathrm{P}\mathrm{b}{)}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$

A detailed and systematic angle-resolved photoemission spectroscopy investigation of the doping dependence of the normal-state Fermi surface (FS) of modulation-free (Pb,Bi)-2212 is presented. The FS does not change in topology away from hole like at any stage. The FS area does not follow the usual curve describing $T_c$ vs x for the hole-doped cuprates, but is downshifted in doping by ca. 0.05 holes per Cu site, indicating the consequences of a significant bilayer splitting of the FS across the whole doping range. The strong k dependence of the FS width is shown to be doping independent. The relative strength of the shadow FS has a doping dependence mirroring that of $T_c.$