  Despite often being dismissively described as exhibiting conventional
Fermi-liquid-like behaviour, heavily overdoped high-Tc cuprates sport several
unexpected features. Thermodynamic properties expected to be roughly constant
with doping decrease towards zero, signalling that a growing fraction of
carriers remain in the normal state below Tc. Near Tc, the superconducting
energy gap fills in with temperature, contrary to the expectations of BCS
theory. Most recently a transition in the Hall number of some cuprates was
found to extend to a very high doping (x~0.27), far beyond the pseudogap
critical point identified by a peak in thermodynamic properties (x=0.19). This
presents a challenge to the view that the pseudogap is a consequence of Fermi
surface reconstruction. In this paper we present a consistent explanation for
all these observations by combining pair-breaking scattering with a Fermi
surface reconstruction model for the pseudogap. Notably, an increase in
pair-breaking with doping leads to a separation of the points where
reconstruction begins and the thermodynamic properties peak. This result
highlights pair-breaking as an essential ingredient in the electronic recipe
for heavily overdoped cuprate superconductors.
