Underdoped cuprates are without doubt complex and exotic. Several correlated states compete near the Fermi surface including superconductivity, charge ordering and the pseudogap 'state'. But for a long time it was thought that overdoped cuprates represented progressively more conventional behaviour - despite the fact that it has been known since quite early that there is a strong suppression of superfluid density as one progresses deeper into the overdoped state. We know that underdoped cuprates also display a suppression of superfluid density due to the pseudogap so this overdoped behaviour came to be known as the 'boomerang effect'. We have found this deeply puzzling because many other overdoped superconducting properties display conventional behaviour. Amongst these are the scaled BCS ratios for the condensation energy, the specific heat jump and the superconducting energy gap. So why should the superfluid density be increasingly suppressed with overdoping when e.g. the condensation energy is not? Techniques for measurement of superfluid density include muon spin relaxation, optics, susceptibility, mutual inductance and the tunnel diode resonator. We have been involved in a number of these earlier reports. But here we measure the superfluid density using field-dependent specific heat measurements on bulk samples of Ca-doped YBa₂Cu₃O_x and Bi₂Sr₂CaCu₂O_8+x and find no suppression of the superfluid density across the overdoped region, consistent with our earlier thermodynamic results mentioned above. Are the overdoped cuprates in this sense conventional after all? And what is the reason for these divergent results amongst so many different techniques? The cuprates continue to fascinate in their rich behaviour.

Keywords: Overdoped cuprates, superfluid density, field-dependent specific heat, condensation energy