Weak coupling d-wave BCS superconductivity and unpaired electrons in overdoped La₂₋ₓSrₓCuO₄ single crystals

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The low-temperature specific heat (SH) of overdoped La₂₋ₓSrₓCuO₄ single crystals (0.178=<x=<0.290) has been measured. For the superconducting samples (0.178=<x=<0.238), the derived gap values (without any adjusting parameters) approach closely onto the theoretical prediction Δ₀=2.14kBTc for the weak-coupling d-wave BCS superconductivity. In addition, the residual term γ(0) of SH at H=0 increases with x dramatically when beyond x 0.22, and finally evolves into the value of a complete normal metallic state at higher doping levels, indicating growing amount of unpaired electrons. We argue that this large γ(0) cannot be simply attributed to the pair breaking induced by the impurity scattering, instead the phase separation is possible.