Locating the missing superconducting electrons in overdoped cuprates

Overdoped high-temperature cuprate superconductors have been widely believed to be described by the physics of d-wave BCS-like superconductivity. However, recent measurements indicate that the superconducting transition temperature (T_c) is correlated with the superfluid density rather than being independent of it as predicted by BCS theory. Here, we combine time-domain THz spectroscopy with kHz range mutual inductance measurements to determine both the superfluid and the uncondensed carrier density as a function of doping for overdoped La_2-xSr_xCuO₄ films. A significant fraction of the carriers remain uncondensed in a Drude-like peak even as T → 0 with a conductivity and scattering rate that rules out disorder as the determining factor in suppressing the superfluid density. Analysis of the low frequency spectral weight distribution in terms of a quantum Debye Waller factor suggests the prominent role of quantum phase fluctuations as the critical doping is approached.