Dependence of the critical temperature in overdoped copper oxides on superfluid density
The physics of underdoped copper-oxide superconductors, including the pseudogap, spin and charge ordering, and their relation to superconductivity 1-3 , is intensely debated. The overdoped side is perceived as simpler, with strongly-correlated fermion physics evolving smoothly into the conventional Bardeen-Cooper-Schrieffer (BCS) behavior. Pioneering studies on a few overdoped samples 4-11 indicated that the superfluid density was much smaller than expected, but this was attributed to pair-breaking, disorder, and phase separation. Here, we test this conjecture by studying how the magnetic penetration depth λ and the phase stiffness ρs depend on temperature and doping, scanning densely the entire overdoped side of the La 2-x Sr x CuO 4 (LSCO) phase diagram. We have measured the absolute values of λ and ρs to the accuracy of ±1% in thousands of cuprate samples; the large statistics reveals clear trends and intrinsic properties. The films are quite homogeneous; variations in the critical temperature (T c ) within a film are very small (< 1 K). At every doping, ρs(T) decreases linearly with temperature. The T c (ρ s0) dependence is linear but with an offset, (T c - T 0 ) ∝ ρs0 where T0 ≈ 7 K, except very close to the origin where Tc ∝ √ρ s0. This scaling law defies the standard BCS description, posing a challenge to theory.