Superconductor-to-Metal Quantum Phase Transition in Overdoped $La_{2-x}Sr_xCuO_4$

We investigate $T_c$ and magnetic penetration depth $λ(T)$ near the superconductor-metal quantum phase transition in overdoped $La_{2-x}Sr_{x}CuO_{4}$ films. Both $T_c$ and superfluid density $n_s$, $\propto λ^{-2}$, decrease with overdoping. They obey the scaling relation $T_c \propto [λ^{-2}(0)]^α$ with $α\approx 1/2$. We discuss this result in the frameworks of disordered d-wave superconductors and of scaling near quantum critical points. Our result, and the linear scaling ($α\approx 1$) found for the more anisotropic $Tl_2Ba_2CuO_{6+δ}$, can both be understood in terms of quantum critical scaling, with different dimensionalities for fluctuations.

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