Anomalously sharp superconducting transitions in overdoped<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mtext>La</mml:mtext></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mo>−</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mtext>Sr</mml:mtext></mml:mrow><mml:mi>x</mml:mi></mml:msub><mml:msub><mml:mrow><mml:mtext>CuO</mml:mtext></mml:mrow><mml:mn>4</mml:mn></mml:msub></mml:mrow></mml:math>films

We present measurements of $ab$-plane resistivity ${\ensuremath{\rho}}_{\text{ab}}(T)$ and superfluid density (${n}_{\text{s}}\ensuremath{\propto}{\ensuremath{\lambda}}^{\ensuremath{-}2}$, $\ensuremath{\lambda}=\text{magnetic}$ penetration depth) in ${\text{La}}_{2\ensuremath{-}x}{\text{Sr}}_{x}{\text{CuO}}_{4}$ (LSCO) films. As Sr concentration $x$ exceeds about 0.22, the superconducting transition sharpens dramatically, becoming as narrow as 200 mK near the super-to-normal-metal quantum critical point. At the same time, ${\ensuremath{\lambda}}^{\ensuremath{-}2}(0)$ and transition temperature ${T}_{\text{c}}$ decrease, and upward curvature develops in ${\ensuremath{\lambda}}^{\ensuremath{-}2}(T)$. Given the sharp transitions, we interpret these results in the context of a homogeneous $d$-wave superconducting state, not a phase-separated state, with elastic scattering that is enhanced relative to underdoped LSCO due to weaker electron correlations.

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