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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>โ</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 $\rho_{ab}(T)$ and superfluid density [$\propto \lambda^{-2}$, $\lambda$ = magnetic penetration depth] in $La_{2-x}Sr_{x}CuO_{4}$ 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, $\rho_{ab}(T)$, โฆ