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Recently, advances in film synthesis methods have enabled a study ofextremely overdoped $La_{2-x}Sr_{x}CuO_{4}$. This has revealed a surprisingbehavior of the superfluid density as a function of doping and temperature, theexplanation of which is vividly debated. One popular class of models positselectronic phase separation, where the superconducting phase fraction decreaseswith doping, while some competing phase (e.g. ferromagnetic) progressivelytakes over. A problem with this scenario is that all the way up to the domeedge the superconducting transition remains sharp, according to mutualinductance measurements. However, the physically relevant scale is the Pearlpenetration depth, $\Lambda_{P}$, and this technique probes the sample on alength scale $L$ that is much larger than $\Lambda_{P}$. In the present paper,we use local scanning SQUID measurements that probe the susceptibility of thesample on the scale $L << \Lambda_{P}$. Our SQUID maps show uniform landscapesof susceptibility and excellent overall agreement of the local penetrationdepth data with the bulk measurements. These results contribute an importantpiece to the puzzle of how high-temperature superconductivity vanishes on theoverdoped side of the cuprates phase diagram.

Scanning SQUID characterization of extremely overdoped $La_{2-x}Sr_{x}CuO_{4}$