Study of overdoped $La_{2-x}Sr_{x}CuO_{4}$ (LSCO) using electrolyte gating.

The demise of superconducting transition temperature in the overdoped region of the phase diagram of LSCO is still one of the open questions in the field of high temperature superconductivity. Several studies have framed this feature in a dirty BCS scenario, where the increased dopant density is increasing the disorder to the point that the pair-breaking becomes dominant and transition temperature decreases. However, experiments on LSCO and other cuprates show that the superfluid density in the overdoped region decreases as doping increases, thus contradicting this dirty-BCS scenario. In our experiment, we tune the carrier density continuously in the overdoped region by means of electrolyte gating. In this technique, an ionic liquid is used to cover the sample and an external gate voltage is applied to obtain higher electric fields compared to standard gate insulator technique. We demonstrate that disorder does not play any significant role in the superconducting transition in this region of the phase diagram, and instead we show evidence of superconducting transition temperature and disorder simultaneously decreasing as doping is increased.