Link Between Mobile Band Population and Superconductivity in SrTiO3$\backslash$LaAlO3 Interface*

The entire superconducting phase diagram of SrTiO3$\backslash$LaAlO3 is scanned using back gate voltage. The superconducting transition temperature Tc and critical field Hc are recorded along with the~Hall resistance and Shubnikov-de Haas (SdH) effect. The latter is sensitive only to the density of the mobile band while the former probes all bands. We find that Tc and Hc follow a similar non-monotonic gate voltage dependence as the SdH frequency and the low field Hall. This suggests that the mobile band is getting depopulated at high gate voltages resulting in the reduction of Tc on the overdoped side. We discuss a possible scenario for this peculiar behavior.