Control of bulk superconductivity by surface charge doping in a BCS superconductor

We investigate the effects of pure charge doping (obtained by using the so-called electric-double layer gating technique) in thin films of the metallic superconductor NbN. Despite the electrostatic screening due to the large intrinsic carrier density of this material, we observe measurable, ambipolar modulations of the superconducting critical temperature, whose amplitude depends on the gate voltage but also on the film thickness. The results unambiguously indicate that the superconducting properties of the whole film are affected by the charge induced in a much thinner surface layer (whose thickness is of the order of the screening length). The results can be interpreted in terms of proximity effect between the surface layer (hosting the induced charge) and the underlying part of the film. Very interestingly, the effective screening length lambda_eff turns out to depend on the induced charge density: it departs from the Thomas-Fermi value and increases – suggesting that there is an upper limit for the volume charge density – on increasing the gate voltage. At very high electric fields, lambda_eff eventually becomes much larger than that predicted by a standard screening theor