The Superconducting Plateau
Two recent experiments in lightly doped strontium titanate have shown that the superconducting critical temperature remains constant in a range of carrier concentrations covering almost three orders of magnitude. The importance of this phenomenon, hereby dubbed a superconducting plateau, is comparable to the celebrated superconducting dome. The dramatic empirical evidence impose severe constraints on any proposal for a superconducting mechanism at low doping. We analyze the experimental results to see what type of theoretical models can be suitable in this regime. We show that the low critical current, absence of diamagnetic screening and the high critical field are all related to the small momentum of the carriers, which is expected at low densities. We quantify the dependency of the critical temperature on density by introducing the "density exponent". We discuss the role of a quantum critical point in the formation of a plateau and comment on the need for more experimental data.