Doping dependence of the dipolar correlation length scale in metallic SrTiO₃

Superconducting domes, ubiquitous across a variety of quantum materials, are often understood as a window in which pairing is favored, opened by the fluctuations of competing orders. Yet, the understanding of how such a window closes is missing. Here, we show that inelastic neutron scattering, by quantifying a length scale associated with the dipoles correlation, ℓ₀, addresses this issue. We find that, within the experimental precision, the end of the superconducting dome coincides with the end of a highly polarizable state (in which ℓ₀ is longer than the interatomic distance). Thus, the superconducting dome is driven by the competition between the increase in the density of states and the inevitable collapse of the quantum paraelectric phase. This is compatible with a crucial role played by the soft ferroelectric mode in driving superconductivity. Such a scenario may also be at work in other quantum paraelectric materials, either bulk or at interfaces.