Superconductivity from energy fluctuations in quantum critical polar metals*

We demonstrate a new mechanism of s-wave superconductivity, that does not require retardation to overcome the Coulomb repulsion. In quantum critical polar metals the latter is heavily screened while the critical transverse optic phonons decouple from the electron charge. We show that the residual interactions between quasiparticles are carried by energy fluctuations of the polar medium and are attractive leading to pairing. This mechanism naturally leads to a dome-like dependence of the superconducting Tc on carrier density. Our estimates show that this mechanism may explain the occurence of superconductivity at low densities in doped SrTiO₃. We provide predictions for the enhancement of superconductivity near polar quantum criticality in two and three dimensional materials that can be used to test our theory.