Superconductivity from energy fluctuations in dilute quantum critical polar metals

Superconductivity in low carrier density metals challenges the conventional electron-phonon theory due to the absence of retardation required to overcome Coulomb repulsion. Here we show that in dilute metals near polar quantum critical points the Coulomb repulsion can be surpassed by the attraction mediated by zero-point energy fluctuations of the critical polar mode. Our estimates show that this mechanism can explain the critical temperatures observed in doped SrTiO₃, and we predict enhanced effects of polar quantum criticality on superconductivity in dilute two-dimensional metals.