Polar metals are intriguing materials where an inversion-symmetry breaking transition (structurally similar to a ferroelectric one) occurs in a conducting system. The polar order fluctuations being equivalent to a transverse optical phonon, it is yet an open question whether novel many-body phenomena may occur in such a system.
I have shown (Phys. Rev. Lett. 124, 237601 (2020)), that a number of novel behaviors including non-Fermi liquid can be realized in topological semimetals (with nodal points or lines) at a polar quantum critical point.
More recently (arXiv:2106.11295), I have demonstrated that nonlinear coupling to the critical fluctuations can drive superconductivity at extremely low densities, possibly giving a key to the puzzle of superconductivity in doped SrTiO3.