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W\"olfle and Balatsky Phys. Rev. B 98, 104505 (2018) have proposed amicroscopic pairing mechanism for doped SrTiO$_3$ (STO) based on the ${\textitgradient}$ coupling of electronic density to the soft TO phonon mode. Sincethis coupling to TO phonons is usually weak, this conclusion is surprising,especially for a low density superconductor such as STO, where the density ofstates is small. A crucial step in the argument made by W\"olfle and Balatskyis that the displacement vector of the TO mode is not strictly perpendicular tothe momentum vector, making a deformation coupling possible. We show that theyhave made a mistake in computing the eigenvector and have grossly overestimatedthis lack of orthogonality. When corrected, the coupling is negligible. We alsouse transport data to put upper bounds on the coupling constant which are muchsmaller than the estimate by W\"olfle and Balatsky. Finally, we also object totheir use of the Eliashberg equation when the phonon frequency is larger thanthe Fermi energy.

Comment on "Superconductivity at low density near a ferroelectric quantum critical point: Doped SrTiO3"