  We study electron-electron Coulomb interactions in electronic systems whose
Fermi surfaces possess a finite electric dipole density. Although this dipole
density averages to zero over the Fermi surface, electric monopole-dipole
interactions can become sufficiently strong in quasi-2D Dirac metals with
spin-orbit coupling to induce unconventional odd-parity superconductivity,
similar to the Balian-Werthamer state of ${}^{3}$He-B. Hence materials with
spin-orbit-induced band inversion, such as the doped topological insulators
Bi${}_{2}$Se${}_{3}$, Bi${}_{2}$Te${}_{3}$, and SnTe, are natural candidate
materials where our theory could be relevant. We discuss the conditions for an
electric dipole density to appear on the Fermi surface and develop the
formalism to describe its coupling to the plasmon field which mediates the
Coulomb interaction. A mechanism for the enhancement of dipolar coupling is
then provided for quasi-2D Dirac systems. Within a large-N renormalization
group treatment, we show that the out-of-plane electric dipole moment is
marginally relevant, in contrast to the monopole coupling constant which is
marginally irrelevant. For physically realistic parameters, we find that dipole
fluctuations can get sufficiently enhanced to result in Cooper pairing.
