Can electrons attract each other without the help of phonons?

It is considered well known since the work of Frohlich in the 1950’s that electrons can have an effective attraction via the exchange of phonons. Here I collect together a number of papers that show that attraction between electrons is possible using Coulomb interaction between electrons alone. Historically the Frohlich interaction played a key role in the BCS theory of superconductivity, but in hindsight that was the result of an inspired sleight of hand by BCS. Recall that the electron-phonon interaction g has its origin in Coulomb interaction between electrons and ions and is ∼ e, and the Frohlich interaction is second order in g. In BCS theory, the first order in e direct Coulomb repulsion was simply ignored. Adding back the Coulomb repulsion will give an interaction that is repulsive at all Matsubara frequencies, (which are the ones that count in BCS or Eliashberg theory, not real frequencies). Only the works by Bogoliubov and Anderson/Morel a few years later justified this step by appealing to the vast difference in energy scale between the phonon and the Fermi energy, leading to a downward renormalization of the Coulomb repulsion relative to the Frohlich attraction. W. Little wrote an influential paper in 1964 suggesting that a nearby polarizable electronic system can play the role of phonons and give rise to possible high temperature superconductivity. Over half a century later, there is scant evidence that this mechanism works in practice. Part of the difficulty is that electronic systems typically do not enjoy the separation of energy scale that was crucial for the phonon induced pairing mechanism. In the