Phonon induced metal-insulator phase transition in a metal

It is attempted to clarify a historically existing misunderstanding that Cooper's pairing leads to superconductivity. It was found that the well-known Cooper instability in the presence of a quiescent Fermi sea for a given attractive interelectronic interaction mediated by any boson field, such as phonon, plasmon, paramagnon, etc, causes a metal-insulator other than superconducting transition. This is because the phase transition in this scenario leads to a vanishing density response and hence vanishing conductivity of the Fermi system when temperature approaches the transition temperature T-c at which Cooper's instability occurs. In contrast, it is argued that the origin of a metal-superconductor transition is due to the repulsive Coulomb field. Nevertheless, the results from BCS theory regarding a gap in the electron spectrum for conventional superconductors remain valid only if the interaction in the BCS Hamiltonian is re-interpreted as an attractive interaction between an electron and a hole.