Interband electron pairing for superconductivity from the breakdown of the Born-Oppenheimer approximation

The origin of interband electron pairing responsible for enhancing superconductivity and the factors controlling its strength were examined. We show that the interband electron pairing is a natural consequence of breaking down the Born-Oppenheimer approximation during the electron-phonon interactions. Its strength is determined by the pair-state excitations around the Fermi surfaces that take place to form a superconducting state. Fermi surfaces favorable for the pairing were found and its implications were discussed.