Electron-phonon locking and superconductivity

The electron-phonon vertex part is investigated as a function of real frequencies in a narrow-band electron system coupled with local phonons. Even though the bare electron-phonon coupling is not very strong, is found to diverge at some characteristic frequencies _l. The divergence induces the vanishment of the electron Green's function at _l. This phenomenon can be interpreted as the locking of an electron by such local phonons. By including this effect in the theory of superconductivity, we suggest an anomalous behavior in the tunneling spectroscopy.