ELECTRON-PHONON LOCKING AND SUPERCONDUCTIVITY

The electron-phonon vertex part Lambda is investigated as a function o f real frequencies in a narrow-band electron system coupled with local phonons. Even though the bare electron-phonon coupling is not very st rong, Lambda is found to diverge at some characteristic frequencies om ega(l). The divergence induces the vanishment of the electron Green's function at omega(l). This phenomenon can be interpreted as the lockin g of an electron by such local phonons. By including this effect in th e theory of superconductivity, we suggest an anomalous behavior in the tunneling spectroscopy.