Non-Adiabatic Effects of Superconductor Silane under High Pressure *

We present the investigations of non-adiabatic effects by including vertex corrections in the standard Eliashberg theory and show that high phonon frequency is unfavorable to superconductivity in the regime of strong vertex correction. This means that it is hard to find high-transition-temperature superconductors in the compounds with light elements if the non-adiabatic effects are strong. The interplay interaction between non-adiabatic effect and Coulomb interaction makes the transition temperature of silane superconductor not so high as predicted by the standard Eliashberg theory.