  Investigations of non-adiabatic effects by including vertex corrections in
the standard Eliashberg theory show that high phonon frequency is unfavorable
to superconductivity in 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.
