  Following the work in graphene, we report a first-principles study of
electron-phonon coupling (EPC) in low-buckled (LB) monolayer silicene and
germanene. Despite of the similar honeycomb atomic arrangement and linear band
dispersion, the EPC matrix-element squares of the $\Gamma$-$E_g$ and K-$A_1$
modes in silicene are only about 50% of those in graphene. However, the smaller
Fermi velocity in silicene compensates this reduction by providing a larger
joint electronic density of states near the Dirac point. We predict that Kohn
anomalies associated with these two optical modes are significant in silicene.
In addition, the EPC-induced frequency shift and linewidth of the Raman-active
$\Gamma$-$E_g$ mode in silicene are calculated as a function of doping. The
results are comparable to those in graphene, indicating a similar non-adiabatic
dynamical origin. In contrast, the EPC in germanene is found to be much
reduced.
