Electron-Phonon Coupling in Two-Dimensional Silicene and Germanene

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.