Probing the topological phase transition via density oscillations in silicene and germanene

We theoretically investigated two kinds of density oscillations, the Friedel oscillation and collective excitation in the silicene and germanene within the random phase approximation, and found that the tunable spin-valley coupled band structure could lead to some exotic properties in these two phenomena. Based on an exact analytical and numerical analysis, we demonstrated that the beating of the screened potential as well as the undamped plasmon mode can be taken as fingerprints of a topological phase transition in doped silicene and doped germanene. Thus our proposal here establishes the connection between the topological phase transition and the density oscillations that can be accessed by a variety of experimental techniques.