Plasmon modes in N-layer silicene structures

We investigate the plasmon properties in N-layer silicene systems consisting of N, up to 6, parallel single-layer silicene under the application of an out-of-plane electric field, taking into account the spin-orbit coupling within the random-phase approximation. Numerical calculations demonstrate that N undamped plasmon modes, including one in-phase optical and (N-1) out-of-phase acoustic modes, continue mainly outside the single-particle excitation area of the system. As the number of layers increases, the frequencies of plasmonic collective excitations increase and can become much larger than that in single layer silicene, more significant for high-frequency modes. The optical (acoustic) plasmon mode(s) noticeably (slightly) decreases with the increase in the bandgap and weakly depends on the number of layers. We observe that the phase transition of the system weakly affects the plasmon properties, and as the bandgap caused by the spin-orbit coupling equal that caused by the external electric field, the plasmonic collective excitations and their broadening function in multilayer silicene behave similarly to those in multilayer gapless graphene structures. Our investigations show that plasmon curves in the system move toward that in single layer silicene as the separation increases, and the impacts of this factor can be raised by a large number of layers in the system. Finally, we find that the imbalanced carrier density between silicene layers significantly decreases plasmon frequencies, depending on the number of layers.