We investigate the plasmon frequency and the broadening function corresponding to Landau damping in a N-MLG structure consisting of N, up to 5, MLG sheets at zero temperature. Our results present that plasmon dispersions in the system include an in-phase optical mode and $$N - 1$$ out-of-phase acoustic ones. The optical (acoustic) plasmon frequency is higher (lower) than that of MLG at the same parameters. The broadening function of plasmon dispersions is quite similar to that in case of taking into account temperature effects. In addition, the increase in separation between layers increases (decreases) acoustic (optical) plasmon frequency, making plasmon curves become identical at smaller wave vector. Besides, the imbalance in carrier density in graphene sheets affects significantly on plasmon frequencies and plasmon pattern because it separates some plasmon branches far away from the others. However, the number of plasmon branches separated from the others depends mainly on the number of layers containing different carrier density but is independent of the order of these layers in the system.

中文翻译：

---

零温度下 N 层石墨烯结构中的等离子体模式

我们研究了在 N-MLG 结构中与兰道阻尼相对应的等离子体频率和展宽函数，该结构由 N，多达 5 个，零温度下的 MLG 片组成。我们的结果表明，系统中的等离子体色散包括同相光学模式和 $$N - 1$$ 异相声学模式。在相同参数下，光（声）等离子体频率高于（低于）MLG。等离子体色散的展宽函数与考虑温度影响的情况非常相似。此外，层间间距的增加会增加（降低）声（光）等离子体频率，使等离子体曲线在较小的波矢量处变得相同。除了，石墨烯片中载流子密度的不平衡对等离子体频率和等离子体模式有显着影响，因为它将一些等离子体分支与其他等离子体分支分开。然而，与其他分离的等离子体分支的数量主要取决于包含不同载流子密度的层数，但与系统中这些层的顺序无关。