碳纳米管中晶格波的研究

Study on the lattice waves of carbon nanotubes

文章采用量子效应修正的库仑屏蔽势,研究了一维无限长(单壁或多壁)碳纳米管中的晶格波,给出了它们的色散关系。结果发现纵波具有声学波性质,横波具有高频光学波性质,并且其色散关系受外界约束的影响较大,当约束不太强时,纵波与横波是耦合的,当约束较强时,纵波与横波之间会出现能隙,能隙的大小与约束强度成正比。文中分析了系统稳定性,研究表明在特定的屏蔽参数区间系统会出现不稳定性,进而发生相变而融化,而在系统稳定的屏蔽参数区间,晶格波的色散关系依赖于屏蔽参数的大小。

By using Screened-Coulomb potential with the quantum effect,both longitudinal and transversal waves in one-dimensional carbon nanotubes are investigated,and the general dispersion relations are derived.It is found that the longitudinal wave is acoustic,while the transverse wave is optical-like.And they are significantly affected by the external confinement.When the confinement strength is weak,the two waves are coupled together;when the confinement is strong enough,an energy gap appears and the size of the energy gap is proportional to the external confinement strength.There exists certain screening parameter region of the system where the instability occurs and the system has a phase transition,that is,it is melted.The effect of the screening parameter on the dispersion relations in the region with stability is also discussed.