Plasmonic Properties In Two-dimensional Atomic Lattice

With the rapid development of the technology of precisely operating single atom with the scanning tunneling microscope (STM), people can actually accurately observe and control molecular and atomic clusters; as a result, the plasmon in various kinds of nano-cluster systems has been studied by researchers. At present, the time-dependent density functional theory and the linear response theory under random-phase approximation have been applied the most in studying the plasmon. However, the calculated quantity of using these two methods is huge, and the final results can be influenced because of the extra external electric field. In this paper, the eigen-equation method is used, on the basis of the linear response theory under random-phase approximation and the density functional theory, to replace the density function theory, thus to study the plasmon in the nano-structure systems. This paper adopts the tight-binding model to study the excitation of the plasmon in the 2D atomic cluster systems in low-dimensional nano-structure systems. Specifically, this paper has conducted researches as follows:(1) The collective oscillation of the electric charge in the nano-structure system, the eigen frequency equation of the plasmon, and the energy absorption spectrum function have been derived using the method of eigen-equation on the basis of the linear response theory under random-phase approximation and the density functional theory; thus an effective method to specifically study the relevant characteristics of the plasmon in the nano-structure systems is provided. (2) The situation of the eigen oscillation of the system is studied using the derived eigen-equation. Under the condition without external field, this paper has systematically described and analyzed all the plasmon modes in the cluster systems, as well as the symmetry of the charge distribution corresponded with different plasmon modes. Under the condition with extra external electric field, the excitation of the plasmon in different polarization directions should be excited by extra electric fields in different directions; the dipole plasmon mode can be excited by both uniform and non-uniform fields; and the multi-polar plasmon mode cannot be excited by the uniform field. (3) Beyond that, this paper has also calculated the charge distribution of the plasmon excitations in different modes in the system, discovering that the symmetry of the charge distribution of the plasmon resonances originates from the inherent attribute of the corresponding eigen plasmon, not from the symmetry of the applied external field. In addition, there is functional dependency among the energy absorption spectrum of the system with the extra external electric field, the size of the system, the electron filling, and the plasmon resonances. That is to say, for a system with given electron density, its excited resonant frequency decreases with the increasing size of the system. Under the condition of maintaining the original atomic cluster system, the excitation energy of the plasmon would present the symmetric relation centered on the half-filling with the changing amount of the filling electron, which indicates that for the electron and holes, the plasmon in the nano-structure system is symmetrical.