The Plasmons In Nano-electronic Systems

Plasmon plays an important role in the study of nano-structure systems, due toits unique properties of charge accumulation, local field enhancement andovercoming the diffraction limit, it has been widely used in the region of materialscience, optical science, medical science, biological science, chemical science andso on. The technology of precise manipulation of single atoms through a scanningtunneling microscope makes the studies of plasmon expansive in the microscopicfield. A large number of researches about plasmon in nano-clusters of various sizeand shape have been reported. For now, the time dependent functional theory is themost widely used method in the investigations of the plasmon. However, thismethod costs a lot of time on the computation, and the derived results are alwaysdependent on the external electric field. For this reason, we propose eigen-equationmethod to find plasmon. Using this method can avoid a lot of time on the iterativecalculations, and can prevent the finding of plasmon mode from the influence of theexternal electric field. By this method, we have found the plasmon in ultrathinmetallic films and one-dimensional linear atomic chain system, and systematicallystudied their fundamental characteristics.In our first research works, we have used the virtual-lattice atomic layer tomimic the ultra-thin metal film, then, on the basis of the self-consist linear responseapproximation, we produce an eigen-equation for the ultra-thin metal film. By theeigen-equation, we calculate plasmon dispersions of both single-layer andmultilayer systems, and find that there are two types of plasmon, two dimensional(2D) mode and bulk-like (BL) mode. The plasmon energy of the2D mode is zero inthe long wave limit, while the one of BL mode is nonzero in the long-wave limit.The induced charge of2D mode is symmetric along the direction perpendicular tothe surface of the film, while that of BL mode may be symmetric and antisymmetricalong the perpendicular direction. In addition, the induced charge of the BL modesis always polarized along the perpendicular direction, while that of2D mode justpolarized on the perpendicular direction in more than two layers, and the2DPlasmon gradually evolves to surface plasmon in more than two-layer systems. The2D plasmon energy decreases with the increase of the numbers of atom layers for agiven surface electron density, but increases with the increase of the numbers of atom layers for a given volume electron density in small wave vectors. In the regionof small wave vector, we have compared the2D plasmon dispersions of differentlayer systems, and find that the2D plasmon dispersions in different layer systemsare close to each other and approach the result of the pure2D system.In our second and third research works, respectively in the free electron gasand tight binding model, we have used one dimensional virtual-lattice systems tomimic linear atomic chain. Then, based on the time-dependent density-functionaltheory and linear response theory, we present the eigen-equations for onedimensional atomic chain system. With the eigen-equations, all modes of plasmonsin the systems can be found out. By comparing the eigen-solution with the dipoleresponse, we find a new mode of plasmon, ie, quadrupole plasmon. In onedimensional system, the dipole plasmon corresponds to the antisymmetricoscillation of charge, and can be shown as a resonance of the dipole response.Different from dipole plasmon, the quadrupole plasmon corresponds to thesymmetric oscillation of charge, and only can be shown as a resonance of thequadrupole response, moreover, the quadrupole plasmon can’t be excited by uniformelectric field. At the quadrupole plasmon frequency, the dipole response vanishes,the motion of the electrons is similar to the vibration of atoms in the breathing modeof phonons.In the free electron gas model, plasmons of confined atomic chain system arehighly sensitive to the system’s size. We find that the size dependence of the dipolemode and the quadrupole mode are similar, and the size dependence obtained by theeigen-equation is in agreement with the plasmon dispersion calculated by therandom phase approximation in an infinite quasi-one-dimensional system. Thefrequency spectra of both plasmons are discrete in short-length system, and becomecontinuous in long-length system. With the increase of the system’s length, thenumbers of the plasmons increase, but both the frequency spectra and the frequencyintervals between neighboring plasmons decrease. The lowest plasmon frequency isnonzero, but has the tendency to zero with the increase of the system’s size.Furthermore, the dipole response and quadrupole response as functions of thesystem’s length are discussed. With the increase of the system’s length, the redshiftof resonance frequency is found, and the intensities of dipole response andquadrupole response are increased. In addition, the resonance of the induced chargedensity are investigated at the frequencies near the dipole and quadrupole plasmonfrequency, it is found that there are considerable changes in the induced charge density with even small changes in the frequency of the external electric field, boththe real parts and imaginary parts of the induced charge density are greatly enhancedat the plasmon frequency. And through the eigen-charge density distribution at thequadrupole plasmon frequency, we know that the formation of quadrupole plasmonis the intrinsic properties of the confined one dimensional system.In the tight binding model, through the calculations, we find that thecharacteristics of plasmons are similar to those in the free electron gas model. Asmentioned in the free electron gas model, with the increase of the system’s length,the numbers of the dipole and quadrupole plasmons increase, the resonancefrequency is red shifted, and the intensities of the dipole and quadrupole responsesare increased. Apart from these characteristics, we find that the plasmon frequencieshave the symmetry with respect to the half filling of the electrons. Before halffilling, the plasmon frequencies increase with the increase of the numbers ofelectrons, after half filling, the plasmon frequencies decrease with the increase ofthe numbers of electrons. And before half filling, the intensities of dipole andquadrupole responses are increased with the increase of the numbers of electrons. Inthe end, we have deduced the eigen-equation for period infinite atomic chain system,and then calculate the plasmon dispersion of the infinite atomic chain.