The Researches On The Nature Of The Plasmon Excitations Of Atomic Cluster Systems From The First-principles Theory

With the development of nanotechnology,surface plasmon builds up its unique research field.Because the coupling of surface plasmon with light in nanoclusters can be used to guide,focus,and manipulate light,hence,they are widely used in biomedical,nanosensors,new energy,stealth materials,catalysis,among other fields.It is worth mentioning that impurity doping in metal nanoclusters provides a potentially effective way to adjust electron excitations.Recently,in the absence of the induced charge density analyses of doped gold chains,Nayyar et al.have predicted the existence of a local plasmon mode that corresponds to the charge oscillations only around the impurity.In this paper,on the one hand,to verify the validity of this conclusion,we use the absorption spectra and the induced charge distributions obtained by the real-time time-dependent density functional theory to study the impurity effects on the nature of the plasmon excitations for the gold atomic array structures.On the other hand,we simulate the electronic structures of small sodium chains on silicon substrates by using the semi-infinite dielectric function and the quasi-one-dimensional electron gas model,and then we calculate the substrate polarization effects on the plasmon by employing the random phase approximation method.The advantage of this method is that it can not only qualitatively discuss the influence of the polarization effects on the nature of the plasmon excitations of atomic clusters,but also explicitly analyze the formation mechanism of the charge distribution of plasmon.Specifically,this topic includes the following aspects of research work:(1)Based on the dipolar absorption spectra and the induced charge distributions obtained by the real-time time-dependent density functional theory,the existence of a local plasmon mode in the doped gold atomic array structures has been systematically investigated.Take the gold chains and the gold arrays doped with single nickel atom as examples,in the studies of the charge distributions of the plasmon in the doped gold chains,it is found that the local dipolar mode as reported by Nayyar et al.does not exist in the longitudinal and transverse plasmon modes,and the induced charges corresponding to the resonant peaks will be redistributed.For the longitudinal modes,the impurity seems to prevent the oscillations of induced charges from one side to another.For some transverse modes,the impurity mainly suppresses the oscillations of the 6s valence electrons in half of the doped chain and destroys the induced charge distributions which do not have obvious characters of the end mode and the central modes.In the studies of the charge distributions of the two-dimensional doped gold array,we also do not find the local dipolar plasmon mode.For the longitudinal modes,the impurity changes the whole distribution of induced charges,especially in the neighborhood of the impurity.For the transverse modes,the local mode does not appear in the charge oscillations dominated by the6 s valence electrons and by the 5d valence electrons.In the studies of the optical absorption spectra of the doped gold chain,under the effects of impurity,the additional peaks appear in the longitudinal and transverse absorption spectra,but the impurity position has less effect on the transverse absorption spectra.In the studies of the absorption spectra of the doped gold array,it is found that the impurity makes the longitudinal plasmon peaks less clear and causes the number of the peaks to increase,while the transverse plasmon peaks slightly change.The results also show that the transverse absorption onset of the two-dimensional gold array is slightly lower than that of the one-dimensional gold chain.It is worth mentioning that for the gold atomic array structures the low-limit resonance energy on the transverse plasmons is large than that on the longitudinal plasmons because the energy requirements of the interband transition are greater than that of the intraband transition.In the studies of the effects of the 5d valence electrons of the gold atom on the plasmon properties of the array structures,the effects of the 5d valence electrons are quite significant.For the pure gold chain,the 5d valence electrons not only reduce the resonance energies and the oscillation intensities of the plasmon but also make the induced charge distributions with the characters of both the end and central modes in the transverse modes unsharp.At the same time,for the pure gold array,the edge mode and the center mode excited by the transverse perturbation disappear completely due to the effect of d electronic screening and the s-d electronic coupling.(2)Employing the random phase approximation method,we derive the plasmon equation of small sodium chains on silicon surfaces.Using the energy absorption spectra and the induced charge distributions,we discuss the effects of substrate polarization on the plasmon properties of atomic cluster systems.In the studies of the absorption spectra,the polarization effects lead to the redshift of the resonant peaks for the transverse and longitudinal absorption spectra and makes the intensity of the main peak change.In particular,the intensities of all the resonant peaks get a very large enhancement when the direction of the perturbation is perpendicular to the silicon surface.In the studies of the dependence of absorption spectra on dielectric constants,we found that with the increase of dielectric constants,the redshifts of the resonant peaks become more obvious.In the studies of the charge distributions of the plasmon,substrate polarization affects the oscillation intensities of the induced charges,especially for the direction of the perturbation which is perpendicular to the silicon surface,while in other cases the influences are small.In addition,in the studies of the formation mechanism of the end mode and the central mode,we conclude through the calculations and analyses that the two transverse plasmon modes are caused by the electron-electron interactions,which reflect the collective electronic excitations caused by the interactions.(3)Based on the quadrupolar absorption spectra and the induced charge distributions obtained by the real-time time-dependent density functional theory,we further investigate the existence of local plasmon modes in the doped gold atomic array structures.In the studies of the charge distributions of the longitudinal plasmon,no matter the doped gold chain or the doped gold array,all the induced charges affected by the impurity do not show a local plasmon mode that corresponds to the charge oscillations only around the impurity,and the whole distribution characters of the induced charges change.In the studies of the longitudinal absorption spectra,with the increase of the number of the resonant peaks,the intensities of the peaks change markedly including some additional peaks with relatively large intensities.In addition,it is shown that applying the transverse symmetric field to the gold atomic array structures does not produce the quadrupolar absorption spectra.In the theoretical analyses of the existence of local modes,we speculate that the local dipolar,quadrupolar,or multipolar plasmon modes do not exist in the doped gold atomic array structures.