利用紧束缚近似下的本征方程方法寻找二维量子点的等离激元。结果表明,电荷可能在横向或纵向分别呈现单极、偶极或四极极化,可能局域于量子点的边界、端点或中心处;根据电荷极化和局域特征提出设想:电中性二维体系可能有24种等离激元模式,带电二维体系可能有27种等离激元模式;各类等离激元模式的尺寸效应不同,纵向尺寸增加时,单极-偶极端点模式的等离激元频率会红移,偶极-单极端点模式的等离激元频率会蓝移。

An eigen-equation method under tight binding approximation is developed to find the plasmon of two-dimensional quantum dots. The results show that the plasmon charges may show monopolar, dipolar, or quadrupolar polariztion in the transverse or longitudinal direction, respectively, which may localize at the center, end, or boundary of quantum dots. According to the charge-polarization and charge-localization characteristics, it is assumed that there exist 24 or 27 plasmon modes in a two-dimensional uncharged or charged system, respectively. In addition, the size effect of various plasmon modes may differ, e.g., the plasmon frequency of the monopole-dipole end mode shifts towards the red end of the spectrum as the longitudinal size increases. In contrast, the frequency of the dipole-monopole end mode shifts towards the blue end of the spectrum as the longitudinal size increases.