Quantization of plasmon in two-dimensional square quantum dot system

Abstract

Plasmon in quantum dot system is one of the most notable research topics in the field of optoelectronics. With the development of nanotechnology, plasmon in nano-structure has received considerable attention due to its potential applications in future natural science areas. To better understand the quantum effect and the properties of plasmon, in this paper we use the linear response theory and the tight-binding approximation to investigate the collective response of charge in a twodimensional square quantum dot system. The results show that when the frequency of the external field equals the frequency of the plasmon, there are strong charge collective oscillations in the quantum dot system, accompanied by great energy absorption and near-field enhancement. Owing to the quantization of plasmon, the collective charge oscillations in a two-dimensional square quantum dot system are found at different frequencies. The number of quantum modes of plasmon increases with the size and electron number of square quantum dots increasing, this behaviour of quantum mode of plasmon is similar to the one of phonon. The reasons for this behaviour are as follows. First, with the increase of quantum dot size, there are more energy levels around the fermi energy, and the electrons can jump from more energy levels to the outside of fermi circle, so there are more collective excitation frequencies (i.e., more quantum modes of plasmon) in a larger size system. Second, with the increase of electron number in quantum dots, there are more energy levels occupied by electrons, so there are more quantum modes of plasmon too. Furthermore, the size dependence of plasmon shows that with the increase of quantum dot size, the frequency interval between two neighbouring modes of plasmon is smaller, and the discrete modes of plasmon will gradually display quasi-continuous characteristic and transform gradually into the classical continuous modes of plasmon, and the frequency spectrum of plasmon turns into the classical dispersion relation. Such a characteristic is in accord with Bohr's correspondence principle, implying that the quantum plasmon and classical plasmon are gradually unified in a macroscopic size. The dependence of plasmon on the size and electron number of quantum dots also show that with the increase of the quantum dot size, the frequencies of the plasmon is red-shifted and the excitation intensity of the plasmon increases; with the increase of the electron number in quantum dot, the frequency of the plasmon is blue-shifted and the excitation intensity of the plasmon increases.