Transformation from Quantum to Classical Mode: the Size Effect of Plasmon in 2D Atomic Cluster System

On the basis of tight-binding approximation, the energy absorption of 2D atomic clusters is calculated by the linear response theory. Through the energy-absorption peaks in the presence of different external potentials, various types of plasmon modes are specified in clusters with dozens to hundreds atoms, such as transverse dipole plasmon, longitudinal dipole plasmon, transverse quadrupole plasmon, and longitudinal quadrupole plasmon. Moreover, the transformation of plasmon from quantum to classical mode is observed in clusters with different shape and different electron density. The particular transformation process demonstrate that: there are only a few modes of plasmon in clusters with few-atoms; as the number of atoms in cluster is increased, the number of plasmon modes increases, the gaps between plasmon frequencies become smaller, the quantum modes of plasmon gradually evolve into continuous modes, and the dispersion of quantum-mode plasmon gradually transforms into the one of classical 2D plasmon. Such process reveals the size effect of plasmon in 2D clusters, which can be explained by the fact that the energy levels near the Fermi energy are denser and more compact in larger-size clusters.