Comparative analysis of electron-gas excitations on a spherical surface and on a flat plane

Abstract

By using the random-phase approximation and the f-sum rule approach, we make a comparative analysis of multipole excitation modes in an electron gas confined on a spherical surface (SSEG) and normal modes in an electron gas constrained to a flat plane (i.e. a two-dimensional electron gas (2DEG)). In the SSEG, we investigate the size dependence of multipole modes by varying the electron number and the sphere radius a simultaneously with the average electron density fixed. The L/a dependence of multipole-mode energies, where L denotes the multipole order, is compared with the energy dispersion of normal modes in the 2DEG. The series of the highest-energy multipole modes corresponds to the two-dimensional (2D) plasmon branch, while all the other multipole modes correspond to the single-particle excitation (SPE) continuum. With decrease in L/a, each multipole mode acquires more definite character of collective excitation or SPE, and the highest-energy multipole mode starts to occupy the greater part of the f-sum intensity. As L increases with L/a fixed, the components of the highest-energy multipole mode and all the other multipole modes in the f-sum intensity approach those of the 2D plasmon mode and the SPE modes at the corresponding wavenumber in the f-sum intensity, respectively. This indicates that multipole modes with higher L are more analogous in character to normal modes in the 2DEG. This analysis elucidates similarities and differences between multipole modes in the SSEG and normal modes in the 2DEG.