On the Spherical Two-Dimensional Electron Gas

We investigate the many-body properties of a two-dimensional electron gas constrained to the surface of a sphere, a system which is physically realized in multielectron bubbles in liquid helium. A second-quantization formalism, suited for the treatment of a spherical two-dimensional electron gas (S2DEG), is introduced. Within this formalism, the dielectric response properties of the S2DEG are derived, and we identify both collective excitations and a spectrum of single-particle excitations. We find that the single-particle excitations are constrained to a well-defined region in the angular momentum - energy plane. The collective excitations differ in two important aspects from those of a flat 2DEG: on a sphere, the 'spherical plasmons' have a discrete frequency spectrum and the lowest frequency is nonzero.