Quantization of Electrons on Closed Surfaces: Sphere and Fullerenes

Hideo Aoki

Department of Physics, University of Tokyo, Hongo, Tokyo 113-0033, Japan

(Received March 31, 1993; Accepted June 14, 1994)

Keywords: Quantization, Closed Surface, Sphere, Fullerene, Magnetic Field

Abstract. The energy levels and wavefunctions of the electrons confined on the surface of a sphere in uniform magnetic fields are obtained from both the exact solution in terms of the spheroidal function and numerical study to exempify peculiar quantization on curved surfaces. An effect of the geometry appear in a "shell structure", in which the crossover from the orbital Zeeman splitting to the Landau quantization regime delineates a series of overlapping bands of Landau levels. The result is compared with the Landau quantization of electrons on closed lattices as realised in icosahedral C₆₀ and C₂₄₀ fullerene structures.