Landau quantization of electrons on a sphere

The energy levels and wave functions of the electrons confined on the surface of a sphere in uniform magnetic fields H are obtained from both the exact solution in terms of the spheroidal function and numerical study. The crossover points between the weak-H (orbital Zeeman splitting) and strong-H (landau quantization) regimes are shown to delineate a series of envelopes, which, together with peculiar bunch of Landau levels, form a series of overlapping bands. The result is compared with the Landau quantization of tight-binding electrons on ${\mathrm{C}}_{60}$ and ${\mathrm{C}}_{240}$ fullerene structures. These spectra are shown to imply an interesting orbital magnetism.