The Spherical Landau Problem

Abstract

The magnetization for electrons on a two-dimensional sphere, under a spherically symmetrical normal magnetic field has been studied in the large field limit. This allows us to use an Euclidean approximation for low energies electron states getting an analytical solution for the problem and avoiding the difficulties of quantization on a curved manifold. At low temperatures our results are exact and allow direct comparisson with the planar Landau case. In this temperature limit we compute the magnetization and show it exhibit an oscillatory de Hass-Van Alphen type of behaviour.