The Spherical Landau Problem

TL;DR

This paper analyzes the magnetization of electrons on a spherical surface under a strong magnetic field, providing an analytical solution that reveals oscillatory behavior similar to the de Haas-van Alphen effect, and compares it with the planar case.

Contribution

It introduces an analytical approximation for the Landau problem on a sphere, enabling direct comparison with the planar case and revealing oscillatory magnetization behavior.

Findings

Analytical solution for low-energy electron states on a sphere

Magnetization exhibits de Haas-van Alphen oscillations

Results are exact at low temperatures and comparable to planar Landau levels

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.