Landau levels in the presence of topological defects

In this paper we study the Landau levels in the presence of topological defects. We analyse the behaviour of electrons moving in a magnetic field in the presence of a continuous distribution of disclinations, a magnetic screw dislocation and a dispiration. We focus on the influence of these topological defects on the spectrum of the electron (or hole) in the magnetic field in the framework of the geometric Katanaev-Volovich theory of defects in solids. The presence of the defect breaks the degeneracy of the Landau levels in different ways depending on the defect. Exact expressions for energies and eigenfunctions are found for all cases. Using Kaluza-Klein theory we solve the Landau level problem for a dispiration and compare the results with the ones obtained in the previous cases.