Landau Levels in the Presence of Topological Defects

We study the Landau levels associated with 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 a magnetic field in the framework of the geometric theory of defects in solids of Katanaev and Volovich. The presence of the defects breaks the degeneracy of the Landau levels in different ways depending on the defect. Exact expressions for energies and eigenfuctions are found for all cases.