Electron on a cylinder with topological defects in a homogeneous magnetic field

Abstract

In this work we study the effects of the geometry and topology of a cylinder on the energy levels of anelectron moving in a homogeneous magnetic field. We consider the existence of topological defects as ascrew dislocation and a disclination. When we take the region of movement as the full cylindrical surface,we find that, by increasing the strength of the screw dislocation, the dispersion on the electronic energylevels is affected and monotonically increasing. For an electron moving in an almost flat region we showthat the dispersion on the Landau levels decrease monotonically as we increase the strength of the screwdislocation. The lowest Landau level can reach a zero value, leaving the energy of the system solely givenby the geometry of the cylinder, which does not depend on the magnetic field. In both situations, as wechange the deficit angle of the disclination, we observe that the energy levels are shifted and the magnitudeof such shift depends on the magnetic field. The Landau levels for a flat sample are recovered in the limit ofan infinite cylinder radius.