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 an electron moving in a homogeneous magnetic field. We consider the existence of topological defects as a screw 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 energy levels is affected and monotonically increasing. For an electron moving in an almost flat region we show that the dispersion on the Landau levels decrease monotonically as we increase the strength of the screw dislocation. The lowest Landau level can reach a zero value, leaving the energy of the system solely given by the geometry of the cylinder, which does not depend on the magnetic field. In both situations, as we change the deficit angle of the disclination, we observe that the energy levels are shifted and the magnitude of such shift depends on the magnetic field. The Landau levels for a flat sample are recovered in the limit of an infinite cylinder radius.

Nonrelativistic quantum dynamics on a cone with and without a constraining potential

“…Curvature effects on the conductance [2][3][4][5] and curvature effects on the magnetization and persistent currents 6 are some phenomena studied in 2DEG's. Usually, before considering any application, the bound state problems of non planar 2DEG's are investigated [7][8][9] .…”

2DEG on a cylindrical shell with a screw dislocation

“…Inspired in these works, in this paper, we will investigate how the deformed potential due to a lattice distortion affects the energy levels of a two dimensional electron gas (2DEG) confined on a cylindrical surface in a 3D semiconductor. The case with the absence of such potential described in the literature can find applications in the context of carbon nanotubes [11][12][13]. We will show that, for a 2DEG confined on a cylindrical shell in a 3D semiconductor like silicon, important quantitative differences exist due to this noncovariant term.…”

Two-dimensional electron gas under the effect of constrained potential and magnetic field in curved space

“…The main drawback of such structures is spatial fluctuations of the curvature of surface in them, which makes the studies of the effect of the curvature on the magnetotransport [24] in such structures a very difficult task. The cylindrical surface is the simplest model for investigating the influence of geometry on physical systems [25,26]. The interest in the electronic properties of quantum systems with cylindrical symmetry has received a boost, because the early proposals of carbon nanotubes [27,28] for building future nanoelectronic devices, have interesting mechanical and electrical properties.…”

“…These figures show that the energy levels versus the radius R of the cylinder have an asymptotic behavior as R increases. In the limit → ∞ R , they become the Landau levels for an electron in a flat space [26].…”