Cylindrical Two-Dimensional Electron Gas in a Transverse Magnetic Field

TL;DR

This paper analyzes the quantum states of electrons confined to a cylindrical surface under magnetic fields, revealing transitions from 2D to 1D regimes and effects like Landau levels and Aharonov-Bohm phenomena.

Contribution

It provides exact solutions for electron states on a cylinder in both homogeneous and modulated magnetic fields, exploring the interplay of multiple length scales.

Findings

Transition from quasi-2D to quasi-1D regimes under homogeneous magnetic field

Carrier confinement into stripes, rings, or dots with modulated magnetic fields

Identification of Landau level formation and Aharonov-Bohm effects

Abstract

We compute the single-particle states of a two-dimensional electron gas confined to the surface of a cylinder immersed in a magnetic field. The envelope-function equation has been solved exactly for both an homogeneous and a periodically modulated magnetic field perpendicular to the cylinder axis. The nature and energy dispersion of the quantum states reflects the interplay between different lengthscales, namely, the cylinder diameter, the magnetic length, and, possibly, the wavelength of the field modulation. We show that a transverse homogeneous magnetic field drives carrier states from a quasi-2D (cylindrical) regime to a quasi-1D regime where carriers form channels along the cylinder surface. Furthermore, a magnetic field which is periodically modulated along the cylinder axis may confine the carriers to tunnel-coupled stripes, rings or dots on the cylinder surface, depending on the ratio between the the field periodicity and the cylinder radius. Results in different regimes are traced to either incipient Landau levels formation or Aharonov-Bohm behaviour.