Cylindrical two-dimensional electron gas in a transverse magnetic field

We compute the single-particle states of a two-dimensional (2D) electron gas confined to the surface of a cylinder immersed in a magnetic field. The envelope-function equation is solved exactly for both a 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 length scales, 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-one-dimensional 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, and dots on the cylinder surface depending on the ratio between the field periodicity and the cylinder radius. Results in different regimes are traced to either incipient Landau-level formation or Aharonov-Bohm behavior.