Abstract
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.
Highlights
The interest in the electronic properties of quantum systems with cylindrical symmetry has received a boost since the early proposals of adopting carbon nanotubes[1,2] as building blocks for future nanoelectronic devices, exploiting their peculiar mechanical and electrical properties.[3,4] In recent years new inorganic semiconductor systems are emerging where carriers are confined on a bent surface, and several possibilities arise to obtain two-dimensional2Delectron gases2DEGswith cylindrical symmetryC2DEGs, which may enrich the wealth of physics and applications of planar semiconductor nanostructures
We show that a transverse homogeneous magnetic field drives carrier states from a quasi-2Dcylindricalregime to a quasi-onedimensional regime where carriers form channels along the cylinder surface
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
Summary
The interest in the electronic properties of quantum systems with cylindrical symmetry has received a boost since the early proposals of adopting carbon nanotubes[1,2] as building blocks for future nanoelectronic devices, exploiting their peculiar mechanical and electrical properties.[3,4] In recent years new inorganic semiconductor systems are emerging where carriers are confined on a bent surface, and several possibilities arise to obtain two-dimensional2Delectron gases2DEGswith cylindrical symmetryC2DEGs, which may enrich the wealth of physics and applications of planar semiconductor nanostructures. The continuous translational symmetry of the cylindrical 2DEG leading to the formation of energy subbands and opens gaps along the cylinder axis In such system the effect of the field depends on the interplay between its intensityor magnetic length, the radius of the tube, and the wavelength of the field modulation.
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