Quantum particles constrained on cylindrical surfaces with non-constant diameter

• Published in: Journal of the Physical Society of Japan Vol. 73; no. 11; pp. 3115 - 3120
• Main Author: FUJITA, Nobuhisa
• Format: Journal Article
• Language: English
• Published: Tokyo Institute of Pure and Applied Physics 01-11-2004; Physical Society of Japan; The Physical Society of Japan
• Subjects: Condensed matter: electronic structure, electrical, magnetic, and optical properties; Electronic structure and electrical properties of surfaces, interfaces, thin films and low-dimensional structures; Electronic transport in mesoscopic systems; Exact sciences and technology; Physics; Band structure; Aharonov-Bohm effect; Bound state; Magnetic field effects; Tubules; cylindrical symmetry; quantum particles; curved surfaces; Electronic structure; Angular momentum; Surface properties; constraint; Curvature
• ISSN: 0031-9015; 1347-4073
• DOI: 10.1143/jpsj.73.3115

We present a theoretical formulation of the one-electron problem constrained on the surface of a cylindrical tubule with varying diameter. Because of the cylindrical symmetry, we may reduce the problem to a one-dimensional equation for each angular momentum quantum number m along the cylindrical axis. The geometrical properties of the surface determine the electronic structures through the geometry dependent term in the equation. Magnetic fields parallel to the axis can readily be incorporated. Our formulation is applied to simple examples such as the catenoid and the sinusoidal tubules. The existence of bound states as well as the band structures, which are induced geometrically, for these surfaces are shown. To show that the electronic structures can be altered significantly by applying a magnetic field, Aharonov-Bohm effects in these examples are demonstrated.