Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2004-08-11
J. Phys. Soc. Jpn. 73, 3115 (2004).
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
7 pages, 7 figures, submitted to J. Phys. Soc. Jpn
Scientific paper
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.
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