Effect of Curvature on the Electronic Structure and Bound State Formation in Rolled-up Nanotubes

Abstract

We analyze the electronic properties of a two-dimensional electron gas rolled-up into a nanotube by both numerical and analytical techniques. The nature and the energy dispersion of the electronic quantum states strongly depend upon the geometric parameters of the nanotube: the typical radius of curvature and the number of windings. The effect of the curvature results in the appearance of atomic-like bound states localized near the points of maximum curvature. For a two-dimensional sheet rolled up into an Archimedean spiral we find that the number of bound states is equal to the number of windings of the spiral.

5 pages, 5 figures

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• Quantum mechanics on curved 2D systems with electric and magnetic fields
• Bending and wrinkling as competing relaxation pathways for strained free-hanging films
• Structural and magnetic properties of an InGaAs/Fe${}_3$Si superlattice in cylindrical geometry

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