Effect of curvature on the electronic structure and bound-state formation in rolled-up nanotubes

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 on 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.