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

TL;DR

This paper investigates how the curvature of rolled-up nanotubes influences their electronic properties, revealing that curvature induces localized bound states and that the number of such states correlates with the number of windings.

Contribution

It provides a combined numerical and analytical analysis of curvature effects on electronic states in rolled-up nanotubes, highlighting the relationship between geometry and bound state formation.

Findings

Curvature induces atomic-like bound states localized near maximum curvature points.

The number of bound states equals the number of windings in an Archimedean spiral nanotube.

Electronic energy dispersion depends strongly on the nanotube's radius and winding number.

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.