Electronic structure of carbon nanotubes on graphene substrates

TL;DR

This paper develops a theoretical framework to understand how the electronic properties of carbon nanotubes are affected by their orientation and displacement relative to graphene substrates, revealing potential for new correlated electron phenomena.

Contribution

It introduces a low-energy theory for nanotube-graphene heterostructures that accounts for rotations and displacements, showing these factors significantly influence electronic structure.

Findings

Electronic properties depend on nanotube orientation and displacement.

Rigid displacements can qualitatively change electronic structure.

The heterostructure Hamiltonian can be periodic or quasi-periodic.

Abstract

Allotropes of carbon, including one-dimensional carbon nanotubes and two-dimensional graphene sheets, continue to draw attention as promising platforms for probing the physics of electrons in lower dimensions. Recent research has shown that the electronic properties of graphene multilayers are exquisitely sensitive to the relative orientation between sheets, and in the bilayer case exhibit strong electronic correlations when close to a magic twist angle. Here, we investigate the electronic properties of a carbon nanotube deposited on a graphene sheet by deriving a low-energy theory that accounts both for rotations and rigid displacements of the nanotube with respect to the underlying graphene layer. We show that this heterostructure is described by a translationally invariant, a periodic or a quasi-periodic Hamiltonian, depending on the orientation and the chirality of the nanotube. Furthermore, we find that, even for a vanishing twist angle, rigid displacements of a nanotube with respect to a graphene substrate can alter its electronic structure qualitatively. Our results identify a promising new direction for strong correlation physics in low dimensions.