Electronic structure of carbon nanotubes on graphene substrates

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 for both 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 quasiperiodic 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 direction for strong correlation physics in low dimensions.