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.
Highlights
Carbon nanotubes and graphene sheets are, respectively, one- and two-dimensional carbon allotropes
For a general translation x⊥ ∈ (0, 1) = 0, 1/2, the nanotube spectrum displays an asymmetry between right goers and left movers and the graphene spectral weight shows a corresponding asymmetry
In the translationally invariant case, we show that, even at a vanishing twist angle, rigid displacements of the nanotube with respect to the graphene layer can strongly alter the electronic properties of the former
Summary
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. Our results identify a promising direction for strong correlation physics in low dimensions
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