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 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.

References in corpus (18)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
• Magic-angle graphene superlattices: a new platform for unconventional superconductivity
• Correlated Insulator Behaviour at Half-Filling in Magic Angle Graphene Superlattices
• Moire bands in twisted double-layer graphene
• Tuning superconductivity in twisted bilayer graphene
• The electronic properties of bilayer graphene
• Tuning carbon nanotube bandgaps with strain
• An exact continuum model for low-energy electronic states of twisted bilayer graphene
• Electronic Structure Theory of Weakly Interacting Bilayers
• Phonon mediated interlayer conductance in twisted graphene bilayers
• Flat band in topological matter: possible route to room-temperature superconductivity
• Minimum model for the electronic structure of twisted bilayer graphene and related structures
• Emergent topological properties in interacting one-dimensional systems with spin-orbit coupling
• Full Momentum and Energy Resolved Spectral Function of a 2D Electronic System
• Fork stamping of pristine carbon nanotubes onto ferromagnetic contacts for spin-valve devices

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• Phonon interference in the array of carbon nanotubes
• Interlayer Conductance in the Armchair Nanotube -- Zigzag Graphene Ribbon Parallel Contact: Theoretical Proposal of Detection of Wavefunction Growing from the Edge to the Center in the Graphene Ribbon
• One-dimensional moiré engineering in zigzag graphene nanoribbons on hBN