Phase diagrams of the metallic zigzag carbon nanotube

Abstract

We investigate a metallic zigzag carbon nanotube by means of a Hubbard model which includes both on-site and nearest neighbour interactions. Assuming weak interactions, a renormalization group analysis of the equivalent two-leg ladder followed by bosonization and refermionization results in a Gross-Neveu model with an enlarged symmetry relative to the original Hamiltonian. For the undoped case the symmetry of the Gross-Neveu model is SO(8), but for the doped case the particle-hole symmetry is broken and the symmetry reduces to SO(6). Four ground state phases are found in the undoped carbon nanotube with repulsive interactions, a d-wave Mott insulator, an s-wave Mott insulator, a p-density wave and a charge density wave. The doped case has two ground state phases, a d-wave superconductor and a phase where a p-density wave and a charge density wave co-exist. We also explore the global phase diagram with a general interaction profile and find several additional states, including a chiral current phase where current flows around the nanotube along the zigzag bonds.

arXiv comment16 pages, 9 figures

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Cited by in corpus (8)

• Competing orders in the generalized Hund chain model at half-filling
• Possible quantum phase-manipulation of a two-leg ladder in mixed-dimensional fermionic cold atoms
• Hierarchy of relevant couplings in perturbative renormalization group transformations
• Generic short-range interactions in two-leg ladders
• Influence of electron-phonon coupling on low temperature phases of metallic single-wall carbon nanotubes
• Renormalization-group exponents for superconducting phases in two-leg ladders
• Terminable Transitions in a Topological Fermionic Ladder
• Correlated insulating states in carbon nanotubes controlled by magnetic field