Phase diagrams of the metallic zigzag carbon nanotube

TL;DR

This paper analyzes the phase diagram of metallic zigzag carbon nanotubes using a Hubbard model, revealing multiple ground states and phases, including superconducting and density wave states, through advanced theoretical methods.

Contribution

It introduces a comprehensive theoretical analysis of phase diagrams in zigzag carbon nanotubes considering weak interactions and symmetry reductions.

Findings

Identified four ground states in undoped nanotubes with repulsive interactions.

Discovered two phases in doped nanotubes: d-wave superconductor and coexisting p-density wave and charge density wave.

Found additional states, including a chiral current phase, in the global phase diagram.

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.