Dynamical symmetry enlargement in metallic zigzag carbon nanotubes

TL;DR

This paper investigates correlation effects in doped metallic zigzag carbon nanotubes, revealing dynamical symmetry enlargement phenomena and characterizing the ground state phase diagram using renormalization group and bosonization methods.

Contribution

It demonstrates the occurrence of dynamical symmetry enlargement to SO(6) and SO(4) in the low-energy excitations of doped zigzag carbon nanotubes, depending on interaction strength.

Findings

Dynamical symmetry enlargement to SO(6) occurs for weak interactions.

For realistic parameters, an SO(4) symmetry persists in the spin sector.

The phase diagram of ground states is mapped using analytic and numeric methods.

Abstract

We revisit correlation effects in doped metallic zigzag carbon nanotubes by using both the one-loop renormalization group and non-perturbative bosonization techniques. Note that, if a nanotube is placed near a conducting plate, the long-range Coulomb interactions are screened and the resulting short-range interactions can be modelled by on-site and nearest-neighbor repulsive interactions $U$, $V$ and $V_{\perp}$ respectively. Using both analytic and numeric means, we determine the phase diagram of the ground states. For $U/t<0.5$ ($t$ is the hopping strength), dynamical symmetry enlargement occurs and the low-energy excitations are described by the SO(6) Gross-Neveu model. However, for realistic material parameters $U/t \sim \mathcal{O}(1)$, the charge sector decouples but there remains an enlarged SO(4) symmetry in the spin sector.