Correlation Effects of Single-Wall Carbon Nanotubes in Weak Coupling

TL;DR

This paper investigates the correlation effects in single-wall carbon nanotubes with weak on-site interactions using renormalization group methods, revealing mappings to Hubbard models and analyzing phase diagrams for specific nanotube configurations.

Contribution

It introduces a controlled renormalization group approach to study weakly interacting nanotubes and establishes mappings to Hubbard chains, providing insights into their phase diagrams.

Findings

Mapping of nanotube models to 2-chain Hubbard models at half filling.

Phase diagrams for (3,3)-armchair and (6,-6)-zigzag nanotubes.

Identification of effective interactions in different nanotube geometries.

Abstract

Single-wall carbon nanotubes with on-site interaction $U \ll t$ are studied by a controlled renormalization group method. When formulated as a system of $N_{f}$ flavors of interacting Dirac fermions, the effective model at generic filling resembles a set of quasi-1D Hubbard chains. For the undoped $(N_{y}, N_{y})$-armchair and the $(N_{x}, -N_{x})$-zigzag with $N_x=3n$, specific mappings to the 2-chain Hubbard model at half filling with effective interaction $u_{eff}=U/N_{y}$ and $2U/N_{x}$ are found from this more general equivalence. The phase diagrams of the (3, 3)-armchair and the (6, -6)-zigzag at generic fillings are studied and compared as an example.