Luttinger Parameter g for Metallic Carbon Nanotubes and Related Systems

TL;DR

This paper uses RPA theory to derive the Luttinger parameter g for metallic carbon nanotubes, showing it is consistent across different nanotube types and affected minimally by gate voltage, validating RPA for plasmon energy calculations.

Contribution

It provides a theoretical derivation of the Luttinger parameter g for all metallic carbon nanotubes using RPA, highlighting its uniformity and applicability.

Findings

All metallic carbon nanotubes have the same g value.

A carbon peapod has a smaller g than a nanotube.

Gate voltage has a second order effect on g.

Abstract

The random phase approximation (RPA) theory is used to derive the Luttinger parameter g for metallic carbon nanotubes. The results are consistent with the Tomonaga-Luttinger models. All metallic carbon nanotubes, regardless if they are armchair tubes, zigzag tubes, or chiral tubes, should have the same Luttinger parameter g. However, a (10,10) carbon peapod should have a smaller g value than a (10,10) carbon nanotube. Changing the Fermi level by applying a gate voltage has only a second order effect on the g value. RPA theory is a valid approach to calculate plasmon energy in carbon nanotube systems, regardless if the ground state is a Luttinger liquid or Fermi liquid. (This paper was published in PRB 66, 193405 (2002). However, Eqs. (6), (9), and (19) were misprinted there.)