Narrow gap Luttinger liquid in Carbon nanotubes

TL;DR

This paper investigates how electron interactions in metallic carbon nanotubes enhance minigaps and induce universal power law behavior, using an exactly solvable model that reveals complex soliton structures and charge dynamics.

Contribution

It introduces an exactly solvable SU(4) symmetric Gross-Neveu model for neutral excitations and analyzes charge solitons with distinct length scales in nanotubes.

Findings

Electron interactions reinforce minigaps and produce universal power law dependence.

Charge excitations are composite solitons with two separate length scales.

Charge compressibility shows a crossover from overlapping to non-overlapping soliton states.

Abstract

Electron interactions reinforce minigaps induced in metallic nanotubes by an external field and turn the gap field dependence into a universal power law. An exactly solvable Gross-Neveau model with an SU(4) symmetry is derived for neutral excitations near half-filling. Charge excitations, described by a sin-Gordon perturbation of Luttinger liquid theory, are composite solitons formed by the charged and neutral fields with two separate length scales. Charge compressibility at finite density, evaluated in terms of inter-soliton interaction, exhibits a crossover from overlapping to non-overlapping soliton state. Implications for the Coulomb blockade measurements are discussed.