One-dimensional Hubbard-Luttinger model for carbon nanotubes

TL;DR

This paper develops a Hubbard-Luttinger model to describe low-temperature electron interactions in carbon nanotubes, using bosonic excitations and Bogolyubov transformation, and compares theoretical results with experimental data.

Contribution

It introduces a Hubbard-Luttinger framework for carbon nanotubes, incorporating bosonic excitations and Green functions, providing a qualitative understanding of electron transport.

Findings

Electron-electron interactions cause deviations from Ohm's law.

Transverse quantization influences electron transport properties.

The model's predictions align with experimental observations.

Abstract

A Hubbard-Luttinger model is developed for qualitative description of one-dimensional motion of interacting Pi-conductivity-electrons in carbon single-wall nanotubes at low temperatures. The low-lying excitations in one-dimensional electron gas are described in terms of interacting bosons. The Bogolyubov transformation allows one to describe the system as an ensemble of non-interacting quasi-bosons. Operators of Fermi-excitations and Green functions of fermions are introduced. The electric current is derived as a function of potential difference on the contact between a nanotube and a normal metal. Deviations from Ohm law produced by electron-electron short-range repulsion as well as by the transverse quantization in single-wall nanotubes are discussed. The results are compared with experimental data.