Crossover from Luttinger liquid to Coulomb blockade regime in carbon nanotubes

TL;DR

This paper presents a theoretical framework for understanding the crossover from Luttinger liquid to Coulomb blockade behavior in carbon nanotubes, capturing experimental conductance oscillations and temperature-dependent regimes.

Contribution

The authors extend Luttinger liquid theory by including discrete spectra, providing a unified description of the crossover regime in 1D electron systems.

Findings

Conductance exhibits oscillating power-law behavior with gate voltage.

Crossover in zero-bias conductance occurs between two temperature regimes.

The model aligns with recent experimental observations.

Abstract

We develop a theoretical approach to the low-energy properties of 1D electron systems aimed to encompass the mixed features of Luttinger liquid and Coulomb blockade behavior observed in the crossover between the two regimes. For this aim we extend the Luttinger liquid description by incorporating the effects of a discrete single-particle spectrum. The intermediate regime is characterized by a power-law behavior of the conductance, but with an exponent oscillating with the gate voltage, in agreement with recent experimental observations. Our construction also accounts naturally for the existence of a crossover in the zero-bias conductance, mediating between two temperature ranges where the power-law behavior is preserved but with different exponent.