Currents and correlations in Luttinger liquids and carbon nanotubes at finite temperature and size: a bosonization study

TL;DR

This paper provides an exact bosonization-based analysis of finite-temperature and finite-size effects on currents and correlations in Luttinger liquids and carbon nanotubes, with applications to transport in Josephson junctions.

Contribution

It introduces a framework for exact calculation of correlation functions under boundary conditions modeling external leads, advancing understanding of transport in one-dimensional systems.

Findings

Exact correlation functions including finite-size and temperature effects.

Explicit computation of Josephson current and pairing profiles.

Demonstration of boundary conditions' impact on transport properties.

Abstract

We consider problems of one dimensional interacting fermions confined to a finite size, multichannel geometry. Concentrating on Luttinger liquids and carbon nanotubes, we use nontrivial boundary conditions to represent the effect of external leads, and apply our framework to transport problems in a Josephson junction setup. We present an exact computation of all correlation functions, including finite-size and temperature effects, for two sets of solvable boundary conditions. In all cases, we compute physical quantities like the Josephson current and the pairing order parameter profile.