Measuring Luttinger Liquid Correlations from Charge Fluctuations in a Nanoscale Structure

TL;DR

This paper proposes an experimental method to observe Luttinger liquid behavior in a one-dimensional nanostructure through charge fluctuation measurements, avoiding transport measurement complications.

Contribution

It introduces a novel experimental setup combining a quantum box and wire to detect Luttinger liquid correlations via charge fluctuations, with theoretical predictions of distinctive scaling behaviors.

Findings

Differential capacitance shows Luttinger liquid scaling with temperature.

Setup effectively models a Luttinger liquid interacting with a Kondo impurity.

Predicted charge fluctuation signatures are experimentally accessible.

Abstract

We suggest an experiment to study Luttinger liquid behavior in a one-dimensional nanostructure, avoiding the usual complications associated with transport measurements. The proposed setup consists of a quantum box, biased by a gate voltage, and side-coupled to a quantum wire by a point contact. Close to the degeneracy points of the Coulomb blockaded box, and in the presence of a magnetic field sufficiently strong to spin polarize the electrons, the setup can be described as a Luttinger liquid interacting with an effective Kondo impurity. Using exact nonperturbative techniques we predict that the differential capacitance of the box will exhibit distinctive Luttinger liquid scaling with temperature and gate voltage.