Measuring the Luttinger liquid parameter with shot noise

TL;DR

This paper proposes a method to determine the Luttinger liquid parameter in 1D interacting electron systems by analyzing low-frequency shot noise generated by quantum point contacts under non-equilibrium conditions.

Contribution

It introduces a novel noise measurement technique to accurately extract the Luttinger liquid parameter $K$ in 1D systems, linking noise characteristics to electron interactions.

Findings

Zero-frequency noise depends on the Luttinger parameter $K$.

The method allows extraction of $K$ from noise measurements.

Noise characteristics vary with QPC transparency and voltage settings.

Abstract

We explore the low-frequency noise of interacting electrons in a one-dimensional structure (quantum wire or interaction-coupled edge states) with counterpropagating modes, assuming a single channel in each direction. The system is driven out of equilibrium by a quantum point contact (QPC) with an applied voltage, which induces a double-step energy distribution of incoming electrons on one side of the device. A second QPC serves to explore the statistics of outgoing electrons. We show that measurement of a low-frequency noise in such a setup allows one to extract the Luttinger liquid constant $K$ which is the key parameter characterizing an interacting 1D system. We evaluate the dependence of the zero-frequency noise on $K$ and on parameters of both QPCs (transparencies and voltages).