Exact non-equilibrium DC shot noise in Luttinger liquids and fractional quantum Hall devices

TL;DR

This paper provides an exact calculation of zero-temperature DC shot noise in Luttinger liquids and fractional quantum Hall devices, revealing a relation between noise, current, and conductance that can confirm fractional quasiparticle charge.

Contribution

It introduces an exact method to compute shot noise in interacting one-dimensional systems using integrability and a quasiparticle basis, extending the Landauer approach.

Findings

Derived a simple relation between shot noise, current, and conductance.

Predicted experimental signatures of fractional charge in quantum Hall devices.

Validated the approach for out-of-equilibrium steady states in integrable models.

Abstract

A point contact in a Luttinger liquid couples the left- and right-moving channels, producing shot noise. We calculate exactly the DC shot noise at zero temperature in the out-of-equilibrium steady state where current is flowing. Integrability of the interaction ensures the existence of a quasiparticle basis where quasiparticles scatter ``one by one'' off the point contact. This enables us to apply a direct generalization of the Landauer approach to shot noise to this interacting model. We find a simple relation of the noise to the current and the differential conductance. Our results should be experimentally-testable in a fractional quantum Hall effect device, providing a clear signal of the fractional charge of the Laughlin quasiparticles.