Theory of "charge" measured by the shot noise experiments in the fractional quantum Hall states

TL;DR

This paper presents a theoretical analysis of shot noise in fractional quantum Hall states at filling factor 2/5, revealing how measured charge depends on temperature and clarifying the distinction between quasiparticle charge and effective charge.

Contribution

It introduces a theory explaining the temperature-dependent measurement of charge via shot noise in fractional quantum Hall states, resolving discrepancies in experimental observations.

Findings

At zero temperature, shot noise measures the filling factor times electron charge, not the quasiparticle charge.

At higher temperatures, quasiparticles with fractional charge dominate the shot noise.

The theory aligns with recent experimental results by Chung et al.

Abstract

Shot noise at filling factor $\nu=2/5$ is investigated theoretically. It is argued that the "charge" $e^*$ measured by the noise at zero temperature is not the quasiparticle charge but simply the filling factor times the electron charge $e$, namely $e^*=2e/5$. At higher temperature quasiparticles with charge $e^*=\pm e/5$ begin to contribute to the backscattering, and the shot noise gives charge $e^*=e/5$. This theory explains recent experiment by Chung et al. [Phys. Rev. Lett. \textbf{91} (2003) 216804.