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

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.