Quasi-Fermi Distribution and Resonant Tunneling of Quasiparticles with Fractional Charges

TL;DR

This paper investigates the resonant tunneling behavior of fractionally charged quasiparticles in the fractional quantum Hall effect, revealing a quasi-Fermi distribution and a new selection rule affecting tunneling resonance.

Contribution

It introduces a novel understanding of quasiparticle tunneling, showing the quasi-Fermi distribution and a selection rule based on electron occupancy at impurities.

Findings

Quasiparticles exhibit a quasi-Fermi distribution near the Fermi energy.

Resonance suppression occurs unless an integer number of electrons occupy the impurity.

The results explain the scaling behavior in mesoscopic conductivity fluctuations.

Abstract

We study the resonant tunneling of quasiparticles through an impurity between the edges of a Fractional Quantum Hall sample. We show that the one-particle momentum distribution of fractionally charged edge quasiparticles has a quasi-Fermi character. The density of states near the quasi-Fermi energy at zero temperature is singular due to the statistical interaction of quasiparticles. Another effect of this interaction is a new selection rule for the resonant tunneling of fractionally charged quasiparticles: the resonance is suppressed unless an integer number of {\em electrons} occupies the impurity. It allows a new explanation of the scaling behavior observed in the mesoscopic fluctuations of the conductivity in the FQHE.