Quasi-particles in Fractional Quantum Hall Effect Edge Theories

TL;DR

This paper introduces a quasi-particle framework for fractional quantum Hall edge theories, identifying fundamental edge electrons and quasi-holes with specific charges and exclusion statistics, and deriving kinetic equations for charge transport.

Contribution

It presents a novel quasi-particle formulation for fractional quantum Hall edge states, including derivation of kinetic equations based on exclusion statistics.

Findings

Edge electrons have charge -e; quasi-holes have charge +e/m.

Derived kinetic equations for charge transport at fractional edges.

Discussed extensions to Jain series filling fractions.

Abstract

We propose a quasi-particle formulation of effective edge theories for the fractional quantum Hall effect. For the edge of a Laughlin state with filling fraction \nu=1/m, our fundamental quasi-particles are edge electrons of charge -e and edge quasi-holes of charge +e/m. These quasi-particles satisfy exclusion statistics in the sense of Haldane. We exploit algebraic properties of edge electrons to derive a kinetic equation for charge transport between a \nu=1/m fractional quantum Hall edge and a normal metal. We also analyze alternative `Boltzmann' equations that are directly based on the exclusion statistics properties of edge quasi-particles. Generalizations to more general filling fractions (Jain series) are briefly discussed.