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Quasi-particles in Fractional Quantum Hall Effect Edge Theories

R. A. J. van Elburg·K. Schoutens
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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 ν=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 ν=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.

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R. A. J. van Elburg, K. Schoutens. 1998-11-12. Quasi-particles in Fractional Quantum Hall Effect Edge Theories. https://doi.org/10.1103/physrevb.58.15704

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