Chern-Simons Theory of Fractional Quantum Hall Effect in (Pseudo) Massless Dirac Electrons

TL;DR

This paper develops an effective field theory for (pseudo) Dirac electrons in 2D, explaining fractional quantum Hall effects with fractional charges and statistics, based on a microscopic Hamiltonian and gauge transformations.

Contribution

It introduces a novel derivation of the effective field theory for fractional quantum Hall states in (pseudo) Dirac systems from microscopic models.

Findings

Quantized Hall conductance: σ_xy = (e^2/h)(2k-1)

Existence of topological excitations with fractional charge

Fractional statistics of excitations

Abstract

We derive the effective field theory from the microscopic Hamiltonian of interacting two-dimensional (pseudo) Dirac electrons by performing a statistic gauge transformation. The quantized Hall conductance are expected to be $\sigma_{xy}=\frac{e^2}{h}(2k-1)$ with $k$ is arbitrary integer. There are also topological excitations which have fractional charge and obey fractional statistics.