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

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.