Fermionic Chern-Simons theory for the Fractional Quantum Hall Effect in Bilayers

TL;DR

This paper extends fermionic Chern-Simons theory to bilayer systems in the fractional quantum Hall effect, predicting collective excitation spectra, optical properties, and the role of gapless modes in interlayer coherence.

Contribution

It introduces a generalized fermionic Chern-Simons framework for bilayer FQHE, including new predictions for collective modes and interlayer coherence phenomena.

Findings

Spectrum of collective excitations has a gap for (m,m,n) states.

(m,m,m) states exhibit a gapless mode linked to interlayer coherence.

Calculated Hall conductance and quasiparticle properties.

Abstract

We generalize the fermion Chern-Simons theory for the Fractional Hall Effect (FQHE) which we developed before, to the case of bilayer systems. We study the complete dynamic response of these systems and predict the experimentally accessible optical properties. In general, for the so called $(m, m, n)$ states, we find that the spectrum of collective excitations has a gap, and the wave function has the Jastrow-Slater form, with the exponents determined by the coefficients $m$, and $n$. We also find that the $(m,m,m)$ states, {\it i.~e.~}, those states whose filling fraction is $1\over m$, have a gapless mode which may be related with the spontaneous appearance of the interlayer coherence. Our results also indicate that the gapless mode makes a contribution to the wave function of the $(m,m,m)$ states analogous to the phonon contribution to the wave function of superfluid $\rm{He}_4$. We calculate the Hall conductance, and the charge and statistics of the quasiparticles. We also present an $SU(2)$ generalization of this theory relevant to spin unpolarized or partially polarized single layers.