Generalised Chern-Simons Theory of Composite Fermions in Bilayer Hall Systems

TL;DR

This paper develops a generalized field theory for composite fermions in bilayer quantum Hall systems, capturing wavefunction features and predicting quantum Hall plateaus with a novel complexified Chern-Simons approach.

Contribution

It introduces a complexified Chern-Simons field theory for bilayer systems that reproduces wavefunction details and extends Jain and Halperin states.

Findings

Predicts quantum Hall plateaus at known filling factors

Reproduces wavefunction phase, modulus, and Gaussian factors

Generalizes Jain and Halperin wavefunctions to bilayer systems

Abstract

We present a field theory of Jain's composite fermion model as generalised to the bilayer quantum Hall systems. We define operators which create composite fermions and write the Hamiltonian exactly in terms of these operators. This is seen to be a complexified version of the familiar Chern Simons theory. In the mean-field approximation, the composite fermions feel a modified effective magnetic field exactly as happens in usual Chern Simons theories, and plateaus are predicted at the same values of filling factors as Lopez and Fradkin and Halperin . But unlike normal Chern Simons theories, we obtain all features of the first-quantised wavefunctions including its phase, modulus and correct gaussian factors at the mean field level. The familiar Jain relations for monolayers and the Halperin wavefunction for bilayers come out as special cases.