Generalized Chern-Simons theory of composite fermions in bilayer Hall systems

Abstract

We present a field theory of Jain's composite fermion model, as generalized to the bilayer quantum Hall systems. We define operators that create composite fermions and write the Hamiltonian exactly in terms of these operators. This is seen to be a complex 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 the usual Chern-Simons theories, and plateaus are predicted at the same values of filling factors as Lopez and Fradkin and Halperin. But unlike the normal Chern-Simons theories, we obtain all features of the first-quantized wave functions including its phase, modulus, and correct Gaussian factors at the mean-field level. The familiar Jain relations for monolayers and the Halperin wave function for bilayers come out as special cases.