Dirac Composite Fermion Theory of General Jain's Sequences

We reconsider the composite fermion theory of general Jain's sequences with filling factor N/(4N+1). We show that the previous proposal of a Dirac composite fermion leads to a violation of the Haldane bound on the coefficient of the static structure factor. To resolve this apparent contradiction, we add to the effective theory a gapped chiral mode that already exists in the Fermi liquid state at 1/4. We interpret the additional mode as an internal degree of freedom of the composite fermion In addition to providing a suitable static structure factor, our model also gives the expected Wen-Zee shift and a Hall conductivity that manifests Galilean invariance. The extra mode can be detected by circular polarized Raman scattering experiments.