Dirac Composite Fermion Theory of General Jain's Sequences

Abstract

We reconsider the composite fermion theory of general Jain's sequences with filling factor $\nu =N/(4N\pm 1)$. We show that Goldman and Fradkin's 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 (or modes) which already exists in the Fermi liquid state at $\nu =1/4$. We interpret the additional mode as an internal degree of freedom of the composite fermion, related to area-preserving deformations of the elementary droplet built up from electrons and correlation holes. 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. We show that the charge density in the model satisfies the long-wavelength version of the Girvin-MacDonald-Platzman algebra.

arXiv commentAccepted version to Physical Review Research, added a derivation of Haldane bound using lowest Landau level Ward's identities,comments are welcome!

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