Dirac Composite Fermion Theory of General Jain's Sequences

TL;DR

This paper revisits the Dirac composite fermion theory for Jain sequences, resolving a key contradiction by introducing a gapped chiral mode, and successfully reproduces known physical properties like the structure factor and Hall conductivity.

Contribution

It proposes an extended Dirac composite fermion model that incorporates a gapped chiral mode to satisfy physical bounds and symmetries in Jain sequences.

Findings

Violates Haldane bound without additional mode

Introduces a gapped chiral mode to fix the theory

Reproduces Wen-Zee shift and Galilean invariance

Abstract

We reconsider the composite fermion theory of general Jain's sequences with filling factor $\nu=N/(4N\pm1)$. 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.