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arXiv · 2105.02092

Dirac Composite Fermion Theory of General Jain's Sequences

Dung Xuan Nguyen·Dam Thanh Son
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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.

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Dung Xuan Nguyen, Dam Thanh Son. 2021-05-05. Dirac Composite Fermion Theory of General Jain's Sequences. https://doi.org/10.1103/physrevresearch.3.033217

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