Dirac composite fermion theory of general Jain sequences

We reconsider the composite fermion theory of general Jain's sequences with filling factor ν = N/(4N ± 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 a...

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Bibliographic Details
Published in:Physical review research 2021-09, Vol.3 (3), p.033217, Article 033217
Main Authors: Nguyen, Dung Xuan, Son, Dam Thanh
Format: Article
Language:English
Subjects:
Bosonization
Duality
Effective field theory
Fractional quantum Hall effect
Gravitons
Two-dimensional electron system
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Summary:We reconsider the composite fermion theory of general Jain's sequences with filling factor ν = N/(4N ± 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 ν = 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.
ISSN:2643-1564
2643-1564
DOI:10.1103/PhysRevResearch.3.033217