Dirac composite fermion theory of general Jain sequences
Abstract
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.
- Publication Date:
- Research Org.:
- Univ. of Chicago, IL (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1819241
- Alternate Identifier(s):
- OSTI ID: 1821676
- Grant/Contract Number:
- FG02-13ER41958; SC0009924
- Resource Type:
- Published Article
- Journal Name:
- Physical Review Research
- Additional Journal Information:
- Journal Name: Physical Review Research Journal Volume: 3 Journal Issue: 3; Journal ID: ISSN 2643-1564
- Publisher:
- American Physical Society
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Fractional quantum Hall effect; Gravitons; Two-dimensional electron system; Bosonization; Duality; Effective field theory
Citation Formats
Nguyen, Dung Xuan, and Son, Dam Thanh. Dirac composite fermion theory of general Jain sequences. United States: N. p., 2021.
Web. doi:10.1103/PhysRevResearch.3.033217.
Nguyen, Dung Xuan, & Son, Dam Thanh. Dirac composite fermion theory of general Jain sequences. United States. https://doi.org/10.1103/PhysRevResearch.3.033217
Nguyen, Dung Xuan, and Son, Dam Thanh. Tue .
"Dirac composite fermion theory of general Jain sequences". United States. https://doi.org/10.1103/PhysRevResearch.3.033217.
@article{osti_1819241,
title = {Dirac composite fermion theory of general Jain sequences},
author = {Nguyen, Dung Xuan and Son, Dam Thanh},
abstractNote = {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.},
doi = {10.1103/PhysRevResearch.3.033217},
journal = {Physical Review Research},
number = 3,
volume = 3,
place = {United States},
year = {Tue Sep 07 00:00:00 EDT 2021},
month = {Tue Sep 07 00:00:00 EDT 2021}
}
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