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Composite fermion nonlinear sigma models

Lee, Chao-Jung and Kumar, Prashant and Mulligan, Michael (2021) Composite fermion nonlinear sigma models. Physical Review B, 104 (12). Art. No. 125119. ISSN 2469-9950. doi:10.1103/physrevb.104.125119.

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We study particle-hole symmetry at the integer quantum Hall plateau transition using composite fermion mean-field theory. Because this theory implicitly includes some electron-electron interactions, it also has applications to certain fractional quantum Hall plateau transitions. Previous work [P. Kumar et al., Phys. Rev. B 100, 235124 (2019)] using this approach showed that the diffusive quantum criticality of this transition is described by a nonlinear sigma model with topological θ = π term. This result, which holds for both the Dirac and Halperin, Lee, and Read composite fermion theories, signifies an emergent particle-hole (reflection) symmetry of the integer (fractional) quantum Hall transition. Here we consider the stability of this result to various particle-hole symmetry-violating perturbations. In the presence of quenched disorder that preserves particle-hole symmetry, we find that finite longitudinal conductivity at this transition requires the vanishing of a symmetry-violating composite fermion effective mass, which if present would generally lead to θ ≠ π and a corresponding violation of particle-hole symmetric electrical transport σ_(xy) ≠ 1/2 e²/h. When the disorder does not preserve particle-hole symmetry, we find that θ can vary continuously within the diffusive regime. Our results call for further study of the universality of the quantum Hall plateau transition.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Lee, Chao-Jung0000-0003-3339-1522
Kumar, Prashant0000-0003-4622-0917
Additional Information:© 2021 American Physical Society. (Received 16 February 2021; accepted 27 August 2021; published 13 September 2021) We thank S. Raghu for useful conversations and correspondence. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award No. DE-SC0020007. M.M. acknowledges the generous hospitality of the Stanford Institute for Theoretical Physics and support provided by the Moore Foundation for this work. P.K. is supported by DOE-BES Grant No. DE-SC0002140.
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0020007
Gordon and Betty Moore FoundationUNSPECIFIED
Department of Energy (DOE)DE-SC0002140
Issue or Number:12
Record Number:CaltechAUTHORS:20210927-213256124
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:111062
Deposited By: George Porter
Deposited On:27 Sep 2021 22:31
Last Modified:27 Sep 2021 22:31

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