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Title: Composite fermion nonlinear sigma models

Abstract

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 σxy ≠ $$\frac1{2}$$$$\frac{e^2}{h}$$ . 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.

Authors:
ORCiD logo [1];  [2];  [3]
  1. California Institute of Technology (CalTech), Pasadena, CA (United States)
  2. Princeton Univ., NJ (United States)
  3. Univ. of California, Riverside, CA (United States)
Publication Date:
Research Org.:
Princeton Univ., NJ (United States); Univ. of California, Riverside, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1850797
Grant/Contract Number:  
SC0002140; SC0020007
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review. B
Additional Journal Information:
Journal Volume: 104; Journal Issue: 12; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Materials Science; Physics; Composite fermions; Electrical conductivity; Fractional quantum Hall effect; Integer quantum Hall effect; Localization; Topological phase transition; Sigma models

Citation Formats

Lee, Chao-Jung, Kumar, Prashant, and Mulligan, Michael. Composite fermion nonlinear sigma models. United States: N. p., 2021. Web. doi:10.1103/physrevb.104.125119.
Lee, Chao-Jung, Kumar, Prashant, & Mulligan, Michael. Composite fermion nonlinear sigma models. United States. https://doi.org/10.1103/physrevb.104.125119
Lee, Chao-Jung, Kumar, Prashant, and Mulligan, Michael. Mon . "Composite fermion nonlinear sigma models". United States. https://doi.org/10.1103/physrevb.104.125119. https://www.osti.gov/servlets/purl/1850797.
@article{osti_1850797,
title = {Composite fermion nonlinear sigma models},
author = {Lee, Chao-Jung and Kumar, Prashant and Mulligan, Michael},
abstractNote = {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 σxy ≠ $\frac1{2}$$\frac{e^2}{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.},
doi = {10.1103/physrevb.104.125119},
journal = {Physical Review. B},
number = 12,
volume = 104,
place = {United States},
year = {Mon Sep 13 00:00:00 EDT 2021},
month = {Mon Sep 13 00:00:00 EDT 2021}
}

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