Composite fermion nonlinear sigma models

Journal Article · Mon Sep 13 00:00:00 EDT 2021 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.104.125119· OSTI ID:1850797

Lee, Chao-Jung ^[1]; Kumar, Prashant ^[2]; Mulligan, Michael ^[3]

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1. California Institute of Technology (CalTech), Pasadena, CA (United States); OSTI
2. Princeton Univ., NJ (United States)
3. Univ. of California, Riverside, CA (United States)

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 ≠ $$\frac1{2}$$$$\frac{e^2}{h}$$ . 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.

• Research Organization: Princeton University, NJ (United States); University of California, Riverside, CA (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• Grant/Contract Number: SC0002140; SC0020007
• OSTI ID: 1850797
• Journal Information: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 12 Vol. 104; ISSN 2469-9950; ISSN PRBMDO
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
Composite fermions
Electrical conductivity
Fractional quantum Hall effect
Integer quantum Hall effect
Localization
Materials Science
Physics
Sigma models
Topological phase transition