skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Composite fermion Hall conductivity and the half-filled Landau level

Abstract

We consider the Hall conductivity of composite fermions in the theory of Halperin, Lee, and Read (HLR). We present a fully quantum mechanical numerical calculation that shows, under suitable conditions, the HLR theory exhibits a particle-hole symmetric dc electrical Hall response in the presence of quenched disorder. Remarkably, this response of the HLR theory remains robust even when the disorder range is of the order of the Fermi wavelength. We nd that deviations from particle-hole symmetric response can appear in the ac Hall conductivity at frequencies su ciently large compared to the inverse system size. Our results agree with a recent semi-classical analysis by Wang et al., Phys. Rev. X 7, 031029 (2017) and complement the arguments based on the fully quantum-mechanical model by Kumar et al., Phys. Rev. B 98, 11505 (2018). These results provide further evidence that the HLR theory is compatible with an emergent particle-hole symmetry.

Authors:
 [1];  [2];  [3]
  1. Stanford Univ., CA (United States)
  2. Stanford Univ., CA (United States); SLAC National Accelerator Lab., Menlo Park, CA (United States)
  3. Univ. of California, Riverside, CA (United States)
Publication Date:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1532379
Alternate Identifier(s):
OSTI ID: 1546223
Grant/Contract Number:  
AC02-76SF00515
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 99; Journal Issue: 23; 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

Citation Formats

Kumar, Prashant, Raghu, S., and Mulligan, Michael. Composite fermion Hall conductivity and the half-filled Landau level. United States: N. p., 2019. Web. doi:10.1103/physrevb.99.235114.
Kumar, Prashant, Raghu, S., & Mulligan, Michael. Composite fermion Hall conductivity and the half-filled Landau level. United States. doi:10.1103/physrevb.99.235114.
Kumar, Prashant, Raghu, S., and Mulligan, Michael. Fri . "Composite fermion Hall conductivity and the half-filled Landau level". United States. doi:10.1103/physrevb.99.235114. https://www.osti.gov/servlets/purl/1532379.
@article{osti_1532379,
title = {Composite fermion Hall conductivity and the half-filled Landau level},
author = {Kumar, Prashant and Raghu, S. and Mulligan, Michael},
abstractNote = {We consider the Hall conductivity of composite fermions in the theory of Halperin, Lee, and Read (HLR). We present a fully quantum mechanical numerical calculation that shows, under suitable conditions, the HLR theory exhibits a particle-hole symmetric dc electrical Hall response in the presence of quenched disorder. Remarkably, this response of the HLR theory remains robust even when the disorder range is of the order of the Fermi wavelength. We nd that deviations from particle-hole symmetric response can appear in the ac Hall conductivity at frequencies su ciently large compared to the inverse system size. Our results agree with a recent semi-classical analysis by Wang et al., Phys. Rev. X 7, 031029 (2017) and complement the arguments based on the fully quantum-mechanical model by Kumar et al., Phys. Rev. B 98, 11505 (2018). These results provide further evidence that the HLR theory is compatible with an emergent particle-hole symmetry.},
doi = {10.1103/physrevb.99.235114},
journal = {Physical Review B},
number = 23,
volume = 99,
place = {United States},
year = {2019},
month = {6}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 2 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Composite-fermion Hall conductance at ν=
journal, June 1997


Theory of the half-filled Landau level
journal, March 1993


Particle-hole symmetry and the composite Fermi liquid
journal, October 2015

  • Barkeshli, Maissam; Mulligan, Michael; Fisher, Matthew P. A.
  • Physical Review B, Vol. 92, Issue 16
  • DOI: 10.1103/PhysRevB.92.165125

Is the Composite Fermion a Dirac Particle?
journal, September 2015


Particle-Hole Symmetry in the Fermion-Chern-Simons and Dirac Descriptions of a Half-Filled Landau Level
journal, August 2017


Topological phase transition underpinning particle-hole symmetry in the Halperin-Lee-Read theory
journal, September 2018


Universal Conductivity at the Quantum Hall Liquid to Insulator Transition
journal, May 1995


Weiss oscillations and particle-hole symmetry at the half-filled Landau level
journal, June 2017


Particle-hole symmetry and electromagnetic response of a half-filled Landau level
journal, March 2017


Composite Fermi liquids in the lowest Landau level
journal, December 2016


Thermoelectric Transport Signatures of Dirac Composite Fermions in the Half-Filled Landau Level
journal, August 2016


Nature of composite fermions and the role of particle-hole symmetry: A microscopic account
journal, June 2016


Incompressible Paired Hall State, Stripe Order, and the Composite Fermion Liquid Phase in Half-Filled Landau Levels
journal, May 2000


The half-filled Landau level: The case for Dirac composite fermions
journal, April 2016


Scaling Theory of Localization: Absence of Quantum Diffusion in Two Dimensions
journal, March 1979


Spin-Orbit Interaction and Magnetoresistance in the Two Dimensional Random System
journal, February 1980

  • Hikami, S.; Larkin, A. I.; Nagaoka, Y.
  • Progress of Theoretical Physics, Vol. 63, Issue 2
  • DOI: 10.1143/PTP.63.707