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Title: Topological phase transition underpinning particle-hole symmetry in the Halperin-Lee-Read theory

Abstract

We present that long wavelength descriptions of a half-filled lowest Landau level (ν = 1/2) must be consistent with the experimental observation of particle-hole (PH) symmetry. The traditional description of the ν = 1/2 state pioneered by Halperin, Lee, and Read (HLR) naively appears to break PH symmetry. However, recent studies have shown that the HLR theory with weak quenched disorder can exhibit an emergent PH symmetry. We find that such inhomogeneous configurations of the ν = 1/2 fluid, when described by HLR mean-field theory, are tuned to a topological phase transition between an integer quantum Hall state and an insulator of composite fermions with a dc Hall conductivity σ$$(cf)\atop{xy}$$ = -$$\frac{1}{2}$$ $$\frac{e2}{h}$$. Finally, our observations help explain why the HLR theory exhibits PH symmetric dc response.

Authors:
 [1];  [2];  [3]
  1. Stanford Univ., CA (United States). Stanford Institute for Theoretical Physics
  2. Univ. of California, Riverside, CA (United States). Department of Physics and Astronomy
  3. Stanford Univ., CA (United States). Stanford Institute for Theoretical Physics; SLAC National Accelerator Lab., Menlo Park, 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) (SC-22)
OSTI Identifier:
1475409
Alternate Identifier(s):
OSTI ID: 1468849
Grant/Contract Number:  
AC02-76SF00515
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 98; Journal Issue: 11; 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, Mulligan, Michael, and Raghu, S. Topological phase transition underpinning particle-hole symmetry in the Halperin-Lee-Read theory. United States: N. p., 2018. Web. doi:10.1103/physrevb.98.115105.
Kumar, Prashant, Mulligan, Michael, & Raghu, S. Topological phase transition underpinning particle-hole symmetry in the Halperin-Lee-Read theory. United States. doi:10.1103/physrevb.98.115105.
Kumar, Prashant, Mulligan, Michael, and Raghu, S. Wed . "Topological phase transition underpinning particle-hole symmetry in the Halperin-Lee-Read theory". United States. doi:10.1103/physrevb.98.115105. https://www.osti.gov/servlets/purl/1475409.
@article{osti_1475409,
title = {Topological phase transition underpinning particle-hole symmetry in the Halperin-Lee-Read theory},
author = {Kumar, Prashant and Mulligan, Michael and Raghu, S.},
abstractNote = {We present that long wavelength descriptions of a half-filled lowest Landau level (ν = 1/2) must be consistent with the experimental observation of particle-hole (PH) symmetry. The traditional description of the ν = 1/2 state pioneered by Halperin, Lee, and Read (HLR) naively appears to break PH symmetry. However, recent studies have shown that the HLR theory with weak quenched disorder can exhibit an emergent PH symmetry. We find that such inhomogeneous configurations of the ν = 1/2 fluid, when described by HLR mean-field theory, are tuned to a topological phase transition between an integer quantum Hall state and an insulator of composite fermions with a dc Hall conductivity σ$(cf)\atop{xy}$ = -$\frac{1}{2}$ $\frac{e2}{h}$. Finally, our observations help explain why the HLR theory exhibits PH symmetric dc response.},
doi = {10.1103/physrevb.98.115105},
journal = {Physical Review B},
number = 11,
volume = 98,
place = {United States},
year = {2018},
month = {9}
}

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Cited by: 5 works
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Works referenced in this record:

Parton construction of a wave function in the anti-Pfaffian phase
journal, July 2018


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


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


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


Universality and phase diagram around half-filled Landau levels
journal, December 1996


Ground State of Two-Dimensional Electrons in Strong Magnetic Fields and 1 3 Quantized Hall Effect
journal, April 1983


Presence of quantum diffusion in two dimensions: Universal resistance at the superconductor-insulator transition
journal, January 1990


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


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


Integer quantum Hall transition: An alternative approach and exact results
journal, September 1994

  • Ludwig, Andreas W. W.; Fisher, Matthew P. A.; Shankar, R.
  • Physical Review B, Vol. 50, Issue 11
  • DOI: 10.1103/PhysRevB.50.7526

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


A Different View of the Quantum Hall Plateau-to-Plateau Transitions
journal, July 1997


Erratum: Fractional charge and zero modes for planar systems in a magnetic field
journal, April 1986


Numerical exploration of trial wave functions for the particle-hole-symmetric Pfaffian
journal, August 2018


A duality web in 2 + 1 dimensions and condensed matter physics
journal, November 2016


Metallic phase of the quantum Hall system at even-denominator filling fractions
journal, October 1992


Model for a Quantum Hall Effect without Landau Levels: Condensed-Matter Realization of the "Parity Anomaly"
journal, October 1988


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


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


Pairing of particle-hole symmetric composite fermions in half-filled Landau level
journal, October 2016


Non-Fermi liquid fixed point in 2 + 1 dimensions
journal, April 1994


Fractional charge and zero modes for planar systems in a magnetic field
journal, May 1984


Gravitational anomalies
journal, April 1984


Experimental evidence for composite fermions
journal, May 1997


Quantized Hall conductivity in two dimensions
journal, May 1981


Percolation, quantum tunnelling and the integer Hall effect
journal, May 1988


Emergent particle-hole symmetry in the half-filled Landau level
journal, August 2016


Fractional quantum Hall effect and Chern-Simons gauge theories
journal, September 1991


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


Pairing instabilities of Dirac composite fermions
journal, September 2016

  • Milovanović, M. V.; Ćirić, M. Dimitrijević; Juričić, V.
  • Physical Review B, Vol. 94, Issue 11
  • DOI: 10.1103/PhysRevB.94.115304

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

Ground state of a spin-½ charged particle in a two-dimensional magnetic field
journal, June 1979


Composite Dirac Liquids: Parent States for Symmetric Surface Topological Order
journal, February 2015


Composite-fermion approach for the fractional quantum Hall effect
journal, July 1989


Universal Conductance at the Superconductor-Insulator Transition
journal, March 1990


Particle-hole symmetry in the anomalous quantum Hall effect
journal, May 1984


Levitation of Extended-State Bands in a Strong Magnetic Field
journal, June 1984


Gauge Noninvariance and Parity Nonconservation of Three-Dimensional Fermions
journal, January 1984


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


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