DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Particle-hole symmetry and electromagnetic response of a half-filled Landau level

Abstract

We derive exact physical consequences of particle-hole symmetry of the ν = 1/2 state of electrons in a strong magnetic field. We show that if the symmetry is not spontaneously broken, the Hall conductivity and the susceptibility satisfy an exact relationship, valid at any wave numbers and any frequencies much below the cyclotron frequency. The relationship holds for clean systems and also for systems with statistically particle-hole symmetric disorder. We work out the constraints this relationship imposes on the theory of the Dirac composite fermion. Here, we also argue that that the exact relationship is violated in the Halperin-Lee-Read (HLR) field theory and present an explicit calculation within a Galilean invariant mean-field approximation to the HLR theory to illustrate the breakdown.

Authors:
 [1];  [1]
  1. Univ. of Chicago, IL (United States)
Publication Date:
Research Org.:
Univ. of Chicago, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP); USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF); Simons Foundation
OSTI Identifier:
1595711
Alternate Identifier(s):
OSTI ID: 1347050
Grant/Contract Number:  
SC0009924; DMR-1254741; FG02-13ER41958
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 95; 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; Composite fermions; Dirac fermions; Fractional quantum Hall effect; Topological phases of matter

Citation Formats

Levin, Michael, and Son, Dam Thanh. Particle-hole symmetry and electromagnetic response of a half-filled Landau level. United States: N. p., 2017. Web. doi:10.1103/PhysRevB.95.125120.
Levin, Michael, & Son, Dam Thanh. Particle-hole symmetry and electromagnetic response of a half-filled Landau level. United States. https://doi.org/10.1103/PhysRevB.95.125120
Levin, Michael, and Son, Dam Thanh. Wed . "Particle-hole symmetry and electromagnetic response of a half-filled Landau level". United States. https://doi.org/10.1103/PhysRevB.95.125120. https://www.osti.gov/servlets/purl/1595711.
@article{osti_1595711,
title = {Particle-hole symmetry and electromagnetic response of a half-filled Landau level},
author = {Levin, Michael and Son, Dam Thanh},
abstractNote = {We derive exact physical consequences of particle-hole symmetry of the ν = 1/2 state of electrons in a strong magnetic field. We show that if the symmetry is not spontaneously broken, the Hall conductivity and the susceptibility satisfy an exact relationship, valid at any wave numbers and any frequencies much below the cyclotron frequency. The relationship holds for clean systems and also for systems with statistically particle-hole symmetric disorder. We work out the constraints this relationship imposes on the theory of the Dirac composite fermion. Here, we also argue that that the exact relationship is violated in the Halperin-Lee-Read (HLR) field theory and present an explicit calculation within a Galilean invariant mean-field approximation to the HLR theory to illustrate the breakdown.},
doi = {10.1103/PhysRevB.95.125120},
journal = {Physical Review B},
number = 12,
volume = 95,
place = {United States},
year = {Wed Mar 15 00:00:00 EDT 2017},
month = {Wed Mar 15 00:00:00 EDT 2017}
}

Journal Article:

Citation Metrics:
Cited by: 26 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

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


Explicit Derivation of Duality between a Free Dirac Cone and Quantum Electrodynamics in ( 2 + 1 ) Dimensions
journal, June 2016


Hall Viscosity and Electromagnetic Response
journal, February 2012


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


Experimental demonstration of a Fermi surface at one-half filling of the lowest Landau level
journal, December 1993


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


Composite fermions with orbital magnetization
journal, October 1996


Shift and spin vector: New topological quantum numbers for the Hall fluids
journal, August 1992


Dual Dirac Liquid on the Surface of the Electron Topological Insulator
journal, November 2015


Geometry of fractional quantum Hall fluids
journal, September 2014


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


On Anyon Superconductivity
journal, July 1989

  • Chen, Yi-Hong; Wilczek, Frank; Witten, Edward
  • International Journal of Modern Physics B, Vol. 03, Issue 07
  • DOI: 10.1142/S0217979289000725

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


Particle-Hole Symmetry and the Pfaffian State
journal, December 2007


How real are composite fermions?
journal, December 1993


Particle-Hole Symmetry and the ν = 5 2 Quantum Hall State
journal, December 2007


Fractional Quantum Hall Effect in a Curved Space: Gravitational Anomaly and Electromagnetic Response
journal, July 2014


Spacetime symmetries of the quantum Hall effect
journal, February 2015


Finite-wave-vector electromagnetic response of fractional quantized Hall states
journal, December 1993


Hydrodynamic Relations in Superconductivity
journal, August 1989


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


Kubo formulas for viscosity: Hall viscosity, Ward identities, and the relation with conductivity
journal, December 2012


Hall viscosity, orbital spin, and geometry: Paired superfluids and quantum Hall systems
journal, August 2011


Particle-Vortex Duality from 3D Bosonization
journal, September 2016


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


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


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


Detection of composite fermions by magnetic focusing
journal, March 1994


Nonabelions in the fractional quantum hall effect
journal, August 1991


On Anyon Superconductivity
journal, September 1989

  • Chen, Yi-Hong; Wilczek, Frank; Witten, Edward
  • International Journal of Modern Physics A, Vol. 04, Issue 15
  • DOI: 10.1142/s0217751x89001631

How real are composite fermions?
journal, May 1995


Particle-Vortex Duality from 3D Bosonization
text, January 2016

  • Karch, Andreas; Tong, David
  • Apollo - University of Cambridge Repository
  • DOI: 10.17863/cam.6036

Particle-hole symmetry and the Pfaffian state
text, January 2007


Spacetime Symmetries of the Quantum Hall Effect
text, January 2014


Is the Composite Fermion a Dirac Particle?
text, January 2015


The half-filled Landau level: the case for Dirac composite fermions
text, January 2015


Thermoelectric transport signatures of Dirac composite fermions in the half-filled Landau level
text, January 2015


Finite-Wavevector Electromagnetic Response of Fractional Quantized Hall States
text, January 1993


Works referencing / citing this record:

Thermopower and Nernst measurements in a half-filled lowest Landau level
journal, June 2018


Berry phase of the composite-fermion Fermi sea: Effect of Landau-level mixing
journal, August 2018


Weiss oscillations and particle-hole symmetry at the half-filled Landau level
text, January 2016


Bimetric Theory of Fractional Quantum Hall States
text, January 2017


Berry phase of the composite-fermion Fermi Sea: Effect of Landau-level mixing
text, January 2018