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

Levin, Michael; Son, Dam Thanh

doi:10.1103/PhysRevB.95.125120

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

Journal Article · Wed Mar 15 00:00:00 EDT 2017 · Physical Review B

DOI:https://doi.org/10.1103/PhysRevB.95.125120· OSTI ID:1595711

Levin, Michael ^[1]; Son, Dam Thanh ^[2]

Univ. of Chicago, IL (United States); University of Chicago
Univ. of Chicago, IL (United States)

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.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Chicago, IL (United States)

Sponsoring Organization:: National Science Foundation (NSF); Simons Foundation; USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)

Grant/Contract Number:: SC0009924

OSTI ID:: 1595711

Alternate ID(s):: OSTI ID: 1535884
OSTI ID: 1347050

Journal Information:: Physical Review B, Journal Name: Physical Review B Journal Issue: 12 Vol. 95; ISSN 2469-9950; ISSN PRBMDO

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Berry phase of the composite-fermion Fermi sea: Effect of Landau-level mixing Pu, Songyang; Fremling, Mikael; Jain, J. K. Physical Review B, Vol. 98, Issue 7 https://doi.org/10.1103/physrevb.98.075304	journal	August 2018
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Dirac Fermion Hierarchy of Composite Fermi Liquids Wang, Jie Physical Review Letters, Vol. 122, Issue 25 https://doi.org/10.1103/physrevlett.122.257203	journal	June 2019
Particle-Hole Symmetry in the Fermion-Chern-Simons and Dirac Descriptions of a Half-Filled Landau Level Wang, Chong; Cooper, Nigel R.; Halperin, Bertrand I. Physical Review X, Vol. 7, Issue 3 https://doi.org/10.1103/physrevx.7.031029	journal	August 2017
Bimetric Theory of Fractional Quantum Hall States Gromov, Andrey; Son, Dam Thanh Physical Review X, Vol. 7, Issue 4 https://doi.org/10.1103/physrevx.7.041032	journal	November 2017
Weiss oscillations and particle-hole symmetry at the half-filled Landau level Cheung, Alfred K. C.; Raghu, S.; Mulligan, Michael arXiv https://doi.org/10.48550/arxiv.1611.08910	text	January 2016
Bimetric Theory of Fractional Quantum Hall States Gromov, Andrey; Son, Dam Thanh arXiv https://doi.org/10.48550/arxiv.1705.06739	text	January 2017
Berry phase of the composite-fermion Fermi Sea: Effect of Landau-level mixing Pu, Songyang; Fremling, Mikael; Jain, J. K. arXiv https://doi.org/10.48550/arxiv.1805.09237	text	January 2018
Dirac Fermion Hierarchy of Composite Fermi Liquids Wang, Jie arXiv https://doi.org/10.48550/arxiv.1808.07529	text	January 2018

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