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

Levin, Michael; Son, Dam Thanh

doi:10.1103/PhysRevB.95.125120

Title: 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 ^[1]

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.

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

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

Grant/Contract Number:: SC0009924; DMR-1254741; FG02-13ER41958

OSTI ID:: 1595711

Alternate ID(s):: OSTI ID: 1347050

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

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 26 works

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Cited By (6)

Thermopower and Nernst measurements in a half-filled lowest Landau level Liu, Xiaoxue; Li, Tingxin; Zhang, Po Physical Review B, Vol. 97, Issue 24 https://doi.org/10.1103/physrevb.97.245425	journal	June 2018
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
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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