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

Michael Levin, Dam Thanh Son

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


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 number and 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. 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.

Original languageEnglish
Article number125120
JournalPhysical Review B
Issue number12
StatePublished - 15 Mar 2017
Externally publishedYes

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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