Nature of composite fermions and the role of particle-hole symmetry: A microscopic account

Ajit C. Balram, J. K. Jain

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Motivated by the issue of particle-hole symmetry for the composite fermion Fermi sea at the half-filled Landau level, Son has made an intriguing proposal [Phys. Rev. X 5, 031027 (2015)2160-330810.1103/PhysRevX.5.031027] that composite fermions are Dirac particles. We ask what features of the Dirac-composite fermion theory and its various consequences may be reconciled with the well-established microscopic theory of the fractional quantum Hall effect and the 12 state, which is based on nonrelativistic composite fermions. Starting from the microscopic theory, we derive the assertion of Son that the particle-hole transformation of electrons at filling factor ν=12 corresponds to an effective time-reversal transformation (i.e., {kj}→{-kj}) for composite fermions, and discuss how this connects to the absence of 2kF backscattering in the presence of a particle-hole symmetric disorder. By considering bare holes in various composite-fermion Λ levels (analogs of electronic Landau levels), we determine the Λ level spacing and find it to be very nearly independent of the Λ level index, consistent with a parabolic dispersion for the underlying composite fermions. Finally, we address the compatibility of the Chern-Simons theory with the lowest Landau level constraint, and find that the wave functions of the mean-field Chern-Simons theory, as well as a class of topologically similar wave functions, are surprisingly accurate when projected into the lowest Landau level. These considerations lead us to introduce a "normal form" for the unprojected wave functions of the n/(2pn-1) states that correctly capture the topological properties even without lowest Landau level projection.

Original languageEnglish (US)
Article number235152
JournalPhysical Review B
Issue number23
StatePublished - Jun 27 2016

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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