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Nonlinear σ model for partially polarized quantum Hall states

T. H. Hansson and A. Karlhede

J. M. Leinaas

  • Department of Physics, Stockholm University, Box 6730, S-11385 Stockholm, Sweden and Centre for Advanced Study, P.O. Box 7606 Skillebekk, 0205 Oslo, Norway

  • Institute of Physics, University of Oslo, P.O. Box 1048 Blindern, N-0316 Oslo, Norway and Centre for Advanced Study, P.O. Box 7606 Skillebekk, 0205 Oslo, Norway

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Phys. Rev. B 54, R11110(R) – Published 15 October, 1996

DOI: https://doi.org/10.1103/PhysRevB.54.R11110

Abstract

We consider a two-component quantum Hall system within a Landau-Ginzburg theory with two Chern-Simons gauge fields. From this theory we derive a sigma model covariantly coupled to one Chern-Simons field and find mean-field solutions that could describe partially polarized quantum Hall states. The quasiparticles in the original model, which have quantized charge and spin, are described in the covariant sigma model by topological excitations, with the correct quantum numbers. They have finite energy due to the presence of the Chern-Simons field, and closely resemble the skyrmions in the usual nonlinear σ model. For the fully polarized states the spin is no longer quantized, but determined by Coulomb and Zeeman interactions.

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Phys. Rev. B 54, R11110(R)– Published 15 October, 1996
  • Received 28 June 1996

© 1996 American Physical Society

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