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1
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84926884469
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Present address: Department of Physics, University of Illinois at Urbana Champaign, 1110 W. Green St., Urbana, Illinois 61801 3080.
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2
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84926884468
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Permanent address: Department of Physics, University of Stockholm, Vanadisvägen 9, S 113,46 Stockholm, Sweden.
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3
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0003414482
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For a general introduction see, edited by, R.E. Prange, S.M. Girvin, Springer Verlag, New York
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(1990)
The Quantum Hall Effect
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11
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84926903196
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Also note that as the perturbation theory is carried out at fixed ν, l/a* propto rs where rs is the radius of the area per particle in atomic units familiar from the theory of the electron gas.
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13
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84926884467
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we calculate the gap as the sum of the gross quasiparticle energies.
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15
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84926922240
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S.L. Sondhi, Ph.D. thesis, UCLA, 1992.
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17
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84926941181
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The effect on the second order term is unknown.
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84926903195
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Our work here complements that of Smith, MacDonald, and Gumbs (Ref. onlinecitesmith), who have computed gaps for the integer states in a dynamic screening approximation which receives partial contributions from all orders higher than the first. They report good agreement with the data. If, as we argue below, the true quasiparticles are not perturbative quasiparticles, this agreement is at first sight fortuitous. However, as we shall see below, is likely that the true quasiparticle involves only a few extra reversed spins, so is reasonable that its creation energy is close to that of the perturbative quasiparticle.
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22
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84926941180
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This conclusion was reached earlier by Haldane (see his article in Ref. onlineciteqhe) in an examination of the truncated pseudopotential models. It has also been verified by finite size and variational studies for the Coulomb interaction;
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84926941179
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We assume that the cyclotron gap is still larger than the Zeeman gap, i.e., we assume the ordering hbar ωc > g uB B gg e2 /l.
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25
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84926903194
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The quasiparticle is of the form φ=(1,0)f where f is the familiar vortex solution of the spinless problem. The antivortex solution of this form corresponds to the quasielectron in the second Landau level. The true quasielectron corresponds to a skyrmion of size l.
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28
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84926884453
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There is also a Hopf term, which is the transcription of the Chern Simons term in ( reflglag) that enforces Fermi statistics for the skyrmions, but can be ignored for our purposes.
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31
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84926884451
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We have also calculated the effect of the finite extent (perpendicular to the interface) of the wave functions on the spin wave velocity, and hence on the skyrmion energy. We find that for GaAs heterojunctions, E(0) is reduced by amounts from 50,70 is unchanged; there will of course be quantitative corrections at nonzero g due to the softened interaction. In the same range of fields the energy of the microscopic (i.e., spin 1 over 2) quasiparticle is reduced by 30 $50, perturbative quasiparticle. None of these numbers includes the effects of Landau level mixing.
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84926922231
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By standard arguments the infinite skyrmion represents a quantum state with S=0; relative to the ground state this is an infinite spin.
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84926884450
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The neutral quasiparticle energies in the terminology of MacDonald and Girvin (Ref. onlinecitefn1).
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