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G. S. Boebinger, Ph.D. thesis, MIT, 1986;
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The estimate of this ratio is as follows (I. L. Aleiner, private communication). The lower bound for the energy of a skyrmion antiskyrmion pair is twice the energy of an infinitely large skyrmion in the absence of the Zeeman coupling. The latter is given by 8 π s / (2 π lB2), where lB = sqrtν /kF is the magnetic length, and s is the spin wave stiffness (Ref. onlineciteSondhi) (one quarter of the coefficient in the spin wave dispersion relation expanded up to the quadratic in the wave vector term). According to Ref. onlineciteAleiner, s = hbarωc lB2 N / 2 π kF aB; therefore, 2 ΔSk / E0 geq 4 N / ln(2 k F aB) gg 1, since we assume N gg kF aB gg 1.
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In fact, for ni aB2<1.9, Eq. ( refTranscendental) has two solutions and we refer to the smaller one. In reality, ni aB2 lesssim 0.1 and the larger solution exceeds the smaller one by orders of magnitude. This larger solution is well beyond the experimentally accessible range of n. Therefore, when we say that n > nsub ast, we at the same time imply that n is smaller than this other solution. Note that in this regime of the two equations ( refN_c2) and ( refN_c3), the former gives a larger value for Nc.
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The collapse of N = 0 peak was studied in Ref. onlineciteGlozman. Results for larger N have been obtained by L. W. Wong, H. W. Jiang, and E. Palm (unpublished). They appear to be in agreement with Eq. ( refN_c_all).
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and references therein.
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Equation ( refG_ex) does not render a small ``bump'' in Gex( bboxr) near r = 2 R. Therefore, the integration of Gex( bboxr) with the help of Eq. ( refG_ex) gives for α a result slightly smaller than the actual one. The difference is only in the numerical coefficient in the argument of the logarithm entering Eq. ( refalpha). The correct coefficient can be obtained using other formulas of Ref. onlineciteAleiner.
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We remind the reader that the real temperature is zero.
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Note that if we directly substitute varepsilon(q) from Eq. ( refepsilon) into Eq. ( refStructure), then the integral in Eq. ( refrho II) will be divergent. Therefore, strictly speaking, completely filled LLS alone can not provide the screening. At small q below some cutoff qmax, the screening is performed by the partially filled LLS and is much stronger than the one described by Eq. ( refepsilon). Thus, wave vectors 0
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For N = 0, the evolution of the edge structure may be different from the one we just described following Ref. onlineciteDempsey. Alternatively [S. L. Sondhi (private communication)], the destruction of the ``0'' ``2'' state proceeds via the creation of spin textures closely related to the skyrmions briefly discussed in Sec. refIntroduction. We believe that similar to the skyrmions, this mechanism is peculiar only to the lowest Landau level, and is not realized in the case of large N, which we consider here.
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