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84926539762
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It may, in theory, be necessary as well to specify a certain topological quantum number, which can be thought of as the number of edge states, in order to uniquely characterize the particular quantum Hall liquid. [See, for example,] However, to date, there is no experimental evidence that there exist two thermodynamically distinct spin-polarized quantum Hall liquid phases with the same value of sxy. Theoretically, the possibility of the existence of two or more distinct quantum Hall liquid states with the same value of sxy seems obvious. Two distinct phases with the same value of sxy can certainly exist when the electron spin is taken into account. For instance, the state with sxy=2 will be spin unpolarized if g μB is less than ωc (as is in GaAs), but would be spin polarized if g μB were greater than ωc. Experimentally, there is evidence of a transition between a spin-polarized and a non-spin-polarized state as a function of the Zeeman energy at ν = case 8 [Truncated]
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(1990)
Phys. Rev. B
, vol.41
, pp. 9733
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Wen, X.G.1
Niu, Q.2
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6
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84926542433
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temperature-independent metallic conductivities are observed to the lowest observation temperature T app 28 mK in moderate mobility samples.
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16
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84926536023
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T. L. Ho, Ohio State University.
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31
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(b) S. Sondhi, A. Karlhede, and S. A. Kivelson (unpublished).
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39
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84926565417
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See also D-, edited by, (World Scientific, Singapore, 1991), p. 202 and
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(1992)
Int. J. Mod. Phys. B
, vol.6
, pp. 25
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Lee, H.1
Anyons2
Chern, S.S.3
Chu, C.W.4
Ting, C.S.5
Zhang, S.-C.6
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40
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84926587214
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for comprehensive reviews of the Chern-Simons theory applied to the quantum Hall effect.
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43
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84926603760
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For more recent developments, see X-F. Wang, Z. Wang, G. Kotliar, and C. Castellani (unpublished).
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62
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84926580797
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and, especially, E. Y. Andrei, F. I. B. Williams, D. C. Glattli, and G. DeVille, in Physics of Low-Dimensional Semiconductor Structures (Plenum, Trieste, in press);
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67
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84926596085
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To get a very crude feeling for whether the magnitudes obtained from this simple scaling theory are half-way reasonable, we imagine that z=1 and Δσapp (estar)2/ curlep ξ0. (There is no theory behind this assumption; is simply the simplest dimensionally correct assumption we can make in order to obtain numbers.) Since 1 GHz and 100 mK both correspond to energies of roughly 10-5 eV, to get reasonable magnitudes with estar= e/5, curlep app 13, is necessary that ξ0app 4000~ A ang, roughly 10 times the spacing between electrons in these samples. This does not seem to us to be an unreasonably long localization length. The same estimates yields a threshold field ETapp estar/ curlep ξ02= 10 mV/cm. While this is slightly larger than the observed ET, given the crudeness of our estimates, is encouragingly close.
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69
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84926580708
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X-G. Wen (unpublished).
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70
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H-W. Jiang (private communication).
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75
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We thank J. K. Jain for pointing this out to us. A possible interpretation of this observation, which was also realized independently by Jain, is that the shape of the phase diagram in the neighborhood of ν = case 2 over 9 reflects the presence of substantial short-range Wigner-crystal order. In the absence of disorder, there could be a direct first-order transition from the sxy= case 2 over 9 quantum Hall liquid to a Wigner crystal, which in the presence of weak disorder would split into a continuous sxy= case 2 over 9 to sxy= case 1 over 5 transition followed by a second continuous sxy= case 1 over 5 to insulator transition. If the disorder is weak, the strip of sxy= case 1 over 5 phase that appears between the sxy= case 2 over 9 phase and the insulator must (by continuity) occupy a very narrow strip of the phase diagram and might, consequently, be difficult to resolve at finite temperature. As emphasized by Jain, according to this interpretation, the observation of reentrant insulating behavior in the neighborhood ν = case 2 over 9 is suggestive of the existence of substantial short-range Wigner-signal order. It would therefore be extremely useful to study the behavior of ρxy at low temperature in this regime.
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