VOLUME 50 NUMBER 18 PHYSICAL REVIEW LETTERS 2MAY1983 and nucleates a particle. This, like a flux line, for helpful discussions. I also wish to thank is surrounded by a vortex of Hall current rotat P. A, Lee, D. Yoshioka, and B I. Halperin f ng in a sense opposite to that induced by the helpful criticism. This work was performed stress under the auspices of the U. S. Department of The role of sample impurities and inhomogenei- Energy by Lawrence Livermore National Labora ties in this theory is the same as that in my tory under Contract No W-7405-Eng-48 theory of the ordinary quantum Hall effect.The electron and hole bands, separated in the im purity-free case by a gap 24, are broadened into a continuum consisting of two bands of ex D. C. Tsui, H. L Stormer, and A. C. Gossard, Phys tended states separated by a band of localized Rev,Iet,48,1559(1982). ones. Small variations of the electron density 2R. B. Laughlin, Phys. Rev. B 27, 3383(1983) move the Fermi level within this localized state 3J. M. Caillol, D. Levesque, J.J. Weis, and J. P band as the extra quasiparticles become trapped Hansen, J. Stat. Phys. 28, 325 (1982) at impurity sites. The Hall conductance is (1/m) 47, 394(1979); D. Yoshioka and P.A. Lee, Phys. Rev X(e/h)because it is related by gauge invariance B 27, 4986(1983), and private communication to the charge of the quasiparticles e* by o hall B. Jancovici, Phys. Rev. Lett. 46, 386(1981).T=2 e*e/h, whenever the Fermi level lies in a corresponds to a full Landau level, for which the total localized state band. As in the ordinary quantum energy equals the Hartree-Fock energy -Vm/8 e/ap- Hall effect disorder sufficient to localize all the This correspondence may be viewed as the underlying states destroys the effect. This occurs when the 6W. P. Su and J. R. Schrieffer, Phys. Rev. Lett. 46 collision time T in the sample in the absence of a magnetic field becomes smaller than T<h/A Mass I wish to thank H. De witt for calling my atten 1965),p.13 tion to the monte carlo work and d, boercker R. B. Laughlin, Phys. Rev. B 23, 5632(1981)