VOLUME 48. NUMBER 22 PHYSICAL REVIEW LETTERS 31MAY1982 at our lowest T of M0. 42 K, and much lower T is pxv=B/ne= 3h/e. As discussed by Baraff and needed to determine if pxx at v= 3 indeed vanishes Tsui, 23 observation of the quantized Hall plateau with vanishing T. Finally, if the data for pxx at may be attributed to the presence of donor states 0. 24 Fig. 2(c)] are replotted on logarithmic inside Al Ga,-x As. The thermal activation of P xx Prr versus inverse T scale, an exponential depen- at v=3 may result from activation of defects in dence on 1/T is seen for T>0.6K, with a preex- the condensate which give rise to dissipation. ponential factor of 13k&/O. This result may be Finally, our data also show weaker but similar nterpreted as due to thermally activated trans structures in Pxx near v=3 and near v=2,ac port with an activation energy of 0.94 K. The pre- companied by slight changes in the slope of p exponential factor is considerably lower than the These structures, though discernible in Fig. 1 maximum metallic sheet resistance of 40 k&/ are well resolved in the data taken from the sam of Landau levels, but comparable to that signify- sec at 1.2 K. In our picture the structure at ing a metal-insulator transition for 2D systems in =2 may be identified as due to the formation of a the absence of B. Moreover, the data for v <3 Wigner solid or CDw of holes, expected from suggest a state of localization, in which the elec- electron-hole symmetry. At v=2, the(0, t)Lar tron mobility is thermally activated, as seen in dau level is completely filled, but the(o, +)level Pxx. The electron density, as seen in the slope of is half filled. Consequently 3 of all the electrons Pxy VS B, remains essentially independent of T. occupy the low-lying(0, t)level, and only the re- The existence of quantized Hall resistance ac- maining 3 with spin may participate in the for companied by the vanishing of Pxx at integral val- mation of a collective ground state. Our data ap ues of v is now well known. Their observation is pear to suggest that this condition is also favored attributed to the existence of an energy gap be for a wigner solid or Cdw ground state. tween the extended states in two adjacent Landau In summary, we observed striking struct levels and the presence of localized states, which in the magnetotransport coefficients of high-u pin E F in the gap, to keep all the extended states 2D electrons in GaAs-Al Ga,.As heterojunctions in finite numbers of Landau levels completely oc- at v=3, and similar, but much weaker, struc cupid for finite regions of B or n. Laughlins tures at v=3 and 2. Their development as a argument based on gauge invariance demon function of T is reminiscent of the quantized p strated that the quantized Hall resistance, given and the concomitant vanishing of cted by Pxy=h/ie2(i=1, 2, ..) results from complete only for integral values of v. We suggest as a occupation of all the extended states in the Lan- possible explanation the formation of a new elec dau level, regardless of the presence of localiza- tronic state, such as a wigner solid or CDw tion, Our observation of a quantized Hall resis- state with a triangular sy mmetry tance of 3h/ e2 at v=3 is a case where Laughlins We thank P. M. Tedrow for the he refrigerator argument breaks down. If we attribute it to the R. B. Laughlin, P. A. Lee, V. Narayanamurti presence of a gap at e when 3 of the lowest Lan- and P. M. Platzman for discussions; and K.Bald dau level is occupied, his argument will lead to win, G. Kaminsky, and W. wiegmann for techni- quasiparticles with fractional electronic charge cal assistance. This work was supported in part of 3, as has been suggested for 3-filled quasi by the National Science Foundation. one-dimensional systems. 2 At the present, there is no satisfactory explana tion for all of phenomenon always occurs at v =3 and that it is a visiting scientist at the Francis Bitter National most striking in samples with the highest electron Magnet Laboratory, Cambridge, Mass. 02139 mobility suggest the formation of a new spin-po- (present address: Department of Electrical En- larized electronic state such as wigner solid gineering and Computer Science, Princeton University, CDw, with a triangular sy mmetry which is Princeton, N.. 08544 favored at v=3. In this picture, the observed E. P. wigne ev.46,1002(1934) features of Pxx and p xy may be attributed to trans 2YE.Lozovik 。日 Yudson, Pis ma Zh. Eksp. 2,11(1975)] SC C. Grimes and G. Adams, Phys. Rev. Lett. ransport is free of dissipation and px is expected 795 (1979) to vanish. Since the number of electrons in this H, Fukuyama, P. M. Platzman, and P. w. Anderson ground state is n=eB/3h, the Hall resistivity Phys.Rev.B19,5211(1979)