VOLUME 48. NUMBER 22 PHYSICAL REVIEW LETTERS 31MAY1982 FILLING FACTOR v 231/2 L 1mm aOouNd 4·1.23x10"cm-2 1.38 10 cm- 048K 王10(ka) OOK 2 .65K o(k/口 415K MAGNETIC FIELD B (kG) TEMPERATURE T《K FIG. 2. T dependence of(a) the slope of Pxy at v=3, Q FIG. 1. pry and pxx vS B, taken from a GaAs-Alo 37 normalized to the slope at 30 K, (b)P at v=a,and V sec, using /=I uA. The Landau level filling factor ig (e)ex, at v=( Gao 7As sample with n=1.23x 10/cm2, H=90000 cm2/ defined by v=nh/eB values of v at higher T. Moreover, for v< 3 and away from the plateau region, pxx shows generacyl6 is seen in the appearance of these strong increase with decreasing T, while p features at odd-integer values of v. As observed shows very weak decrease or essentially inde earlier, the plateaus in Pry as well as the van- pendence of T. This behavior has been seen to ishing of pxx become increasingly pronounced as v=0. 21, the smallest v attained in this experi T is dec ment In the extreme quantum limit, v<l, only the Figure 2 illustrates the development of Pxr and lower spin state of the lowest Landau level,i.e, pxy at fixed B as a function of T. Figure 2(a) the(0, t)level, remains partially occupied. In shows the slope of Px at v=3, normalized to the this regime(i.e, B>50 kG in Fig. 1), the sys- slope at high T( 30 K), for three samples with tem is completely spin polarized. For T>4.2K, slightly different n. Figure 2(b)shows the ac Prv=B/ne, and px shows also nearly linear de companying P xx minimum(at v=3), and Fig. 2(c) pendence on B, as expected from the free-elec shows pxr at v =0. 24 to illustrate its T dependence tron theory of Ando and Uemura ,L6 At lower T, for v<s, away from the Hall plateau. Several Pxy deviates from pxy=B/ne at v 3. This devia- points should be noted. First, the slope of pat tion becomes more pronounced as t decreases v =3 approaches zero at T-0. 4 K, indicative of a and approaches a plateau of Pxy=3h/e2, within an true quantized Hall plateau. Second, replotting accuracy better than 1% at 0. 42 K. The appear- the data in Fig. 2(a)on logarithmic slope versus ance of this plateau is accompanied by a minimum inverse T scale shows a linear portion for data in pxx, as apparent in the lower panel of Fig. 1. taken at Te1.1 K. This fact allows us to extrapo- The development of these features is similar to late the normalized slope to 1 at To=5 K, which that of the quantized Hall resistance and the con- we identify as the temperature for the onset of comitant vanishing of Pxx, observed at integral his phenomenon. Third, Pxx at v=3is w6 ks/u 1560