VolUMe 63. NUMBER 2 PHYSICAL REVIEW LETTERS 10 JULY 198 ly spin polarized, and is obtained by choosing in y +p the IK. von Klitzing, G. Dorda, and M. Pepper, Phys. Rev. Lett p lowest LL's with the same spin orientation. However, 45,494(1980) g Is D. C. Tsui. H. L. St to consider situations in which y+e has LL's with both Lett. 48, 1559(1982) spin orientations occupied, so that in y p the two lowest SFor a review, see The Quantum Hall Efect, edited by R.E spin-split Landau bands are occupied. Thus, for small Prange and s. M. Girvin(Springer-Verlag, New York, 1987) spin splitting, there are in general many candidates for 4R. B. Laughlin, Phys. Rev. B 23, 5632(1981);B IHalpe the incompressible state rin, Phys. Rev. B 25, 2185(1982) completely spin polarized states, spin unpolarized SR. B Laughlin, Phys. Rev. Lett. 50, 1395(1983) 6F. D. M. Haldane, Phys. Rev. Lett. 51, 605(1983)B states, 4 and partially spin polarized states There seems to be a close analogy between the com- Surf. Sci. 141, 11(1984). and in Ref. 3. There have also been posite fermion states proposed in this paper and the stan nonhierarchical states proposed for certain higher-level frac- dard hierarchical states. To illustrate this we consider tions: see.A.H.MacDonald C. Aers, and M.w. C. the example of the state which is obtained by multi- Dharma-wardana, Phys. Rev. B 31, 5529(1985);Y. Yoshioka, plying y+I by Z. It can be shown that the state Y+ A. H. MacDonald, and S. M. Girvin, Phys. Rev. B 38, 3636 with one hole similarly produces the state with a (1988): Phys. Rev. B 39, 1932(1989);R. Morf, N. D'Ambru quasielectron would be obtained by me state with a menil, and B. I.Halperin, Phys. Rev. B 34, 3037(1986) he state with the lowest (I-0)LL fully occupied and 8F. D M. Haldane and E. H. Rezay Phys. Rev. Lett. 60 956(1988) one electron in the I-1 LL. The state with fully occu 9S. Kivelson, C. Kallin, D. P. Arovas, and J.R.Schrieffer pied lowest LL and 8 electrons in the /l LL then cor- Phys. Rev. Lett. 56, 873(1986) responds to the state with 8 quasielectrons. Thus the 10F. wilczek, Phys. Rev. Lett.49, 957(1982);F,Wilczek s state can be viewed in the present approach as the and A. Zee, Phys. Rev. Lett. 51, 2250(1983);D.P.Arovas,J state with N/2 quasielectrons, and similarly the, state R. SchriefFer, F. wilczek, and A. Zee, Nucl. Phys. B251,117 can be viewed as the 3 state with N/3 quasielectrons This assignment is in exact agreement with that of the IR. B. Laughlin, Phys. Rev. Lett. 60, 2677(1988) standard hierarchy theory. One can also show that the 12B. 1. Halperin, Helv. Phys. Acta. 56, 75(1983) quasiparticles described above have the sam 13S. M. Girvin and A. H. MacDonald, Phys. Rev.Lett.5 e char those in the standard scheme. The analogy is, howev- 1252(1987); E H. Rezayi and F. D M. Haldane, Phys. Rev er,not complete. In the standard picture stability is ob- Kivelson, Phys. Rev. Lett. 62, 82(1989): N Read, Phys. Rev tained when the quasielectrons form a Laughlin-type Lett 62, 86(1989) state, whereas in the composite-fermion scheme the 14F D. M. Haldane in ref. 3 derive their arrangement from the higher LL. Also, tak ISR. willett et al., Surf. Sci. 196, 257(1988); A.M.Chang ing the above example, in the standard picture one aL, Phys. Rev, Lett, 53, 997(1984) obtain both the, and the 3 states from the state 6R.G. Clark et al,Sur.Sci.196,219(1988);196,257 whereas the composite-fermion approach does not yield (1988) the experimentally unobserved i3 state at this level r7V. J. Goldman, M. Shayegan, and D. C. Tsui, Phys.Rev In conclusion, this paper proposes that the FQhe car Lett.61,881(1988). 18N Read(private communication be accessed from the IQHE by adding an even number 19v. J. Goldman, D. C.Ts ui, and M. Shayegan, in Proceed of flux quanta to each electron. This analogy between ings of the Nineteenth International Conference on the Physics FQHE and IQHE suggests a natural generalization of of Semiconductors Warsaw, Poland. 1988(World Scientific the Laughlin states. Singapore, to be published) I thank N. Read, D. Stone, S. Kivelson, A. Mac- 20R. G. Clark et al., Phys. Rev. Lett. 62, 1536(1989);J.P Donald, A. Chang, V. Goldman, and H. Stormer for Eisenstein et al., ibid. 62, 1540(1989) helpful conversations 2 J. K. Jain(to be published)VOLUME 63, NUMBER 2 PHYSICAL REVIEW LETTERS IO JULY 1989 ly spin polarized, and is obtained by choosing in + w~ the p lowest LL's with the same spin orientation. However, when the spin splitting is insignificant, it may be useful to consider situations in which y~~ has LL's with both spin orientations occupied, so that in ++~ the two lowest spin-split Landau bands are occupied. Thus, for small spin splitting, there are in general many candidates for the incompressible state' ' for a given fraction: the completely spin polarized states, spin unpolarized states, ' ' and partially spin polarized states. There seems to be a close analogy between the com￾posite fermion states proposed in this paper and the stan￾dard hierarchical states. To illustrate this, we consider the example of the 3 state which is obtained by multi￾plying +~~ by Z . It can be shown ' that the state @+1 with one hole similarly produces the 3 state with a Laughlin quasihole. By analogy, the 3 state with a quasielectron would be obtained by multiplying by Z the state with the lowest (l=0) LL fully occupied and one electron in the I=1 LL. The state with fully occu￾pied lowest LL and 8 electrons in the I=I LL then cor￾responds to the 3 state with 6 quasielectrons. Thus the state can be viewed in the present approach as the state with N/2 quasielectrons, and similarly the 7 state can be viewed as the —' , state with N/3 quasielectrons. This assignment is in exact agreement with that of the standard hierarchy theory. One can also show that the quasiparticles described above have the same charge as those in the standard scheme. ' The analogy is, howev￾er, not complete. In the standard picture stability is ob￾tained when the quasielectrons form a Laughlin-type state, whereas in the composite-fermion scheme they derive their arrangement from the higher LL. Also, tak￾ing the above example, in the standard picture one can obtain both the 7 and the, '& states from the 5 state, whereas the composite-fermion approach does not yield the experimentally unobserved —,', state at this level. In conclusion, this paper proposes that the FQHE can be accessed from the IQHE by adding an even number of flux quanta to each electron. This analogy between FQHE and IQHE suggests a natural generalization of the Laughlin states. I thank N. Read, D. Stone, S. Kivelson, A. Mac￾Donald, A. Chang, V. Goldman, and H. Stormer for helpful conversations. 'K. von Klitzing, G. Dorda, and M. Pepper, Phys. Rev. Lett. 45, 494 (1980). 2D. C. Tsui, H. L. Stormer, and A. C. Gossard, Phys. Rev. Lett. 48, 1559 (1982). 3For a review, see The Quantum Hal! Effect, edited by R. E. Prange and S. M. Girvin (Springer-Verlag, New York, 1987). 4R. B. Laughlin, Phys. Rev. B 23, 5632 (1981);B. I. Halpe￾rin, Phys. Rev. B 25, 2185 (1982). sR. B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983). 6F. D. M. Haldane, Phys. Rev. Lett. 51, 605 (1983); B. I. Halperin, Phys. Rev. Lett. 52, 1583 (1984); R. B. Laughlin, Surf. Sci. 141, 11 (1984), and in Ref. 3. There have also been nonhierarchical states proposed for certain higher-level frac￾tions; see, A. H. MacDonald, G. C. Aers, and M. W. C. Dharma-wardana, Phys. Rev. B 31, 5529 (1985); Y. Yoshioka, A. H. MacDonald, and S. M. Girvin, Phys. Rev. B 38, 3636 (1988); Phys. Rev. B 39, 1932 (1989); R. Morf, N. D'Ambru￾menil, and B. I. Halperin, Phys. Rev. B 34, 3037 (1986). 7R. Willett et al. , Phys. Rev. Lett. 59, 1776 (1987). 8F. D. M. Haldane and E. H. Rezayi, Phys. Rev. Lett. 60, 956 (1988). S. Kivelson, C. Kallin, D. P. Arovas, and J. R. SchrieAer, Phys. Rev. Lett. 56, 873 (1986). 'OF. Wilczek, Phys. Rev. Lett. 49, 957 (1982); F. Wilczek, and A. Zee, Phys. Rev. Lett. 51, 2250 (1983); D. P. Arovas, J. R. Schrieff'er, F. Wilczek, and A. Zee, Nucl. Phys. B251, 117 (1985). ''R. B. Laughlin, Phys. Rev. Lett. 60, 2677 (1988). '2B. I. Halperin, Helv. Phys. Acta. 56, 75 (1983). ' S. M. Girvin and A. H. MacDonald, Phys. Rev. Lett. 58, 1252 (1987); E. H. Rezayi and F. D. M. Haldane, Phys. Rev. Lett. 61, 1985 (1988); S. C. Zhang, T. H. Hansson, and S. Kivelson, Phys. Rev. Lett. 62, 82 (1989); N. Read, Phys. Rev. Lett. 62, 86 (1989). '4F. D. M. Haldane, in Ref. 3. '5R. Willett er al. , Surf. Sci. 196, 257 (1988); A. M. Chang et al. , Phys. Rev. Lett. 53, 997 (1984). '6R. G. Clark et al. , Surf. Sci. 196, 219 (1988); 196, 257 (1988). ' V. J. Goldman, M. Shayegan, and D. C. Tsui, Phys. Rev. Lett. 61, 88 1 (1988). 'sN. Read (private communication). ' V. J. Goldman, D. C. Tsui, and M. Shayegan, in Proceed￾ings of the Nineteenth International Conference on the Physics of Semiconductors Warsaw, Poland, 1988 (World Scientific, Singapore, to be published). 2oR. G. Clark et al. , Phys. Rev. Lett. 62, 1536 (1989);J. P. Eisenstein er al. , ibid 62, 1540 (198.9). 2'J. K. Jain (to be published). 202