Ground state, quasihole, a pair of quasihole wave functions, and instability in bilayer quantum Hall systems

Physical Review B - Condensed Matter and Materials Physics

Volumn 74, Issue 24, 2006, Pages

  Jiang, Longhua ^a   Ye, Jinwu ^a  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33845417209     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.74.245311     Document Type: Article

References (44)

1. Laughlin, in The Quantum Hall Effects, 2nd ed., edited by, R. E. Prange, and, S. M. Girvin, (Springer-Verlag, New York, 1990).
2. J. K. Jain, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.63.199 63, 199 (1989).
3. For reviews of bilayer quantum Hall systems, see S. M. Girvin and A. H. Macdonald, in Perspectives in Quantum Hall Effects, edited by, S. Das Sarma, and, Aron Pinczuk, (Wiley, New York, 1997).
4. J. P. Eisenstein, L. N. Pfeiffer, and K. W. West, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.69.3804 69, 3804 (1992);
5. Song He, P. M. Platzman, and B. I. Halperin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.71.777 71, 777 (1993).
6. I. B. Spielman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84. 5808 84, 5808 (2000);
7. I. B. Spielman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87. 036803 87, 036803 (2001).
8. M. Kellogg, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88. 126804 88, 126804 (2002).
9. M. Kellogg, cond-mat/0401521 (unpublished).
10. For a review, see J. P. Eisenstein and A. H. MacDonald, cond-mat/0404113 (unpublished).
11. M. Kellogg, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90. 246801 90, 246801 (2003).
12. I. B. Spielman, cond-mat/0406067 (unpublished).
13. B. I. Halperin, Helv. Phys. Acta HPACAK 0018-0238 56, 75 (1983);
14. B. I. Halperin, Surf. Sci. SUSCAS 0039-6028 10.1016/0039-6028(94)90850-8 305, 1 (1994).
15. H. A. Fertig, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.40.1087 40, 1087 (1989);
16. X. G. Wen and A. Zee, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.69.1811 69, 1811 (1992);
17. Z. F. Ezawa and A. Iwazaki, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.47.7295 47, 7295 (1993);
18. Z. F. Ezawa and A. Iwazaki, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.48.15189 48, 15189 (1993);
19. Z. F. Ezawa and A. Iwazaki, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.70.3119 70, 3119 (1993).
20. Kun Yang, K. Moon, L. Zheng, A. H. MacDonald, S. M. Girvin, D. Yoshioka, and S. C. Zhang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.72.732 72, 732 (1994);
21. K. Moon, H. Mori, Kun Yang, S. M. Girvin, A. H. MacDonald, L. Zheng, D. Yoshioka, and S. C. Zhang, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.51. 5138 51, 5138 (1995).
22. Gun Sang Jeon and Jinwu Ye, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.71.035348 71, 035348 (2005).
23. Jinwu Ye, cond-mat/0606639 (unpublished).
24. Jinwu Ye, cond-mat/0407088 (unpublished).
25. Jinwu Ye, cond-mat/0310512 (unpublished).
26. J. Ye, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.71.125314 71, 125314 (2005).
27. S. M. Girvin and A. H. MacDonald, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.58.1252 58, 1252 (1987);
28. S. C. Zhang, T. H. Hansson, and S. Kivelson, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.62.82 62, 82 (1989);
29. S. Z. Zhang, Int. J. Mod. Phys. B IJPBEV 0217-9792 10.1142/ S0217979292000037 6, 25 (1992);
30. N. Read, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.62.86 62, 86 (1989).
31. Recently, trial wave functions involving the coexistence of composite bosons and composite fermions at finite distance were proposed by S. H. Simon, E. H. Rezayi, and M. V. Milovanovic, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.046803 91, 046803 (2003);
32. M. V. Milovanovic and I. Stanic, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.72.155306 72, 155306 (2005).
33. We put quotes here because Eq. 20 is decoupled only in its face form. As shown explicitly in Ref., in the balanced case, there is a spin-charge separation only in the ground state. However, in any excited states such as meron excitations, there are spin-charge connection which leads to the correct meron fractional charge and polarization listed in Table 1 in Ref.. It is this spin-charge connection which leads to the constraint of the vortices in the two layers J0 v+ (x)= J0 v- (x)=-δ(x) used in this section and J0 v± =δ (x - z0) ±δ (x - w0) used in the next section.
34. As shown in detail in Ref., the functional form achieved from the composite boson theory is the same at that achieved from the microscopic LLL+HF approach. But the coefficients should be taken from the LLL+HF approach.
35. The above form of the phonon contributions to the ground-state wave function, but with different dependence on the distance d was already derived from composite fermion Chern-Simon theory in A. Lopez and E. Fradkin, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.51.4347 51, 4347 (1995).
36. The same transformation is needed to transform the modulus of the quasi-hole wave function in SLQH at Laughlin's series ν=1 m with m odd Ψqh = i N1 zi Ψm back to its final form Ψqh = i N1 zi Ψm. To the best of the authors' knowledge, this very subtle and important point was not explicitly spelled out in any previous work.
37. It was shown in Ref. that although the quasihole and the meron wave functions listed in Eq. 1 are completely different at any finite distance, they have finite comparable expectation energies at d=0, So we expect the quasihole's expectation energy in Eq. 24 is comparable to both at d=0. However, as explained in the main text, all these wave functions are not interesting anymore at d=0.
38. L. Brey, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.65.903 65, 903 (1990);
39. R. Cote, L. Brey, and A. H. MacDonald, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.46.10239 46, 10239 (1992);
40. X. M. Chen and J. J. Quinn, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.67.895 67, 895 (1991);
41. X. M. Chen and J. J. Quinn, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.45.11054 45, 11054 (1992);
42. X. M. Chen and J. J. Quinn, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.47.3999 47, 3999 (1993);
43. L. Zheng and H. A. Fertig, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.52.12282 52, 12282 (1995);
44. S. Narasimhan and Tin-Lun Ho, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.52.12291 52, 12291 (1995).