Liquid-crystal phases of quantum hall systems

Physical Review B - Condensed Matter and Materials Physics

Volumn 59, Issue 12, 1999, Pages 8065-8072

  Kivelson, StevenA ^b  

^a University of Illinois at Urbana Champaign   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000694594     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.59.8065     Document Type: Article

References (31)

1. S. A. Kivelson and V. J. Emery, Synth. Met. 80, 151 (1996), and references therein.
2. J. M. Tranquada, et al., Nature (London) 375, 561 (1995);
3. J. M. TranquadaPhys. Rev. Lett. 78, 338 (1997).
4. S-W. Cheong, et al., Phys. Rev. Lett. 67, 1791 (1991);
5. Phys. Rev. Lett.T. E. Mason, et al., 68, 1414 (1992);
6. T. R. Thurston, et al., Phys. Rev. B 46, 9128 (1992);
7. K. Yamada, et al., Phys. Rev. Lett. 75, 1626 (1995).
8. M. M. Fogler, A. A. Koulakov, and B. I. Shklovskii, Phys. Rev. Lett. 76, 499 (1996);
9. M. M. FoglerA. A. KoulakovB. I. ShklovskiiPhys. Rev. B 54, 1853 (1996).
10. R. Moessner and J. T. Chalker, Phys. Rev. B 54, 5006 (1996).
11. S. A. Kivelson, E. Fradkin, and V. J. Emery, Nature (London) 393, 550 (1998).
12. The lower critical dimension for a smectic liquid crystal is three. For a discussion see P. G. de Gennes and J. Prost, The Physics of Liquid Crystals (Oxford Science Publications, London, 1994), and references therein.
13. D. R. Nelson and B. I. Halperin, Phys. Rev. B 19, 2457 (1979);
14. Phys. Rev. BA. P. Young, 19, 1855 (1979).
15. J. P. Eisenstein (unpublished);
16. M. P. Lilly, K. B. Cooper, J. P. Eisenstein, L. N. Pfeiffer, and K. W. West, Phys. Rev. Lett. 82, 394 (1999).
17. B. I. Halperin, Phys. Rev. B 25, 2185 (1982).
18. X-G. Wen, Phys. Rev. B 41, 12 838 (1990).
19. M. Stone, Phys. Rev. B 42, 8399 (1990).
20. As is well known, the gapless modes of one-dimensional quantum systems with “spontaneously broken continuous symmetries” are not strictly Goldstone modes since these symmetries cannot be broken, by virtue of the Mermin-Wagner theorem. These systems are actually quantum critical and the gaplessness of the modes is actually a consequence of scale invariance.
21. V. J. Emery, in Highly Conducting One-Dimensional Solids, edited by J. T. Devreese, R. P. Evrard, and V. E. van Doren (Plenum, New York, 1979), p. 327.
22. Strictly speaking these couplings are also nonlocal in time.
23. V. J. Emery, E. Fradkin, and S. A. Kivelson (unpublished).
24. Bubble phases which have the symmetry, but different periodicities, are also possible. See Ref. 4.
25. L. Bonsall and A. A. Maradudin, Phys. Rev. B 15, 1959 (1977).
26. Z. Nussinov, J. Rudnick, S. A. Kivelson, and L. Chayes, cond-mat/9808349 (unpublished).
27. The interpretation of these data in terms of stripes was first made by J. P. Eisenstein (private communication).
28. In the pure system the transition between the two crystal states is first order and it is rounded by disorder.
29. R. L. Willett, K. W. West, and L. N. Pfeiffer, Phys. Rev. Lett. 78, 4478 (1997).
30. A similar intuitive picture has been proposed by D. H. Lee (private communication) and one of us (E.F.), but without the spatial asymmetry, for the compressible (Formula presented) state in the lowest Landau level.
31. We thank B. I. Spivak for this observation.