Vortex pinning and non-Hermitian quantum mechanics

Physical Review B - Condensed Matter and Materials Physics

Volumn 56, Issue 14, 1997, Pages 8651-8673

  Hatano, Naomichi ^a   Nelson, David R ^b  

^a UNIVERSITY OF TOKYO   (Japan)

^b HARVARD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000600130     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.56.8651     Document Type: Article

References (24)

1. L. P. Kadanoff and J. Swift, Phys. Rev. 165, 310 (1968).
2. H. C. Fogedby, A. B. Eriksson, and L. V. Mikheev, Phys. Rev. Lett. 75, 1883 (1995).
3. D. Kim, Phys. Rev. E 52, 3512 (1995).
4. B. M. McCoy and T. T. Wu, Nuovo Cimento B 56, 311 (1968); see also E. H. Lieb and F. Y. Wu, in Phase Transitions and Critical Phenomena Vol. 1, edited by C. Domb and M. S. Green (Academic, London, 1972), p. 331.
5. N. Hatano and D. R. Nelson, Phys. Rev. Lett. 77, 570 (1996).
6. For a review see The Quantum Hall Effect, 2nd ed., edited by R. E. Prange and S. M. Girvin (Springer-Verlag, New York, 1990).
7. D. R. Nelson and N. Shnerb, cond-mat/9708071 (unpublished).
8. L. Civale, A. D. Marwick, T. K. Worthington, M. A. Kirk, J. R. Thompson, L. Krusin-Elbaum, Y. Sun, J. R. Clem, and F. Holtzberg, Phys. Rev. Lett. 67, 648 (1991).
9. R. C. Budhani, M. Suenaga, and S. H. Liou, Phys. Rev. Lett. 69, 3816 (1992).
10. D. R. Nelson and V. Vinokur, Phys. Rev. B 48, 13 060 (1993).
11. L. Balents and D. R. Nelson, Phys. Rev. B 52, 12 951 (1995).
12. M. P. A. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, Phys. Rev. B 40, 546 (1989).
13. D. R. Nelson and P. Le Doussal, Phys. Rev. B 42, 10 113 (1990).
14. L.-W. Chen, L. Balents, M. P. A. Fisher, and M. C. Marchetti, Phys. Rev. B 54, 12 798 (1996).
15. J. Miller and J. Wang, Phys. Rev. Lett. 76, 1461 (1996).
16. M. C. Marchetti and V. M. Vinokur, Phys. Rev. B 51, 16 276 (1995).
17. P. Le Doussal (unpublished);see also Sec. IV D of Ref. 10.
18. U. Täuber and D. R. Nelson, Phys. Rep. (to be published).
19. J. T. Edwards and D. J. Thouless, J. Phys. C 5, 807 (1972).
20. D. C. Liccardello and D. J. Thouless, J. Phys. C 8, 4157 (1975).
21. A study of Hermitian localization has suggested a diverging localization length κ precisely at the band center for another type of the probability distribution. In this case, the state with (Formula presented) for (Formula presented) is delocalized as soon as (Formula presented) becomes nonzero. See M. O. Robbins and B. Koiller, Phys. Rev. B 32, 4576 (1985).
22. D. R. Nelson and L. Radzihovsky, Phys. Rev. B 54, 6845 (1996).
23. B. I. Shklovskii and A. L. Efros, Electronic Properties of Doped Semiconductors (Springer-Verlag, New York, 1984).
24. T. Hwa, D. R. Nelson, and V. M. Vinokur, Phys. Rev. B 48, 1167 (1993). [See Fig. 55 of this reference for a schematic of (Formula presented)-dimensional tilted vortex lines in the presence of columnar pins.]