Unifying Model for Several Classes of Two-Dimensional Phase Transition

Yonatan Dubi,¹ Yigal Meir,^1,2 and Yshai Avishai^1,2

¹Physics Department, Ben-Gurion University, Beer Sheva 84105, Israel
²The Ilse Katz Center for Meso- and Nano-scale Science and Technology, Ben-Gurion University, Beer Sheva 84105, Israel

(Received 29 September 2004; published 22 April 2005)

A relatively simple and physically transparent model based on quantum percolation and dephasing is employed to construct a global phase diagram which encodes and unifies the critical physics of the quantum Hall, "two-dimensional metal-insulator," classical percolation and, to some extent, superconductor-insulator transitions. Using real-space renormalization group techniques, crossover functions between critical points are calculated. The critical behavior around each fixed point is analyzed and some experimentally relevant puzzles are addressed. ©2005 The American Physical Society

URL: http://link.aps.org/abstract/PRL/v94/e156406
doi:10.1103/PhysRevLett.94.156406
PACS: 71.30.+h, 73.43.Nq, 74.20.Mn        Additional Information

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References

1. B. Huckestein, Rev. Mod. Phys. 67, 357 (1995).
   
2. C. V. Mil`nikov and I. M. Sokolov, JETP Lett. 48, 536 (1988). [SPIN] [ISI]
   
3. H. P. Wei et al., Phys. Rev. Lett. 61, 1294 (1988); [ISI]
   S. Koch et al., Phys. Rev. Lett. 67, 883 (1991). [ISI]
   
4. A. A. Shashkin et al., Phys. Rev. B 49, 14486 (1994);
   R. B. Dunford et al., Physica B (Amsterdam), 298, 496 (2001). [Inspec]
   
5. D. Shahar et al., Solid State Commun. 107, 19 (1998); [Inspec] [ISI]
   N. Q. Balaban et al., Phys. Rev. Lett. 81, 4967 (1998). [ISI]
   
6. P. Hopkins et al., Phys. Rev. B 39, 12708 (1989); [ISI]
   M. Hilke et al., Nature (London) 395, 675 (1998). [ISI]
   
7. L. P. Pryadko and A. Auerbach, Phys. Rev. Lett. 82, 1253 (1999). [ISI]
   
8. D. B. Haviland, Y. Liu, and A. M. Goldman, Phys. Rev. Lett. 62, 2180 (1989). [ISI]
   
9. Y. Liu et al., Phys. Rev. Lett. 67, 2068 (1991). [ISI]
   
10. A. F. Hebard and M. A. Paalanen, Phys. Rev. Lett. 65, 927 (1990); [ISI]
    A. Yazdani and A. Kapitulnik, Phys. Rev. Lett. 74, 3037 (1995); [ISI]
    D. Ephron et al., Phys. Rev. Lett. 76, 1529 (1996); [ISI]
    N. Mason and A. Kapitulnik, Phys. Rev. Lett. 82, 5341 (1999). [ISI]
    
11. E. Abrahams, S. V. Kravchenko, and M. P. Sarachik, Rev. Mod. Phys. 73, 251 (2001) and references therein. [ISI]
    
12. Y. Meir, Phys. Rev. Lett. 83, 3506 (1999), and experimental references therein. [ISI]
    
13. S. Das Sarma et al., cond-mat/0406655.
    
14. A. A. Shashkin et al., Phys. Rev. Lett. 73, 3141 (1994); [ISI]
    I. V. Kukushkin et al., Phys. Rev. B 53, R13260 (1996).
    
15. D. Kowal and Z. Ovadyahu, Solid State Commun. 90, 783 (1994). [Inspec] [ISI]
    
16. S. He and X. C. Xie, Phys. Rev. Lett. 80, 3324 (1998). [ISI]
    
17. E. Shmishoni, A. Auerbach, and A. Kapitulnik, Phys. Rev. Lett. 80, 3352 (1998). [ISI]
    
18. Y. Dubi, Y. Meir, and Y. Avishai, Phys. Rev. B 71, 125311 (2005).
    
19. J. T. Chalker and P. D. Coddington, J. Phys. C 21, 2665 (1988). [Inspec]
    
20. M. Buttiker, Phys. Rev. B 33, 3020 (1986); [ISI]
    see also J. Shi, S. He, and X. C. Xie, cond-mat/9904393.
    
21. D. P. Arovas, M. Janssen, and B. Shapiro, Phys. Rev. B 56, 4751 (1997); [ISI]
    A. G. Galstyan and M. E. Raikh, Phys. Rev. B 56, 1422 (1997); [ISI]
    Y. Avishai, Y. Band, and D. Brown, Phys. Rev. B 60, 8992 (1999). [ISI]
    
22. E. Shimshoni, cond-mat/0406703.
    
23. Y. Hanein et al., Nature (London) 400, 735 (1999). [ISI]
    
24. Y. Liu et al., Phys. Rev. B 47, 5931 (1993). [ISI]
    
25. A. Kapitulnik et al., Phys. Rev. B 63, 125322 (2001).