Critical level statistics and anomalously localized states at the Anderson transition

Physical Review B - Condensed Matter and Materials Physics

Volumn 71, Issue 3, 2005, Pages

  Obuse, H ^a   Yakubo, K ^a  

^a HOKKAIDO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CALCULATION; DENSITY; ENERGY; MATHEMATICAL ANALYSIS; POISSON DISTRIBUTION; SPECTRUM; STATISTICS;

EID: 15444378917     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.71.035102     Document Type: Article

References (56)

1. L. P. Gorkov and G. M. Eliashberg, Sov. Phys. JETP 21, 940 (1965).
2. K. B. Efetov, Adv. Phys. 32, 53 (1983).
3. B. L. Altshuler and B. I. Shklovskii, Zh. Eksp. Teor. Fiz. 91, 220 (1986) [Sov. Phys. JETP 64, 127 (1986)].
4. B. L. Altshuler and B. I. Shklovskii, Zh. Eksp. Teor. Fiz. 91, 220 (1986) [Sov. Phys. JETP 64, 127 (1986)].
5. B. L. Altshuler, I. Kh. Zharekeshev, S. A. Kotochigova, and B. I. Shklovskii, Zh. Eksp. Teor. Fiz, 94, 343 (1988) [Sov. Phys. JETP 63, 625 (1988)].
6. B. L. Altshuler, I. Kh. Zharekeshev, S. A. Kotochigova, and B. I. Shklovskii, Zh. Eksp. Teor. Fiz, 94, 343 (1988) [Sov. Phys. JETP 63, 625 (1988)].
7. M. L. Mehta, Random Matrices, 2nd ed. (Academic, New York, 1991).
8. S. N. Evangelou, Phys. Rev. B 39, 12 895 (1989).
9. E. Hofstetter and M. Schreiber, Phys. Rev. B 48, 16 979 (1993).
10. B. I. Shklovskii, B. Shapiro, B. R. Sears, P. Lambrianides, and H. B. Shore, Phys. Rev. B 47, 11 487 (1993).
11. Y. Ono and T. Ohtsuki, J. Phys. Soc. Jpn. 62, 3813 (1993).
12. I. Kh. Zharekeshev and B. Kramer, Phys. Rev. B 51, 17 239 (1995).
13. I. Varga, E. Hofstetter, and J. Pipek, Phys. Rev. Lett. 82, 4683 (1999).
14. M. L. Ndawana, R. A. Römer, and M. Schreiber, Eur. Phys. J. B 27, 399 (2002).
15. H. Aoki, J. Phys. C 16, L205 (1983); Phys. Rev. B 33, 7310 (1986).
16. H. Aoki, J. Phys. C 16, L205 (1983); Phys. Rev. B 33, 7310 (1986).
17. F. Wegner, Z. Phys. B: Condens. Matter 36, 209 (1980).
18. For a recent review, see T. Nakayama and K. Yakubo, Fractal Concepts in Condensed Matter Physics (Springer-Verlag, Berlin, 2003).
19. J. T. Chalker, V. E. Kravtsov, and I. V. Lerner, Pis'ma Zh. Eksp. Teor. Fiz. 64, 355 (1996) [JETP Lett. 64, 386 (1996)].
20. J. T. Chalker, V. E. Kravtsov, and I. V. Lerner, Pis'ma Zh. Eksp. Teor. Fiz. 64, 355 (1996) [JETP Lett. 64, 386 (1996)].
21. A. G. Aronov, V. E. Kravtsov, and I. V. Lerner, Pis'ma Zh. Eksp. Teor. Fiz. 59, 40 (1994) [JETP Lett. 59, 39 (1994)].
22. A. G. Aronov, V. E. Kravtsov, and I. V. Lerner, Pis'ma Zh. Eksp. Teor. Fiz. 59, 40 (1994) [JETP Lett. 59, 39 (1994)].
23. V. E. Kravtsov, I. V. Lerner, B. L. Altshuler, and A. G. Aronov, Phys. Rev. Lett. 72, 888 (1994).
24. L. Schweitzer and I. Kh. Zharekeshev, J. Phys.: Condens. Matter 7, L377 (1995).
25. S. N. Evangelou, Phys. Rev. Lett. 75, 2550 (1995).
26. T. Ohtsuki and Y. Ono, J. Phys. Soc. Jpn. 64, 4088 (1995).
27. T. Kawarabayashi, T. Ohtsuki, K. Slevin, and Y. Ono, Phys. Rev. Lett. 77, 3593 (1996).
28. I. Kh. Zharekeshev and B. Kramer, Phys. Rev. Lett. 79, 717 (1997).
29. V. E. Kravtsov and K. A. Muttalib, Phys. Rev. Lett. 79, 1913 (1997).
30. S. M. Nishigaki, Phys. Rev. E 58, R6915 (1998); S. M. Nishigaki, ibid. 59, 2853 (1999).
31. S. M. Nishigaki, Phys. Rev. E 58, R6915 (1998); S. M. Nishigaki, ibid. 59, 2853 (1999).
32. H. Obuse, K. Yakubo, Phys. Rev. B 69, 125301 (2004).
33. B. L. Altshuler, V. E. Kravtsov, and I. V. Lerner, Pis'ma Zh. Eksp. Teor. Fiz. 45, 160 (1987) [JETP Lett. 45, 199 (1987)].
34. B. L. Altshuler, V. E. Kravtsov, and I. V. Lerner, Pis'ma Zh. Eksp. Teor. Fiz. 45, 160 (1987) [JETP Lett. 45, 199 (1987)].
35. For a comprehensive review, see A. D. Mirlin, Phys. Rep. 326, 259 (2000).
36. B. A. Muzykantskii and D. E. Khmelnitskii, Phys. Rev. B 51, 5480 (1995).
37. V. I. Fal'ko and K. B. Efetov, Phys. Rev. B 52, 17 413 (1995).
38. V. Uski, B. Mehlig, R. A. Römer, and M. Schreiber, Phys. Rev. B 62, R7699 (2000); V. Uski, B. Mehlig, and M. Schreiber, ibid. 66, 233104 (2002).
39. V. Uski, B. Mehlig, R. A. Römer, and M. Schreiber, Phys. Rev. B 62, R7699 (2000); V. Uski, B. Mehlig, and M. Schreiber, ibid. 66, 233104 (2002).
40. B. K. Nikolić, Phys. Rev. B 64, 014203 (2001); 65, 012201 (2001); B. K. Nikolic and V. Z. Cerovski, Eur. Phys. J. B 30, 227 (2002).
41. B. K. Nikolić, Phys. Rev. B 64, 014203 (2001); 65, 012201 (2001); B. K. Nikolic and V. Z. Cerovski, Eur. Phys. J. B 30, 227 (2002).
42. B. K. Nikolić, Phys. Rev. B 64, 014203 (2001); 65, 012201 (2001); B. K. Nikolic and V. Z. Cerovski, Eur. Phys. J. B 30, 227 (2002).
43. T. Kottos, A. Ossipov, and T. Geisel, Phys. Rev. E 68, 066215 (2003); A. Ossipov, T. Kottos, and T. Geisel, Europhys. Lett. 62, 719 (2003).
44. T. Kottos, A. Ossipov, and T. Geisel, Phys. Rev. E 68, 066215 (2003); A. Ossipov, T. Kottos, and T. Geisel, Europhys. Lett. 62, 719 (2003).
45. It has been pointed out that values of raultifractal exponents de-pend on averaging procedures in a random Dirac fermion model. [H. E. Castillo, C. C. Chamon, E. Fradkin, P. M. Goldbart, and C. Mudry, Phys. Rev. B 56, 10 668 (1997)].
46. Y. Asada, K. Slevin, and T. Ohtsuki, Phys. Rev. Lett. 89, 256601 (2002).
47. M. Janssen, Int. J. Mod. Phys. B 8, 943 (1994).
48. A. Kyrala, Theoretical Physics: Applications of Vectors, Matrices, Thensors and Quaternions (Philadelphia, London, 1967).
49. T. Nakayama and K. Yakubo, Phys. Rep. 349, 239 (2001).
50. Details of the forced oscillator method for quaternion-real matrices will be published elsewhere.
51. T. Ando, Phys. Rev. B 40, 5325 (1989).
52. The power law behavior in a ALS tail region has been predicted by Ref. 30 in a metallic phase of two-dimensional symplectic systems.
53. There exist another type of ALS in the metallic phase, which are exponentially localized. [V. M. Apalkov, M. E. Raikh, and B. Shapiro, Phys. Rev. Lett. 89, 016802 (2002); 89, 126601 (2002); 92, 066601 (2004)]. However, we do not find such exponentially localized states at the critical point.
54. There exist another type of ALS in the metallic phase, which are exponentially localized. [V. M. Apalkov, M. E. Raikh, and B. Shapiro, Phys. Rev. Lett. 89, 016802 (2002); 89, 126601 (2002); 92, 066601 (2004)]. However, we do not find such exponentially localized states at the critical point.
55. There exist another type of ALS in the metallic phase, which are exponentially localized. [V. M. Apalkov, M. E. Raikh, and B. Shapiro, Phys. Rev. Lett. 89, 016802 (2002); 89, 126601 (2002); 92, 066601 (2004)]. However, we do not find such exponentially localized states at the critical point.
56. Three terms in the right-hand side of Eq. (15) are single-peak functions with different peak positions. This does not mean that the sum of these three terms has three peaks, because the peak positions are very close each other.