Multiband energy spectra of spin electrons with two-dimensional magnetic modulations

Physical Review B - Condensed Matter and Materials Physics

Volumn 57, Issue 20, 1998, Pages 13002-13009

  Chang, Ming Che ^a   Yang, Min Fong ^b  

^a NATIONAL TSING HUA UNIVERSITY   (Taiwan)

^b CHANG GUNG UNIVERSITY   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0346050335     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.57.13002     Document Type: Article

References (54)

1. D. P. Xue and G. Xiao, Phys. Rev. B 45, 5986 (1992).
2. Phys. Rev. BF M. Peeters and P. Vasilopoulos, 47, 1466 (1993).
3. R. Yagi and Y. Iye, J. Phys. Soc. Jpn. 62, 1279 (1993).
4. I. S. Ibrahim and F. M. Peeters, Phys. Rev. B 52, 17 321 (1995).
5. Phys. Rev. BA. Krakovsky, 53, 8469 (1996).
6. Phys. Rev. BQ. W. Shi and K. Y. Szeto, 55, 4558 (1997).
7. X. Wu and S. E. Ulloa, Phys. Rev. B 47, 7182 (1993).
8. H. L. Cui, V. Fessatidis, and P. Vasilopoulos, Phys. Rev. B 52, 13 765 (1995).
9. A. Akjouj and B. Djafari-Rouhani, Solid State Commun. 103, 161 (1997).
10. A. Manolescu and R. R. Gerhardts, Phys. Rev. B 56, 9707 (1997).
11. Phys. Rev. BU. J. Gossmann, A. Manolescu, and R. R. Gerhardts, 57, 1680 (1998).
12. G. Gumbs, D. Miessein, and D. Huang, Phys. Rev. B 52, 14 755 (1995).
13. Phys. Rev. BG. Y. Oh and M. H. Lee, 53, 1225 (1996).
14. A. O. Barut and J. P. Dowling, Phys. Rev. Lett. 68, 3571 (1992).
15. H. A. Carmona, A. K. Geim, A. Nogaret, P. C. Main, T. J. Foster, M. Henini, S. P. Beaumont, and M. G. Blamire, Phys. Rev. Lett. 74, 3009 (1995).
16. P. D. Ye, D. Weiss, R. R. Gerhardts, M. Seeger, K. von Klitzing, K. Eberl, and H. Nickel, Phys. Rev. Lett. 74, 3013 (1995).
17. X. Wu and S. E. Ulloa, Phys. Rev. B 47, 10 028 (1993).
18. R. R. Gerhardts, Phys. Rev. B 53, 11 064 (1996).
19. Phys. Rev. BR. R. Gerhardts, D. Pfannkuche, and V. Gudmundsson, 53, 9591 (1996).
20. D. Yoshiyoka and Y. Iye, J. Phys. Soc. Jpn. 87, 448 (1987).
21. M. C. Chang and Q. Niu, Phys. Rev. B 50, 10 843 (1994).
22. B. A. Dubrovin and S. P. Novikov, Sov. Phys. JETP 52, 511 (1980).
23. B. A. DubrovinS. P. NovikovSov. Math. Dokl. 22, 240 (1980) [Dokl. Akad. Nauk. SSSR 253, 1293 (1980)];
24. Dokl. Akad. Nauk. SSSRS. P. Novikov, ibid.23, 298 (1981) [ 257, 538 (1981)].
25. A. Y. Rom, Phys. Rev. B 55, 11 025 (1997).
26. R. R. Gerhardts, D. Weiss, and K. von Klitzing, Phys. Rev. Lett. 62, 1173 (1989).
27. Phys. Rev. Lett.R. W. Winkler, J. P. Kotthaus, and K. Ploog, 62, 1177 (1989).
28. Phys. Rev. Lett.P. Vasilopoulos and F. M. Peeters, 63, 2120 (1989).
29. Phys. Rev. Lett.C. W. J. Beenakker, 62, 2020 (1989).
30. C. Zhang and R. R. Gerhardts, Phys. Rev. B 41, 12 850 (1990).
31. Phys. Rev. BR. R. Gerhardts, 45, 3449 (1991).
32. D. R. Hofstadter, Phys. Rev. 14, 2239 (1976).
33. M. Wilkinson, J. Phys. A 17, 3459 (1984).
34. J. Phys. AM. Wilkinson 20, 4337 (1987).
35. J. Phys. AM. Wilkinson 23, 2529 (1990).
36. R. Rammal and J. Bellissard, J. Phys. (Paris) 51, 1803 (1990).
37. D. J. Thouless, in The Quantum Hall Effect, 2nd ed., edited by R. E. Prange and S. M. Girvin (Springer-Verlag, New York, 1990).
38. P. D. Ye, D. Weiss, K. von Klitzing, K. Eberl, and H. Nickel, Appl. Phys. Lett. 67, 1441 (1995).
39. P. D. Ye, D. Weiss, and R. R. Gerhardts, J. Appl. Phys. 81, 5444 (1997).
40. Some experimental indications of the fractal structure in 2DEM systems can be found in R. R. Gerhardts, D. Weiss, and U. Wulf, Phys. Rev. B 43, 5192 (1991).
41. I. N. Harris, H. D. M. Davies, J. F. Ryan, A. J. Turberfield, C. T. Foxon, and J. J. Harris, Europhys. Lett. 29, 333 (1995).
42. R. Alicki, J. R. Klauder, and J. Lewandowski, Phys. Rev. A 48, 2538 (1993). Alicki et al. extend Dubrovin and Novikov’s result (Ref. 14) to a more general case, where the 2DEG resides on a general 2D curved surface with a nonuniform magnetic field everywhere perpendicular to the surface.
43. L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Pergamon Press, Oxford, 1985).
44. J. Zak, Phys. Rev. 136, A776 (1964).
45. Phys. Rev.J. Zak 134, A1602 (1964).
46. A similar multiband calculation has been done recently for the 2DEM systems by using a matrix continued fraction expansion; see G. Petschel and T. Geisel, Phys. Rev. Lett. 71, 239 (1993).
47. Also see D. Springsguth, R. Ketzmerick, and T. Geisel, Phys. Rev. B 56, 2036 (1997).
48. Y. Aharonov and A. Casher, Phys. Rev. A 19, 2461 (1979). In this paper, the authors show that the zero-energy states always exist for a 2DEG under a localized nonuniform magnetic field.
49. L. E. Gendenshtein, Sov. J. Nucl. Phys. 41, 166 (1985).
50. M. J. Snelling, G. P. Flinn, A. S. Plant, R. T. Harley, A. C. Tropper, R. Eccleston, and C. C Philips, Phys. Rev. B 44, 11 345 (1991).
51. R. M. Hannak, M. Oestreich, S. P. Heberle, and W. W. Ruhle, Solid State Commun. 93, 313 (1995).
52. D. K. Maude, M. Potemski, J. C. Portal, M. Henini, L. Eaves, G. Hill, andn M. A. Pate, Phys. Rev. Lett. 77, 4604 (1996).
53. J. Rammer and A. L. Shelankov, Phys. Rev. B 36, 3135 (1987).
54. M. C. Chang, M. F. Yang, and T. M. Hong, Phys. Rev. B 56, 3602 (1997), and references therein.