Geometrical phase effects on the Wigner distribution of Bloch electrons

Physical Review B - Condensed Matter and Materials Physics

Volumn 74, Issue 3, 2006, Pages

  Culcer, Dimitrie ^a   Niu, Qian ^a  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33746255849     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.74.035209     Document Type: Article

References (48)

1. N. W. Ashcroft and N. D. Mermin, Solid State Physics, 2nd ed. (Saunders College Publishing, New York, 1976).
2. D. Culcer, J. Sinova, N. A. Sinitsyn, T. Jungwirth, A. H. MacDonald, and Q. Niu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.046602 93, 046602 (2004).
3. D. Culcer, Yugui Yao, A. H. MacDonald, and Q. Niu, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.72.045215 72, 045215 (2005).
4. J. Sinova, D. Culcer, Q. Niu, N. A. Sinitsyn, T. Jungwirth, and A. H. MacDonald, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.126603 92, 126603 (2004).
5. S. Murakami, N. Nagaosa, and S.-C. Zhang, Science SCIEAS 0036-8075 10.1126/science.1087128 301, 1348 (2003).
6. S. Murakami, N. Nagaosa, and S.-C. Zhang, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.69.235206 69, 235206 (2004).
7. S. Zhang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.393 85, 393 (2000).
8. S. Zhang and Z. Yang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.066602 94, 066602 (2005).
9. L. Hu, J. Gao, and S. Q. Shen, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.70.235323 70, 235323 (2004).
10. J. I. Inoue, G. E. W. Bauer, and L. W. Molenkamp, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.67.033104 67, 033104 (2003).
11. E. G. Mishchenko, A. V. Shytov, and B. I. Halperin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.226602 93, 226602 (2004).
12. O. V. Dimitrova, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.71.245327 71, 245327 (2005).
13. G. Y. Guo, Y. Yao, and Q. Niu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.226601 94, 226601 (2005).
14. Y. Yao and Z. Fang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.156601 95, 156601 (2005).
15. J. Callaway, Quantum Theory of the Solid State (Academic Press, New York, 1976).
16. G. Sundaram and Q. Niu, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.59.14915 59, 14915 (1999).
17. M. V. Berry, Proc. R. Soc. London, Ser. A PRLAAZ 1364-5021 392, 45 (1984).
18. D. Culcer, A. MacDonald, and Q. Niu, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.68.045327 68, 045327 (2003).
19. T. Jungwirth, Q. Niu, and A. H. MacDonald, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.207208 88, 207208 (2002).
20. Yugui Yao, Leonard Kleinman, A. H. MacDonald, Jairo Sinova, T. Jungwirth, Ding-sheng Wang, Enge Wang, and Qian Niu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.037204 92, 037204 (2004).
21. D. Culcer, Yugui Yao, and Q. Niu, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.72.085110 72, 085110 (2005).
22. R. Shindou and K. Imura, Nucl. Phys. B NUPBBO 0550-3213 10.1016/j.nuclphysb.2005.05.019 720 [FS], 399 (2005).
23. S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnar, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, Science SCIEAS 0036-8075 10.1126/science.1065389 294, 1488 (2001).
24. P. R. Hammar and M. Johnson, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.066806 88, 066806 (2002).
25. Y. K. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, Science SCIEAS 0036-8075 10.1126/science.1105514 306, 1910 (2004).
26. J. Wunderlich, B. Kaestner, J. Sinova, and T. Jungwirth, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.047204 94, 047204 (2005).
27. Y. K. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.176601 93, 176601 (2004).
28. L. E. Reichl, A Modern Course in Statistical Physics (University of Texas Press, Austin, 1980).
29. An interesting recent article, G. A. Fiete and E. G. Heller, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.022112 68, 022112 (2003), discusses this topic from a somewhat different point of view.
30. R. G. Littlejohn and W. G. Flynn, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.44.5239 44, 5239 (1991).
31. M. Marder, Condensed Matter Physics (John Wiley, New York, 2000).
32. M. I. Dyakonov and V. I. Perel, JETP Lett. JTPLA2 0021-3640 35A, 459 (1971).
33. M. I. Dyakonov and V. I. Perel, Sov. Phys. JETP SPHJAR 0038-5646 33, 1053 (1971).
34. M. I. Dyakonov and V. I. Perel, Sov. Phys. Solid State SPSSA7 0038-5654 13, 3023 (1972).
35. M. I. Dyakonov and V. Y. Kachorovskii, Sov. Phys. Semicond. SPSEAX 0038-5700 20, 110 (1986).
36. E. L. Ivchenko, Y. B. Lyanda-Geller, and G. E. Pikus, Sov. Phys. JETP SPHJAR 0038-5646 71, 550 (1990).
37. G. E. Pikus and A. N. Titkov, in Optical Orientation (Elsevier Science Publications, Amsterdam, 1984).
38. A. G. Aronov, Yu. B. Lyanda-Geller, and G. E. Pikus, Sov. Phys. JETP SPHJAR 0038-5646 73, 537 (1991).
39. Y. N. Qi and S. Zhang, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.65. 214407 65, 214407 (2002);
40. Y. N. Qi and S. Zhang, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.67. 052407 67, 052407 (2003).
41. U. Fano, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.29.74 29, 74 (1957).
42. A. Messiah, Quantum Mechanics (Dover Publications, New York, 2000).
43. J. Shi, P. Zhang, D. Xiao, and Q. Niu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.076604 96, 076604 (2006).
44. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1999), Sec. 6.6, pp. 248-258.
45. J. M. Luttinger, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.102.1030 102, 1030 (1956).
46. M. Zarea and S. E. Ulloa, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.73.165306 73, 165306 (2006).
47. A. M. Dudarev, R. B. Diener, I. Carusotto, and Q. Niu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.153005 92, 153005 (2004).
48. Y. Kato, Nature (London) NATUAS 0028-0836 10.1038/nature02202 427, 50 (2004).