Electron-spin relaxation in bulk III-V semiconductors from a fully microscopic kinetic spin Bloch equation approach

Physical Review B - Condensed Matter and Materials Physics

Volumn 79, Issue 12, 2009, Pages

  Jiang, J H ^a,b   Wu, M W ^a,b  

^a UNIVERSITY OF SCIENCE AND TECHNOLOGY OF CHINA   (China)

^b UNIVERSITY OF SCIENCE AND TECHNOLOGY OF CHINA   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 65549135019     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.79.125206     Document Type: Article

References (132)

1. F. Meier and B. P. Zakharchenya, Optical Orientation (North-Holland, Amsterdam, 1984).
2. S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnár, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, Science 294, 1488 (2001). 10.1126/science.1065389 (Pubitemid 33063913)
3. Semiconductor Spintronics and Quantum Computation, edited by, D. D. Awschalom, D. Loss, and, N. Samarth, (Springer-Verlag, Berlin, 2002)
4. I. Autić, J. Fabian, and S. Das Sarma, Rev. Mod. Phys. 76, 323 (2004) 10.1103/RevModPhys.76.323
5. J. Fabian, A. Matos-Abiague, C. Ertler, P. Stano, and I. Autić, Acta Phys. Slov. 57, 565 (2007)
6. Spin Physics in Semiconductors, edited by, M. I. D'yakonov, (Springer, Berlin, 2008), and references therein.
7. J. M. Kikkawa and D. D. Awschalom, Phys. Rev. Lett. 80, 4313 (1998). 10.1103/PhysRevLett.80.4313
8. Long spin relaxation time was also observed in R. I. Dzhioev, V. L. Korenev, I. A. Merkulov, B. P. Zakharchenya, D. Gammon, Al. L. Efros, and D. S. Katzer, Phys. Rev. Lett. 88, 256801 (2002) 10.1103/PhysRevLett.88.256801
9. J. S. Colton, T. A. Kennedy, A. S. Bracker, D. Gammon, and J. B. Miller, Phys. Rev. B 67, 165315 (2003) 10.1103/PhysRevB.67.165315
10. M. Oestreich, M. Römer, R. J. Haug, and D. Hägele, Phys. Rev. Lett. 95, 216603 (2005). 10.1103/PhysRevLett.95.216603
11. J. M. Kikkawa and D. D. Awschalom, Nature (London) 397, 139 (1999). 10.1038/16420 (Pubitemid 29050912)
12. J. M. Kikkawa and D. D. Awschalom, Science 287, 473 (2000). 10.1126/science.287.5452.473 (Pubitemid 30061037)
13. M. Oestreich, M. Bender, J. Hübner, D. Hägele, W. W. Rühle, T. Hartmann, P. J. Klar, W. Heimbrodt, M. Lampalzer, K. Volz, and W. Stolz, Semicond. Sci. Technol. 17, 285 (2002). 10.1088/0268-1242/17/4/302 (Pubitemid 34410678)
14. I. Malajovich, J. M. Kikkawa, D. D. Awschalom, J. J. Berry, and N. Samarth, Phys. Rev. Lett. 84, 1015 (2000). 10.1103/PhysRevLett.84.1015
15. J. A. Gupta, R. Knobel, N. Samarth, and D. D. Awschalom, Science 292, 2458 (2001). 10.1126/science.1061169 (Pubitemid 32601652)
16. Y. Kato, R. C. Myers, D. C. Driscoll, A. C. Gossard, J. Levy, and D. D. Awschalom, Science 299, 1201 (2003). 10.1126/science.1080880 (Pubitemid 36237455)
17. Y. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, Nature (London) 427, 50 (2004). 10.1038/nature02202 (Pubitemid 38094816)
18. L. Meier, G. Salis, I. Shorubalko, E. Gini, S. Schön, and K. Ensslin, Nat. Phys. 3, 650 (2007). 10.1038/nphys675
19. Y. Yafet, Phys. Rev. 85, 478 (1952) 10.1103/PhysRev.85.478
20. R. J. Elliott, Phys. Rev. 96, 266 (1954). 10.1103/PhysRev.96.266
21. M. W. Wu and C. Z. Ning, Eur. Phys. J. B 18, 373 (2000) 10.1007/s100510070021
22. M. W. Wu and H. Metiu, Phys. Rev. B 61, 2945 (2000) 10.1103/PhysRevB.61. 2945
23. M. W. Wu, J. Phys. Soc. Jpn. 70, 2195 (2001). 10.1143/JPSJ.70.2195 (Pubitemid 33317803)
24. M. I. D'yakonov and V. I. Perel', Zh. Eksp. Teor. Fiz.. 60, 1954 (1971)
25. M. I. D'yakonov and V. I. Perel', Fiz. Tverd. Tela (Leningrad) 13, 3581 (1971)
26. M. I. D'yakonov and V. I. Perel', Sov. Phys. JETP 33, 1053 (1971);
27. M. I. D'yakonov and V. I. Perel', Sov. Phys. Solid State 13, 3023 (1972).
28. G. L. Bir, A. G. Aronov, and G. E. Pikus, Zh. Eksp. Teor. Fiz. 69, 1382 (1975);
29. G. L. Bir, A. G. Aronov, and G. E. Pikus, Sov. Phys. JETP 42, 705 (1976).
30. R. I. Dzhioev, K. V. Kavokin, V. L. Korenev, M. V. Lazarev, B. Y. Meltser, M. N. Stepanova, B. P. Zakharchenya, D. Gammon, and D. S. Katzer, Phys. Rev. B 66, 245204 (2002). 10.1103/PhysRevB.66.245204
31. Z. Chen, S. G. Carter, R. Bratschitsch, P. Dawson, and S. T. Cundiff, Nat. Phys. 3, 265 (2007). 10.1038/nphys537
32. Y. V. Pershin and V. Privman, Nano Lett. 3, 695 (2003). 10.1021/nl034009l (Pubitemid 37140582)
33. For localized electrons, besides the hyperfine interaction, the antisymmetric Dzyaloshinskii-Moriya interaction also leads to spin relaxation. This mechanism was studied recently with renewed interest [see, K. V. Kavokin, Phys. Rev. B 64 075305 (2001) 10.1103/PhysRevB.64.075305
34. K. V. Kavokin, Phys. Status Solidi A 190, 221 (2002) 10.1002/1521- 396X(200203)190:1<221::AID-PSSA221>3.0.CO;2-H
35. K. V. Kavokin, Semicond. Sci. Technol. 23, 114009 (2008) 10.1088/0268-1242/23/11/114009
36. L. P. Gor'kov and P. L. Krotkov, Phys. Rev. B 67, 033203 (2003) 10.1103/PhysRevB.67.033203
37. W. O. Putikka and R. Joynt, Phys. Rev. B 70, 113201 (2004) 10.1103/PhysRevB.70.113201
38. P. I. Tamborenea, D. Weinmann, and R. A. Jalabert, Phys. Rev. B 76, 085209 (2007) 10.1103/PhysRevB.76.085209]. Other spin relaxation mechanisms for localized electrons are proposed in a recent work
39. [Putikka and Joynt, Phys. Rev. B 70, 113201 (2004)], where both the localized and itinerant electrons are considered with the spin dynamics treated in a phenomenological way. 10.1103/PhysRevB.70.113201
40. P. H. Song and K. W. Kim, Phys. Rev. B 66, 035207 (2002). 10.1103/PhysRevB.66.035207
41. M. Q. Weng and M. W. Wu, Phys. Rev. B 68, 075312 (2003). 10.1103/PhysRevB.68.075312
42. M. Q. Weng, M. W. Wu, and L. Jiang, Phys. Rev. B 69, 245320 (2004). 10.1103/PhysRevB.69.245320
43. M. Q. Weng and M. W. Wu, Phys. Rev. B 70, 195318 (2004). 10.1103/PhysRevB.70.195318
44. C. Lü, J. L. Cheng, and M. W. Wu, Phys. Rev. B 73, 125314 (2006). 10.1103/PhysRevB.73.125314
45. J. Zhou, J. L. Cheng, and M. W. Wu, Phys. Rev. B 75, 045305 (2007). 10.1103/PhysRevB.75.045305
46. J. Zhou and M. W. Wu, Phys. Rev. B 77, 075318 (2008). 10.1103/PhysRevB.77.075318
47. P. Zhang, J. Zhou, and M. W. Wu, Phys. Rev. B 77, 235323 (2008). 10.1103/PhysRevB.77.235323
48. J. H. Jiang, M. W. Wu, and Y. Zhou, Phys. Rev. B 78, 125309 (2008). 10.1103/PhysRevB.78.125309
49. M. M. Glazov and E. L. Ivchenko, Pis'ma Zh. Eksp. Teor. Fiz. 75, 476 (2002)
50. M. M. Glazov and E. L. Ivchenko, JETP Lett. 75, 403 (2002) 10.1134/1.1490009
51. M. M. Glazov and E. L. Ivchenko, Zh. Eksp. Teor. Fiz. 126, 1465 (2004)
52. M. M. Glazov and E. L. Ivchenko, JETP 99, 1279 (2004). 10.1134/1.1854815 (Pubitemid 44261878)
53. W. J. H. Leyland, G. H. John, R. T. Harley, M. M. Glazov, E. L. Ivchenko, D. A. Ritchie, I. Farrer, A. J. Shields, and M. Henini, Phys. Rev. B 75, 165309 (2007). 10.1103/PhysRevB.75.165309
54. X. Z. Ruan, H. H. Luo, Y. Ji, Z. Y. Xu, and V. Umansky, Phys. Rev. B 77, 193307 (2008). 10.1103/PhysRevB.77.193307
55. L. H. Teng, P. Zhang, T. S. Lai, and M. W. Wu, Europhys. Lett. 84, 27006 (2008). 10.1209/0295-5075/84/27006
56. M. W. Wu, M. Q. Weng, and J. L. Cheng, in Physics, Chemistry and Application of Nanostructures: Reviews and Short Notes to Nanomeeting 2007, edited by, V. E. Borisenko, V. S. Gurin, and, S. V. Gaponenko, (World Scientific, Singapore, 2007), p. 14 (and references therein).
57. D. Stich, J. Zhou, T. Korn, D. Schuh, R. Schulz, W. Wegscheider, M. W. Wu, and C. Schüller, Phys. Rev. Lett. 98, 176401 (2007) 10.1103/PhysRevLett.98.176401
58. D. Stich, J. Zhou, T. Korn, D. Schuh, R. Schulz, W. Wegscheider, M. W. Wu, and C. Schüller, Phys. Rev. B 76, 205301 (2007). 10.1103/PhysRevB.76. 205301
59. T. Korn, D. Stich, R. Schulz, D. Schuh, W. Wegscheider, and C. Schüller, Adv. Solid State Phys. 48, 143 (2009). 10.1007/978-3-540-85859-1- 12
60. C. Yang, X. Cui, S.-Q. Shen, Z. Xu, and W. Ge, arXiv:0902.0484 (unpublished).
61. G. Fishman and G. Lampel, Phys. Rev. B 16, 820 (1977). 10.1103/PhysRevB.16.820
62. K. Zerrouati, F. Fabre, G. Bacquet, J. Bandet, J. Frandon, G. Lampel, and D. Paget, Phys. Rev. B 37, 1334 (1988). 10.1103/PhysRevB.37.1334
63. P. Zhang and M. W. Wu, Phys. Rev. B 76, 193312 (2007). 10.1103/PhysRevB.76.193312
64. The magnetic field dependence of the spin relaxation has been studied in previous works [E. L. Ivchenko, Sov. Phys. Solid State 15, 1048 (1973)
65. F. X. Bronold, I. Martin, A. Saxena, and D. L. Smith, Phys. Rev. B 66, 233206 (2002) 10.1103/PhysRevB.66.233206]
66. Moreover, the magnetic field could enable the spin relaxation due to the inhomogeneous broadened g factor, i.e., the energy dependent of g factor provides another inhomogeneous broadening besides the k -dependent SOC [see, M. W. Wu and C. Z. Ning, Eur. Phys. J. B 18, 373 (2000) 10.1007/s100510070021
67. F. X. Bronold, I. Martin, A. Saxena, and D. L. Smith, Phys. Rev. B 66, 233206 (2002) 10.1103/PhysRevB.66.233206]
68. Also note that a recent experimental result reveals anomalous magnetic field dependence of the spin relaxation time in the insulator phase [J. S. Colton, M. E. Heeb, P. Schroeder, A. Stokes, L. R. Wienkes, and A. S. Bracker, Phys. Rev. B 75, 205201 (2007)]. 10.1103/PhysRevB.75.205201
69. L. Jiang and M. W. Wu, Phys. Rev. B 72, 033311 (2005). 10.1103/PhysRevB.72.033311 (Pubitemid 41506651)
70. D. Stich, J. H. Jiang, T. Korn, R. Schulz, D. Schuh, W. Wegscheider, M. W. Wu, and C. Schüller, Phys. Rev. B 76, 073309 (2007). 10.1103/PhysRevB.76.073309
71. A. W. Holleitner, V. Sih, R. C. Myers, A. C. Gossard, and D. D. Awschalom, New J. Phys. 9, 342 (2007). 10.1088/1367-2630/9/9/342 (Pubitemid 47511019)
72. F. Zhang, H. Z. Zheng, Y. Ji, J. Liu, and G. R. Li, Europhys. Lett. 83, 47006 (2008). 10.1209/0295-5075/83/47006
73. F. Zhang, H. Z. Zheng, Y. Ji, J. Liu, and G. R. Li, Europhys. Lett. 83, 47007 (2008). 10.1209/0295-5075/83/47007
74. M. W. Wu and C. Z. Ning, Phys. Status Solidi B 222, 523 (2000). 10.1002/1521-3951(200011)222:2<523::AID-PSSB523>3.0.CO;2-0 (Pubitemid 33212395)
75. A. G. Aronov, G. E. Pikus, and A. N. Titkov, Zh. Eksp. Teor. Fiz. 84, 1170 (1983);
76. G. E. Pikus, and A. N. Titkov, Sov. Phys. JETP 57, 680 (1983).
77. I. Malajovich, J. J. Berry, N. Samarth, and D. D. Awschalom, Nature (London) 411, 770 (2001). 10.1038/35081014 (Pubitemid 32588093)
78. F. X. Bronold, A. Saxena, and D. L. Smith, Phys. Rev. B 70, 245210 (2004). 10.1103/PhysRevB.70.245210
79. H. Haug and A. P. Jauho, Quantum Kinetics in Transport and Optics of Semiconductors (Springer, Berlin, 1996).
80. G. Dresselhaus, Phys. Rev. 100, 580 (1955). 10.1103/PhysRev.100.580
81. D. J. Hilton and C. L. Tang, Phys. Rev. Lett. 89, 146601 (2002). 10.1103/PhysRevLett.89.146601
82. M. Krauß, M. Aeschlimann, and H. C. Schneider, Phys. Rev. Lett. 100, 256601 (2008). 10.1103/PhysRevLett.100.256601
83. We assume that the potential fluctuation mainly comes from the ionized impurities, and neglect the scattering by dislocation. The effect of the electron-dislocation scattering on spin relaxation has been studied in [D. Jena, Phys. Rev. B 70, 245203 (2004)]. 10.1103/PhysRevB.70.245203
84. G. D. Mahan, Many-Particle Physics (Plenum, New York, 1990).
85. J. Schliemann, Phys. Rev. B 74, 045214 (2006). 10.1103/PhysRevB.74.045214
86. M. Z. Maialle, E. A. de Andrada e Silva, and L. J. Sham, Phys. Rev. B 47, 15776 (1993). 10.1103/PhysRevB.47.15776
87. Semiconductors, edited by, O. Madelung, (Springer-Verlag, Berlin, 1987), Vol. 17a.
88. W. Ekardt, K. Lösch, and D. Bimberg, Phys. Rev. B 20, 3303 (1979). 10.1103/PhysRevB.20.3303
89. J. Y. Fu, M. Q. Weng, and M. W. Wu, Physica E 40, 2890 (2008). 10.1016/j.physe.2008.02.006
90. J.-M. Jancu, R. Scholz, E. A. de Andrada e Silva, and G. C. La Rocca, Phys. Rev. B 72, 193201 (2005). 10.1103/PhysRevB.72.193201
91. U. Rössler and H.-R. Trebin, Phys. Rev. B 23, 1961 (1981). 10.1103/PhysRevB.23.1961
92. R. J. Seymour, M. R. Junnarkar, and R. R. Alfano, Phys. Rev. B 24, 3623 (1981). 10.1103/PhysRevB.24.3623
93. Lists of the SOC parameters γD in GaAs calculated and measured via various methods are given in the supplementary information of [J. J. Krich and B. I. Halperin, Phys. Rev. Lett. 98, 226802 (2007) 10.1103/PhysRevLett.98. 226802] and in
94. [A. N. Chantis, M. van Schilfgaarde, and T. Kotani, Phys. Rev. Lett. 96, 086405 (2006)]. Our fitting value of γD is in the reasonable range in these lists. 10.1103/PhysRevLett.96.086405 (Pubitemid 43327443)
95. The EY spin relaxation due to the electron-electron Coulomb scattering was studied in [P. Boguslawski, Solid State Commun. 33, 389 (1980) 10.1016/0038-1098(80)91177-1
96. P. I. Tamborenea, M. A. Kuroda, and F. L. Bottesi, Phys. Rev. B 68, 245205 (2003)]. The latter also included the electron-impurity scattering, showing that the EY mechanism is ineffective in bulk GaAs which is also consistent with our results. 10.1103/PhysRevB.68.245205
97. A. Amo, L. Viña, P. Lugli, C. Tejedor, A. I. Toropov, and K. S. Zhuravlev, Phys. Rev. B 75, 085202 (2007). 10.1103/PhysRevB.75.085202
98. M. A. Brand, A. Malinowski, O. Z. Karimov, P. A. Marsden, R. T. Harley, A. J. Shields, D. Sanvitto, D. A. Ritchie, and M. Y. Simmons, Phys. Rev. Lett. 89, 236601 (2002). 10.1103/PhysRevLett.89.236601
99. W. J. H. Leyland, R. T. Harley, M. Henini, A. J. Shields, I. Farrer, and D. A. Ritchie, Phys. Rev. B 76, 195305 (2007). 10.1103/PhysRevB.76.195305
100. W. J. H. Leyland, R. T. Harley, M. Henini, A. J. Shields, I. Farrer, and D. A. Ritchie, Phys. Rev. B 77, 205321 (2008). 10.1103/PhysRevB.77.205321
101. R. T. Harley, in Spin Physics in Semiconductors, edited by, M. I. D'yakonov, (Springer, Berlin, 2008).
102. S. Krishnamurthy, M. van Schilfgaarde, and N. Newman, Appl. Phys. Lett. 83, 1761 (2003). 10.1063/1.1606873
103. W. H. Lau, J. T. Olesberg, and M. E. Flatte, Phys. Rev. B 64, 161301 (R) (2001). 10.1103/PhysRevB.64.161301
104. Z. G. Yu, S. Krishnamurthy, M. van Schilfgaarde, and N. Newman, Phys. Rev. B 71, 245312 (2005). 10.1103/PhysRevB.71.245312 (Pubitemid 41702956)
105. A. Dyson and B. K. Ridley, Phys. Rev. B 69, 125211 (2004). 10.1103/PhysRevB.69.125211
106. M. Z. Maialle, Phys. Rev. B 54, 1967 (1996). 10.1103/PhysRevB.54.1967
107. J. N. Chazalviel, Phys. Rev. B 11, 1555 (1975). 10.1103/PhysRevB.11.1555
108. The spin-orbit parameter is another quantity which may affect the ratio. To check the parameter we used, we calculate the SRT corresponding to that measured in a recent experiment [P. Murzyn, C. R. Pidgeon, P. J. Phillips, J-P. Wells, N. T. Gordon, T. Ashley, J. H. Jefferson, T. M. Burke, J. Giess, M. Merrick, B. N. Murdin, and C. D. Maxey, Phys. Rev. B 67, 235202 (2003)], where ne =2× 1015 cm-3 and Nex = 1016 cm-3 at 150 K. We get a SRT of 15.2 ps which is close to the measured value of 16 ps. 10.1103/PhysRevB.67.235202
109. The spin-orbit parameter is also checked by comparing with the experimental results in Ref.. A best fitting gives γD =99.2eV3 in InAs which is 2.3 times as large as that in Ref.. This only enhances the DP spin relaxation by 5.5 times and strengthens our conclusion that the DP mechanism is more efficient (6 times) than the EY mechanism in InAs. It is noted that the fitted γD =99.2eV 3 is comparable with the value γD =105eV 3 calculated in 10.1063/1.1290143
110. The spin-orbit parameter γD in GaAs fitted from experiments is 2.9 times smaller than that in Table 1. Even for such a γD, the spin relaxation due to the DP mechanism is still much more efficient (20 times) than that due to the EY mechanism [see also Appendix].
111. K. L. Litvinenko, L. Nikzad, J. Allam, B. N. Murdin, C. R. Pidgeon, J. J. Harris, and L. F. Cohen, J. Supercond. 20, 461 (2007). 10.1007/s10948-007-0237- 4 (Pubitemid 47476908)
112. G. F. Giulianni and G. Vignale, Quantum Theory of the Electron Liquid (Cambridge University Press, Cambridge, England, 2005).
113. B. N. Murdin, K. Litvinenko, J. Allam, C. R. Pidgeon, M. Bird, K. Morrison, T. Zhang, S. K. Clowes, W. R. Branford, J. Harris, and L. F. Cohen, Phys. Rev. B 72, 085346 (2005). 10.1103/PhysRevB.72.085346
114. K. L. Litvinenko, B. N. Murdin, J. Allam, C. R. Pidgeon, T. Zhang, J. J. Harris, L. F. Cohen, D. A. Eustace, and D. W. McComb, Phys. Rev. B 74, 075331 (2006). 10.1103/PhysRevB.74.075331
115. P. E. Hohage, G. Bacher, D. Reuter, and A. D. Wieck, Appl. Phys. Lett. 89, 231101 (2006). 10.1063/1.2398909
116. B. Beschoten, E. Johnston-Halperin, D. K. Young, M. Poggio, J. E. Grimaldi, S. Keller, S. P. DenBaars, U. K. Mishra, E. L. Hu, and D. D. Awschalom, Phys. Rev. B 63, 121202 (2001). 10.1103/PhysRevB.63.121202
117. S. Oertel, J. Hübner, and M. Oestreich, Appl. Phys. Lett. 93, 132112 (2008). 10.1063/1.2993344
118. H. Saarikoski and G. E. W. Bauer, Phys. Rev. Lett. 102, 097204 (2009). 10.1103/PhysRevLett.102.097204
119. As demonstrated in Sec. 5, the BAP mechanism is more important in GaAs than in GaSb, thus in GaSb the BAP mechanism is also negligible. Also a recent experimental investigation indicates that the BAP mechanism is unimportant in intrinsic InSb [B. N. Murdin, K. Litvinenko, D. G. Clarke, C. R. Pidgeon, P. Murzyn, P. J. Phillips, D. Carder, G. Berden, B. Redlich, A. F. G. van der Meer, S. Clowes, J. Harris, L. F. Cohen, T. Ashley, and L. Buckle, Phys. Rev. Lett. 96, 096603 (2006)]. 10.1103/PhysRevLett.96.096603 (Pubitemid 43385260)
120. Note that the SOC parameter we used in this section (γD =23.9eV 3) is larger than the value (γD =8.2eV 3) fitted from experimental data (see Appendix). However, as the DP spin relaxation is more than two orders of magnitude larger than the BAP spin relaxation, the choice of the γD does not change the conclusion that the BAP mechanism is unimportant.
121. Further calculation indicates that the results from Eq. 28 deviate more from the calculation via the KSBEs at small spin polarization as the Pauli blocking of spin-flip scattering is more pronounced when both spin bands are nearly equally populated.
122. According to Eq. 27, the effect of the Coulomb HF term can be estimated by τs (P) = τs (P=0) [1+ (V q0 ne P τ) 2] where V q0 describes the average Coulomb interaction with q0, ne, P being the average momentum, the electron density, and the initial spin polarization, respectively. Thus the effect of the Coulomb HF term is more pronounced for larger ne, P and weaker scattering (i.e., larger τ). Moreover, increase in the temperature would reduce the effect as q0 becomes larger and V q0 becomes smaller.
123. The EY mechanism is checked to be unimportant in the parameter region we studied for both p-GaAs and p-GaSb.
124. The initial spin polarization dependence of the SRT is weak due to the fact that the impurity density is larger than the electron density according to the analysis in Sec. 3 3.
125. H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 4th ed. (World Scientific, Singapore, 2004).
126. J. H. Jiang, Y. Zhou, T. Korn, C. Schüller, and M. W. Wu, arXiv:0901.0061 (unpublished).
127. J. Y. Fu and M. W. Wu, J. Appl. Phys. 104, 093712 (2008). 10.1063/1.3018600
128. Spin relaxation in ZnO has attracted much interest recently. Experiment indicates very long spin relaxation time [S. Ghosh, V. Sih, W. H. Lau, D. D. Awschalom, S.-Y. Bae, S. Wang, S. Vaidya, and G. Chapline, Appl. Phys. Lett. 86, 232507 (2005) 10.1063/1.1946204] and the electrical control of spin lifetime was also achieved
129. [S. Ghosh, D. W. Steuerman, B. Maertz, K. Ohtani, H. Xu, H. Ohno, and D. D. Awschalom, Appl. Phys. Lett. 92, 162109 (2008) 10.1063/1.2913049]
130. a theoretical study including both the localized and conduction electrons with the Wurzite-structure-induced Rashba-like SOC considered was performed [N. J. Harmon, W. O. Putikka, and R. Joynt, Phys. Rev. B 79, 115204 (2009)]. 10.1103/PhysRevB.79.115204
131. M. Krauß, R. Bratschitsch, Z. Chen, S. T. Cundiff, and H. C. Schneider, arXiv:0902.0270 (unpublished).
132. J. L. Cheng, Ph.D. thesis, University of Science and Technology of China, 2007.