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Rashba spin splitting coefficients for the first two subbands1,2 and intersubband spin-orbit coupling coefficient 12 are obtained by projecting the characteristic equation into the subspace of conduction band. Then Schrdinger and the Poisson equations are solved self-consistently to calculate1,2 and 12 under different gate voltages. Then contributions to the spin-orbit coupling coefficients from the well, the left and the right heterointerfaces and the left and the right barriers of the quantum well are discussed. Resulsts show that the spin-orbit coupling coefficient can be modulated by the gate voltage, and the intersubband spin-orbit coupling coefficients calculated here are a little smaller than the Rashba coefficients1,2, but they are basically of the same order.
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Keywords:
- Rashba spin splitting /
- intersubband spin-orbit coupling /
- self-consistent calculation /
- two dimensional electron gas
[1] Zutic I, fabian J, Das Sarma S 2004 Rev. Mod. Phys. 76 323
[2] Ikai Lo, Gau M H, Tsai J K, Chen Y L, Chang Z J, Wang W T, Chiang J C, Aggerstam T, Lourdudoss S 2007 Phys. Rev. B 75 245307
[3] He X W, Shen B, Tang Y Q, Tang N, Yin C M, Xu F J, Yang Z J, Zhang G y, Chen Y H, Tang C G, Wang Z G 2007 Appl. Phys. Lett. 91 071912
[4] Litvinov V I 2003 Phys. Rev. B 68 155314
[5] Pfeffer P, Zawadzki W 1999 Phys. Rev. B 59 5312
[6] Weber W, Ganichev S D, Danilov S N, Weiss D, Prettl W, Kvon N D, Bel’kov V V Golub L E, Cho H I, Lee J H 2005 Appl. Phys. Lett. 87 262106
[7] Ganichev S D, Bel’kov V V, Golub L E, Ivchenko E L, Schneider P, Giglberger S, Eroms J, De Boeck J, Borghs G, Wegscheider W, Weiss D, Prettl W 2004 Phys. Rev. Lett. 92, 256601
[8] Chao Z J, Gui Y S, Shu X Z, Dai N, Guo S L, Chu J H 2004 Acta Phys. Sin. 53 1186 (in Chinese) [仇志军, 桂永胜, 疏小舟, 戴宁, 郭少令, 禇君浩 2004 53 1186]
[9] Dresselhaus G 1955 Phys. Rev. 100 580
[10] Bychkov Y A, Rashba E I 1984 J. Phys. C 17 6039
[11] Sun H Z, Zhang P, Duang S Q, Zhao X G 2006 Chin. Phys. 15 3019
[12] Yan Y Z, Hu L B 2010 Chin. Phys. B 19 047203
[13] Li Y G, Li B Z 2005 Chin. Phys. 14 1021
[14] Wolf S A, Awschalom D D, Buhrman R A, Daughton J M, von Molnár S, Roukes M L, Chtchelkanova A Y, Treger D M 2001 Science 294 1488
[15] Awschalom D, Loss D, Samarth N 2002 Semiconductor Spintronics and Quantum Computation (Berlin Springer) p1–3
[16] Wang X H, An X T, Liu J J 2009 Chin. Phys. B 18 749
[17] Sheng W, Wang Y, Zhuo G H 2007 Chin. Phys. 16 533
[18] Tang N, Shen B, Zheng Z W, Liu J, Chen D J, Lu J, Zhang R, Shi Y, Zheng Y D, Gui Y S, Jiang C P, Qiu Z J, Guo S L, Chu J H, Hoshino K, Someya T, Arakawa Y 2003 J. Appl. Phys. 94 5420
[19] Zheng Z W, Shen B, Jiang C P, Gui Y S, Someya Y, Zhang R, Shi Y, Zheng Y D, Guo S L, Chu J H, Arakawa Y 2003 J. Appl. Phys. 93 1651
[20] Winkler R 2003 Spin-Orbit coupling effects in two-dimensional electron and hole systems (Berlin Springer) p77–86
[21] Calsaverini R S, John Schliemann, Esmerindo Bernardes, Carlos Egues J, Daniel Loss 2008 Phys. Rev. B 78 155313
[22] Esmerindo Bernardes, Calsaverini R S, Esmerindo Bernardes, Carlos Egues J, Daniel Loss 2007 Phys. Rev. Lett. 99 076603
[23] Jaroslav Fabian, Alex Matos-Abiaguea, Christian Ertlera, Peter Stano, Igoř Zuti′c 2007 Acta Physica Slovaca 57 565
[24] Chuang S L, Chang C S 1996 Phys. Rev. B 54 2491
[25] Litvinov V I 2006 Appl. Phys. Lett. 89 222108
[26] Li M, Zhang R, Zhang Z, Yan Y S, Liu B, Fu D, Zhao C J, Xie Z L, Xiu X Q, Zheng Y D 2010 Superlattice and Microstructure 47 522
[27] Li M, Zhang R, Zhang Z, Yan W S, Liu B, Fu D, Zhao C Z, Xie Z L, Xiu X Q, Zheng Y D May 2009 13th International Workshop on Computational Electronics p230–233
[28] Li M, Zhang R, Zhang Z, Liu B, Fu D Y, Zhao C Z, Xie Z L, Xiu X Q, Zheng Y D 2011 Phys. Status Solidi B 248 187
[29] Tan I H, Snider G L, Chang L D, Hu E L 1990 J. Appl. Phys. 68 4071
[30] Kumagai M, Chuang S L, Ando H 1998 Phys. Rev. B 57 15303
[31] Suzuki M, Uenoyama T, Yanase A 1995 Phys. Rev. B 52 8132
[32] Ikai Lo, Tsai J K, Yao W J, Ho P C, Tu L W, Chang T C, Elhamri S, Mitchel W C, Hsieh K Y, Huang J H, Huang H L, Tsai W C 2002 Phys. Rev. B 65 R161306
[33] Tsubaki, Maeda N, Saitoh T, Kobayashi N 2002 Appl. Phys. Lett. 80 3126
[34] Schmult, Manfra M J, Punnoose A, Sergent A M, Baldwin K W, Molnar R J 2006 Phys. Rev. B 74 033302
[35] Koga T, Nitta J, Akazaki T, Takayanagi H 2002 Phys. Rev. Lett. 89 046801
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[1] Zutic I, fabian J, Das Sarma S 2004 Rev. Mod. Phys. 76 323
[2] Ikai Lo, Gau M H, Tsai J K, Chen Y L, Chang Z J, Wang W T, Chiang J C, Aggerstam T, Lourdudoss S 2007 Phys. Rev. B 75 245307
[3] He X W, Shen B, Tang Y Q, Tang N, Yin C M, Xu F J, Yang Z J, Zhang G y, Chen Y H, Tang C G, Wang Z G 2007 Appl. Phys. Lett. 91 071912
[4] Litvinov V I 2003 Phys. Rev. B 68 155314
[5] Pfeffer P, Zawadzki W 1999 Phys. Rev. B 59 5312
[6] Weber W, Ganichev S D, Danilov S N, Weiss D, Prettl W, Kvon N D, Bel’kov V V Golub L E, Cho H I, Lee J H 2005 Appl. Phys. Lett. 87 262106
[7] Ganichev S D, Bel’kov V V, Golub L E, Ivchenko E L, Schneider P, Giglberger S, Eroms J, De Boeck J, Borghs G, Wegscheider W, Weiss D, Prettl W 2004 Phys. Rev. Lett. 92, 256601
[8] Chao Z J, Gui Y S, Shu X Z, Dai N, Guo S L, Chu J H 2004 Acta Phys. Sin. 53 1186 (in Chinese) [仇志军, 桂永胜, 疏小舟, 戴宁, 郭少令, 禇君浩 2004 53 1186]
[9] Dresselhaus G 1955 Phys. Rev. 100 580
[10] Bychkov Y A, Rashba E I 1984 J. Phys. C 17 6039
[11] Sun H Z, Zhang P, Duang S Q, Zhao X G 2006 Chin. Phys. 15 3019
[12] Yan Y Z, Hu L B 2010 Chin. Phys. B 19 047203
[13] Li Y G, Li B Z 2005 Chin. Phys. 14 1021
[14] Wolf S A, Awschalom D D, Buhrman R A, Daughton J M, von Molnár S, Roukes M L, Chtchelkanova A Y, Treger D M 2001 Science 294 1488
[15] Awschalom D, Loss D, Samarth N 2002 Semiconductor Spintronics and Quantum Computation (Berlin Springer) p1–3
[16] Wang X H, An X T, Liu J J 2009 Chin. Phys. B 18 749
[17] Sheng W, Wang Y, Zhuo G H 2007 Chin. Phys. 16 533
[18] Tang N, Shen B, Zheng Z W, Liu J, Chen D J, Lu J, Zhang R, Shi Y, Zheng Y D, Gui Y S, Jiang C P, Qiu Z J, Guo S L, Chu J H, Hoshino K, Someya T, Arakawa Y 2003 J. Appl. Phys. 94 5420
[19] Zheng Z W, Shen B, Jiang C P, Gui Y S, Someya Y, Zhang R, Shi Y, Zheng Y D, Guo S L, Chu J H, Arakawa Y 2003 J. Appl. Phys. 93 1651
[20] Winkler R 2003 Spin-Orbit coupling effects in two-dimensional electron and hole systems (Berlin Springer) p77–86
[21] Calsaverini R S, John Schliemann, Esmerindo Bernardes, Carlos Egues J, Daniel Loss 2008 Phys. Rev. B 78 155313
[22] Esmerindo Bernardes, Calsaverini R S, Esmerindo Bernardes, Carlos Egues J, Daniel Loss 2007 Phys. Rev. Lett. 99 076603
[23] Jaroslav Fabian, Alex Matos-Abiaguea, Christian Ertlera, Peter Stano, Igoř Zuti′c 2007 Acta Physica Slovaca 57 565
[24] Chuang S L, Chang C S 1996 Phys. Rev. B 54 2491
[25] Litvinov V I 2006 Appl. Phys. Lett. 89 222108
[26] Li M, Zhang R, Zhang Z, Yan Y S, Liu B, Fu D, Zhao C J, Xie Z L, Xiu X Q, Zheng Y D 2010 Superlattice and Microstructure 47 522
[27] Li M, Zhang R, Zhang Z, Yan W S, Liu B, Fu D, Zhao C Z, Xie Z L, Xiu X Q, Zheng Y D May 2009 13th International Workshop on Computational Electronics p230–233
[28] Li M, Zhang R, Zhang Z, Liu B, Fu D Y, Zhao C Z, Xie Z L, Xiu X Q, Zheng Y D 2011 Phys. Status Solidi B 248 187
[29] Tan I H, Snider G L, Chang L D, Hu E L 1990 J. Appl. Phys. 68 4071
[30] Kumagai M, Chuang S L, Ando H 1998 Phys. Rev. B 57 15303
[31] Suzuki M, Uenoyama T, Yanase A 1995 Phys. Rev. B 52 8132
[32] Ikai Lo, Tsai J K, Yao W J, Ho P C, Tu L W, Chang T C, Elhamri S, Mitchel W C, Hsieh K Y, Huang J H, Huang H L, Tsai W C 2002 Phys. Rev. B 65 R161306
[33] Tsubaki, Maeda N, Saitoh T, Kobayashi N 2002 Appl. Phys. Lett. 80 3126
[34] Schmult, Manfra M J, Punnoose A, Sergent A M, Baldwin K W, Molnar R J 2006 Phys. Rev. B 74 033302
[35] Koga T, Nitta J, Akazaki T, Takayanagi H 2002 Phys. Rev. Lett. 89 046801
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