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Study of Rashba spin splitting and intersubband spin-orbit coupling effect in AlGaN/GaN quantum wells

Li Ming Zhang Rong Liu Bin Fu De-Yi Zhao Chuan-Zhen Xie Zhi-Li Xiu Xiang-Qian Zheng You-Dou

Study of Rashba spin splitting and intersubband spin-orbit coupling effect in AlGaN/GaN quantum wells

Li Ming, Zhang Rong, Liu Bin, Fu De-Yi, Zhao Chuan-Zhen, Xie Zhi-Li, Xiu Xiang-Qian, Zheng You-Dou
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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.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos?60990311, 60721063, 60906025, 60936004), the State Key Development Program for Basic Research of China (Grant No?2011CB301900), the State Development Program for Research on Advanced technology of China (Grant No. 2009AA03A198), the Natural Science Foundation of Jiangsu Province (Grant Nos?BK2008019, BK2009255, BK2010178), and the Research Foundation for School of Yangzhou Photonic and Electronic research of Nanjing University.
    [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 物理学报 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

  • [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 物理学报 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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  • Received Date:  18 July 2010
  • Accepted Date:  29 March 2011
  • Published Online:  05 January 2012

Study of Rashba spin splitting and intersubband spin-orbit coupling effect in AlGaN/GaN quantum wells

  • 1. Jiangsu Provincial Key Laboratory of Advanced Photonic and Electronic Materials, School of Electronic Science and Engineering, Nanjing University, Nanjing National Lab of Microstructures, Nanjing 210093, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant Nos?60990311, 60721063, 60906025, 60936004), the State Key Development Program for Basic Research of China (Grant No?2011CB301900), the State Development Program for Research on Advanced technology of China (Grant No. 2009AA03A198), the Natural Science Foundation of Jiangsu Province (Grant Nos?BK2008019, BK2009255, BK2010178), and the Research Foundation for School of Yangzhou Photonic and Electronic research of Nanjing University.

Abstract: 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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