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In this paper, we study the effects of external electric field and Al content on the transverse and longitudinal g-factor (g┴ and g//) and its anisotropy (δg) of wurtzite AlGaN/GaN quantum wells (QWs). The Δg┴=(g┴-g0)=g┴bulk + gw and Δg//=(g//-g0)=g//bulk are mainly contributed by the bulk structure (g//bulk and g┴bulk) respectively, but the difference between g//bulk and g┴bulk is small and almost remains unchanged when the external electric field and Al content are varied. So the anisotropy of the g factor in AlGaN/GaN QWs induced by the bulk wurtzite structure is small, while the anisotropy induced by the quantum confined effect (gw) is considerable. When the direction of the external electric field is the same as (opposite to) the polarization electric field, the magnitudes of g//bulk and g┴bulk both increase (decrease) with increasing external electric field. This is induced mainly by the variations of envelope function and confined energy with the electric field. With the external electric field changing from -1.5×108 V·m-1 to 1.5×108 V· m-1, the confined energy ε1 increases slowly, and the magnitude of the envelope function at the left heterointerface increases. So the contribution to Δg┴ from the heterointerface ΓInter is positive and increases slowly, and that from the well ΓW is negative and increases slowly in magnitude. The magnitude of ΓInter is larger than that of ΓW, but the magnitude of the latter increases more rapidly. All the above factors make the g-factor anisotropy δg>0 and decrease in magnitude with electric field increasing. With increasing Al content of the barrier, both β>1 (g┴bulk) and γ>1 (g//bulk) decrease if the strain effects are ignored (S1, 2=0), because the confined energy decreases and the peak of the envelope function shifts towards the left heterointerface. By considering the strain effects (S1, 2 ≠ 0), the magnitude of β>1 (g┴bulk) and γ>1 (g//bulk) increase with Al content increasing. The strain effect has a great influence on the confined potential V(z), leading to the rapid increase of β(z) when z > zp, which the situation for γ (z) is similar to. With increasing Al content, the magnitudes of ΓInter and ΓW both increase, but the magnitude of ΓInter is larger and increases more rapidly. Therefore δg increases slowly. The magnitude of Δ g┴ first decreases with increasing Al content, then it increases with Al content increasing, and since g┴bulk g-factor and its anisotropy in AlGaN/GaN QWs can be greatly modulated by the external electric field, the Al content in the barrier, the strain effects and the quantum confined effect. Results obtained here are of great importance for designing the spintronic devices.
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Keywords:
- spin-orbit coupling /
- Rashba effect /
- Zeeman effect /
- g factor
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[2] Snelling M J, Flinn G P, Plaut A S, Harley R T, Tropper A C, Eccleston R, Phillips C C 1991 Phys. Rev. B 44 11345
[3] Hannak R M, Oestreich M, Heberle A P, Rhle W W, Köhler K 1995 Solid State Commun. 93 313
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[5] Le Jeune P, Robart D, Marie X, Amand T, Brosseau M, Barrau J, Kalevcih V 1997 Semicond. Sci. Technol. 12 380
[6] Tomimoto S, Nozawa S, Terai Y, Kuroda S, Takita K, Masumoto Y 2010 Phys. Rev. B 81 125313
[7] de Sousa R, Das Sarma S 2003 Phys. Rev. B 68 155330
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[12] Pfeffer P, Zawadzki W 2006 Phys. Rev. B 74 233303
[13] Roth L M, Lax B, Zwerdling S 1959 Phys. Rev. 114 90
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[19] Litvinov V I 2003 Phys. Rev. B 68 155314
[20] Litvinov V I 2006 Appl. Phys. Lett. 89 222108
[21] Li M, Zhang R, Zhang Z, Yan W S, Liu B, Fu D Y, Zhao C Z, Xie Z L, Xiu X Q, Zheng Y D 2011 Superlattices Microstruct. 47 522
[22] de Andrada e Silva E A, La Rocca G C, Bassani F 1994 Phys. Rev. B 50 8523
[23] de Andrada e Silva E A, La Rocca G C, Bassani F 1997 Phys. Rev. B 55 16293
[24] Bychkov Y A, Rashba E I 1984 J. Phys. C 17 6039
[25] Yang W, Chang K 2006 Phys. Rev. B 73 113303
[26] Yang W, Chang K 2006 Phys. Rev. B 74 193314
[27] Pfeffer P, Zawadzki W 1999 Phys. Rev. B 59 R5312
[28] Koga T, Nitta J, Akazaki T, Takayanagi H 2002 Phys. Rev. Lett. 89 046801
[29] Schmult S, Manfra M J, Punnoose A, Sergent A M, Baldwin K W, Molnar R J 2006 Phys. Rev. B 74 033302
[30] Li M, L Y H, Yang B H, Zhao Z Y, Sun G, Miao D D, Zhao C Z 2011 Solid State Commun. 151 1958
[31] Li M, Feng Z B, Fan L B, Zhao Y L, Han H P, Feng T H 2016 J. Magnet. Magnet. Mater. 403 81
[32] Zhao Z Y, Wang H L, Li M 2016 Acta Phys. Sin. 65 097101 (in Chinese) [赵正印, 王红玲, 李明 2016 物理学报 65 097101]
[33] Hao Y F 2014 J. Appl. Phys. 115 244308
[34] Hao Y F 2015 J. Appl. Phys. 117 013911
[35] Hao Y F, Chen Y H, Hao G D, Wang Z G 2009 Chin. Phys. Lett. 26 037103
[36] Hao Y F, Chen Y H, Hao G D, Wang Z G 2009 Chin. Phys. Lett. 26 077104
[37] Miao M S, Yan Q, van de Walle C G, Lou W K, Li L L, Chang K 2012 Phys. Rev. Lett. 109 186803
[38] Zhang D, Lou W K, Miao M S, Zhang S C, Chang K 2013 Phys. Rev. Lett. 111 156402
[39] Chuang S L Chang C S 1996 Phys. Rev. B 54 2491
[40] Fabian J, Matos-Abiague A, Ertler C, Stano P, Žutić I 2007 Acta Phys. Slovaca 57 677
[41] Yu L S, Qiao D J, Xing Q J, Lau S S, Boutros K S, Redwing J M 1998 Appl. Phys. Lett. 73 238
[42] Kumagai M, Chuang S L, Ando H 1998 Phys. Rev. B 57 15303
[43] Suzuki M, Uenoyama T, Yanase A 1995 Phys. Rev. B 52 8132
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[1] Hanson R, Witkamp B, Vandersypen L M K, Willems van Beveren L H, Elzerman J M, Kouwenhoven L P 2003 Phys. Rev. Lett. 91 196802
[2] Snelling M J, Flinn G P, Plaut A S, Harley R T, Tropper A C, Eccleston R, Phillips C C 1991 Phys. Rev. B 44 11345
[3] Hannak R M, Oestreich M, Heberle A P, Rhle W W, Köhler K 1995 Solid State Commun. 93 313
[4] Sirenko A A, Ruf T, Cardona M, Yakovlev D R, Ossau W, Waag A, Landwehr G 1997 Phys. Rev. B 56 2114
[5] Le Jeune P, Robart D, Marie X, Amand T, Brosseau M, Barrau J, Kalevcih V 1997 Semicond. Sci. Technol. 12 380
[6] Tomimoto S, Nozawa S, Terai Y, Kuroda S, Takita K, Masumoto Y 2010 Phys. Rev. B 81 125313
[7] de Sousa R, Das Sarma S 2003 Phys. Rev. B 68 155330
[8] Ivchenko E L, Kiselev A A 1992 Fiz. Tekh. Poluprovodn. (S. Peterburg) 26 1471 [1992 Sov. Phys. Semicond. 26 827]
[9] Ivchenko E, Kiselev A, Willander M 1997 Solid State Commun. 102 375
[10] Kiselev A A, Ivchenko E L, Rössler U 1998 Phys. Rev. B 58 16353
[11] Kiselev A A, Kim K W, Ivchenko E L 1999 Phys. Status Solidi B 215 235
[12] Pfeffer P, Zawadzki W 2006 Phys. Rev. B 74 233303
[13] Roth L M, Lax B, Zwerdling S 1959 Phys. Rev. 114 90
[14] de Dios-Leyva M, Reyes-Gómez E, Perdomo-Leiva C A, Oliveira L E 2006 Phys. Rev. B 73 085316
[15] Toloza Sandoval M A, Ferreira da Silva A, de Andrada e Silva E A, La Rocca G C 2012 Phys. Rev. B 86 195302
[16] Toloza Sandoval1 M A, de Andrada e Silva1 E A, Ferreira da Silva A, La Rocca G C 2016 Semicond. Sci. Technol. 31 115008
[17] Jiang H W, Eli Y 2001 Phys. Rev. B 64 041307
[18] Nitta J, Lin Y, Akazaki T, Koga T 2003 Appl. Phys. Lett. 83 4565
[19] Litvinov V I 2003 Phys. Rev. B 68 155314
[20] Litvinov V I 2006 Appl. Phys. Lett. 89 222108
[21] Li M, Zhang R, Zhang Z, Yan W S, Liu B, Fu D Y, Zhao C Z, Xie Z L, Xiu X Q, Zheng Y D 2011 Superlattices Microstruct. 47 522
[22] de Andrada e Silva E A, La Rocca G C, Bassani F 1994 Phys. Rev. B 50 8523
[23] de Andrada e Silva E A, La Rocca G C, Bassani F 1997 Phys. Rev. B 55 16293
[24] Bychkov Y A, Rashba E I 1984 J. Phys. C 17 6039
[25] Yang W, Chang K 2006 Phys. Rev. B 73 113303
[26] Yang W, Chang K 2006 Phys. Rev. B 74 193314
[27] Pfeffer P, Zawadzki W 1999 Phys. Rev. B 59 R5312
[28] Koga T, Nitta J, Akazaki T, Takayanagi H 2002 Phys. Rev. Lett. 89 046801
[29] Schmult S, Manfra M J, Punnoose A, Sergent A M, Baldwin K W, Molnar R J 2006 Phys. Rev. B 74 033302
[30] Li M, L Y H, Yang B H, Zhao Z Y, Sun G, Miao D D, Zhao C Z 2011 Solid State Commun. 151 1958
[31] Li M, Feng Z B, Fan L B, Zhao Y L, Han H P, Feng T H 2016 J. Magnet. Magnet. Mater. 403 81
[32] Zhao Z Y, Wang H L, Li M 2016 Acta Phys. Sin. 65 097101 (in Chinese) [赵正印, 王红玲, 李明 2016 物理学报 65 097101]
[33] Hao Y F 2014 J. Appl. Phys. 115 244308
[34] Hao Y F 2015 J. Appl. Phys. 117 013911
[35] Hao Y F, Chen Y H, Hao G D, Wang Z G 2009 Chin. Phys. Lett. 26 037103
[36] Hao Y F, Chen Y H, Hao G D, Wang Z G 2009 Chin. Phys. Lett. 26 077104
[37] Miao M S, Yan Q, van de Walle C G, Lou W K, Li L L, Chang K 2012 Phys. Rev. Lett. 109 186803
[38] Zhang D, Lou W K, Miao M S, Zhang S C, Chang K 2013 Phys. Rev. Lett. 111 156402
[39] Chuang S L Chang C S 1996 Phys. Rev. B 54 2491
[40] Fabian J, Matos-Abiague A, Ertler C, Stano P, Žutić I 2007 Acta Phys. Slovaca 57 677
[41] Yu L S, Qiao D J, Xing Q J, Lau S S, Boutros K S, Redwing J M 1998 Appl. Phys. Lett. 73 238
[42] Kumagai M, Chuang S L, Ando H 1998 Phys. Rev. B 57 15303
[43] Suzuki M, Uenoyama T, Yanase A 1995 Phys. Rev. B 52 8132
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