A New Method to Calculate the Rashba Spin Splitting in III-Nitride Heterostructures
LI Ming** , SUN Gang, FAN Li-Bo
College of Electrical and Information Engineering, Xuchang University, Xuchang 461000
Abstract :By constructing proper basis functions, the Kane Hamiltonian is transformed to two separate Hamiltonians, and the Schr?dinger equation for conduction-band envelope functions can be obtained by eliminating the valence band components of the envelope functions. Then we decouple the up-spin and down-spin states and derive the expression for the Rashba coefficient and single-particle energy, considering the spin-orbit coupling and the nonparabolicity corrections. Finally, we calculate the Rashba spin splitting for Alx Ga1?x N/GaN heterostructures by using the variational method. The Rashba spin splitting calculated here is of the same order of magnitude as in other III–V materials, showing that the internal electric field caused by the high concentration of the 2DEG is crucial for considerable Rashba spin splitting
收稿日期: 2012-07-19
出版日期: 2013-03-04
:
71.70.-d
(Level splitting and interactions)
73.21.-b
(Electron states and collective excitations in multilayers, quantum wells, mesoscopic, and nanoscale systems)
78.30.Fs
(III-V and II-VI semiconductors)
[1] Zutic I, Fabian J and 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 and 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 and Wang Z G 2007 Appl. Phys. Lett. 91 071912 [4] Wolf S A and Awschalom D D 2001 Science 294 1488 [5] Datta S and Das B 1990 Appl. Phys. Lett. 56 665 [6] Bychkov Yu A and Rashba E I 1984 J. Exp. Theor. Phys. Lett. 39 78 [7] Litvinov V I 2003 Phys. Rev. B 68 155314 [8] Pfeffer P and Zawadzki W 1999 Phys. Rev. B 59 R5312 [9] Weber W, Ganichev S D, Danilov S N, Weiss D, Prettl W, Kvon Z D, Bel'kov V V, Golub L E, Cho H I and Lee J H 2005 Appl. Phys. Lett. 87 262106 [10] Ganichev S D, Bel'kov V V, Golub L E, Ivchenko E L, Petra Schneider, Giglberger S, Eroms J, J De Boeck, Borghs G, Wegscheider W, Weiss D and Prettl W 2004 Phys. Rev. Lett. 92 256601 [11] 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) [12] Gui Y S, Zheng G Z, Guo S L, Chu J H, Tang D Y 1999 Acta Phys. Sin. 48 121 (in Chinese) [13] Shang L Y, Yu G L, Lin T, Zhou W Z, Guo S L, Dai N, Chu J H 2008 Chin. Phys. Lett. 25 2194 [14] Hao Y F, Chen Y H, Hao G D, Wang Z G 2009 Chin. Phys. Lett. 26 037103 Hao Y F, Chen Y H, Hao G D, Wang Z G 2009 Chin. Phys. Lett. 26 077104 [15] Song H Z, Zhang P, Duan S Q, Zhao X G 2006 Chin. Phys. 15 3019 [16] Dresselhaus G 1955 Phys. Rev. 100 580 [17] Bychkov Y A and Rashba E I 1984 J. Phys. C 17 6039 [18] Ohkawa F J and Uemura Y 1974 J. Phys. Soc. Jpn. 37 1325 [19] Beschoten B, Johnston-Halperin E, Young D K, Poggio M, Grimaldi J E, Keller S, DenBaars S P, Mishra U K, Hu E L and Awschalom D D 2001 Phys. Rev. B 63 121202 [20] Tang N, Shen B, Wang M J, Han K, Z J Yang Z J, Xu K, Zhang G Y, Lin T, Zhu B, Zhou W Z and Chu J H 2006 Appl. Phys. Lett. 88 172112 [21] Cho K S, Liang C T, Chen Y F, Tang Y Q and Shen B 2007 Phys. Rev. B 75 085327 [22] Zhang Z, Zhang R, Xie Z L, Liu B, Li M, Fu D Y, Fang H N, X Q Xiu X Q, Lu H, Zheng Y D, Chen Y H, Tang C G, Wang Z G 2009 Solid State Commun. 149 1004 [23] Andrada e Silva E A de, La Rocca G C and Bassani F 1994 Phys. Rev. B 50 8523 Andrada e Silva E A de, La Rocca G C and Bassani F 1997 Phys. Rev. B 55 16293 [24] Kane E O 1957 J. Phys. Chem. Solids 1 249 [25] Chuang S L 1995 Phys. Optoelectron. Devices (New York: Wiley) Chap 4 p126 [26] Chuang S L and Chang C S 1996 Phys. Rev. B 54 2491 [27] Yang W and Chang K 2006 Phys. Rev. B 73 113303 and Phys. Rev. B 74 193314 [28] Ekenberg U and Gvozdi? D M 2008 Phys. Rev. B 78 205317 [29] Ikai Lo, Tsai J K, Yao W J, Ho P C, Tu L W, Chang T C, Elhamri S and Mitchel W C, Hsieh K Y, Huang J H, Huang H L and Tsai W C 2002 Phys. Rev. B 65 161306 [30] Tsubaki, Maeda N, Saitoh T and Kobayashi N 2002 Appl. Phys. Lett. 80 3126 [31] Schmult, Manfra M J, Punnoose A, Sergent A M, Baldwin K W and Molnar R J 2006 Phys. Rev. B 74 033302 [32] Koga T, Nitta J, Akazaki T and Takayanagi H 2002 Phys. Rev. Lett. 89 046801 [33] V I Litvinov 2006 Appl. Phys. Lett. 89 222108 [34] Li M, Lv Y H, Yang B H, Zhao Z Y, Sun G, Miao D D and Zhao C Z 2011 Solid State Commun. 151 1958 [35] Li M, Zhang R, Zhang Z, Yan W S, Liu B, Fu D Y, Zhao C Z, Xie Z L, Xiu X Q and Zheng Y D 2010 Superlattice Microstructure 47 522 [36] Li M, Zhang R, Liu B, Fu D Y, Zhao C Z, Xie Z L, Xiu X Q and Zheng Y D 2012 Acta Phys. Sin. 61 027103 (in Chinese)
[1]
. [J]. 中国物理快报, 2019, 36(7): 77501-.
[2]
MA Lei. Kink Structures of Spin-Polarized Electrons due to Electron--Magnon Scattering in Ferromagnetic State [J]. 中国物理快报, 2007, 24(12): 3516-3519.
[3]
LI Kai-hang;HUANG Mei-chun;ZHU Zi-zhong;ZHANG Zhi-peng. Electronic and Optical Properties of (GaN)n /(AlN)n (001) Superlattices [J]. 中国物理快报, 1999, 16(6): 437-439.
[4]
HE Guo-min;LI Kai-hang;WANG Ren-zhi;ZHENG Yong-mei. Electronic Structure of InAsx P1-x /InP Strained Quantum Wires [J]. 中国物理快报, 1998, 15(8): 594-596.
[5]
LONG Fei;LIU Shenzhi*;MEI Fei;MIAO Jingqi;LIANG Jingguo. Electronic Structure of Type-II InAs/GaSb Misaligned Superlattice [J]. 中国物理快报, 1994, 11(2): 109-112.