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本文在处理InAs单电子量子点哈密顿模型时,将自旋-轨道(SO)相互作用作为微扰项,计算在Fock-Darwin本征函数下SO相互作用的矩阵元,利用其对能级和波函数的二阶修正,并且考虑新的能级对g因子和有效质量m*的影响,计算得到在声子协助下电子的自旋弛豫率Γ的表达式.给出了InAs量子点中声子协助的电子自旋弛豫率Γ对于限制势频率ω0、温度T、纵向高度z0
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关键词:
- 自旋弛豫率 /
- 自旋-轨道(SO)相互作用 /
- InAs量子点 /
- Fock-Darwin本征函数
To deal with the Hamiltonian model in InAs QDs with a single electron, we’ve taken the SO interaction as a perturbation term, calculated the SO matrix elements under Fock-Darwin eigenfunction which are used for second order corrections on the energies and wave functions, and considered the influence of new energy levels on g factor and effective mass m*. The expression of phonon-assisted electron spin relaxation rate Γ in InAs QDs is deduced, which shows different dependences on confined potential frequency ω0, temperature T, vertical height z0 and magnetic field B. Among them, temperature for the electron spin relaxation plays a dominant role, followed by lateral confinement potential frequency, magnetic field and the vertical height, in order of importance. (1) Growth of ω0, which corresponds to the decrease of the effective transverse size d in InAs QDs, suppresses the increase of the rate Γ. (2) The temperature T affects the rate Γ evidently, which will reduce the inhibition of ω0 on Γ. With increase of the temperature from 1 K to 7 K, the spin inversion relaxation rate grows explosively from 103 s－1 to 108 s－1. (3) The rate Γ decreases with the growth of the vertical height z0 and have the order of magnitude 100－103 s-1 at T=1 K, whereas the influence of the temperature increase (at T=6 K) on the rate will gradually exceed that of the height growth. (4) At different frequencies ω0 all curves of the rate Γ versus magnetic field B have a peak that almost appears at the same field, which is attributed to the contribution of the Zeeman term H ^ Z exceeding that of H ^ SO since there is a considerable g factor in InAs material.-
Keywords:
- spin relaxation rate /
- spin-orbit (SO) interactions /
- InAs quantum dots /
- Fock-Darwin eigenfunction
[1] Datta S, Das B 1990 Appl. Phys. Lett. 56 665
[2] Loss D, DiVincenzo D P 1998 Phys. Rev. A 57 120
[3] Kouwenhoven L P, Elzerman J M, Hanson R, Willems van Beveren L H, Vandersypen L M K 2006 Phys. Status Solidi B 243 3682
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[7] Wu Y, Jiao Z X, Lei L, Wen J H, Lai T S, Lin W Z 2006 Acta Phys. Sin. 55 2961 (in Chinese) [吴 羽、 焦中兴、 雷 亮、 文锦辉、 赖天树、 林位株 2006 物理学报 55 2961]
[8] Rugar D, Budakian R, Mamin H J, Chui B W 2004 Nature 430 329
[9] Elzerman J M, Hanson R, Willems van Beveren L H, Witkamp B, Vandersypen L M K, Kouwenhoven L P 2004 Nature 430 431
[10] 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
[11] Pfund A, Shorubalko I, Ensslin K, Leturcq R 2009 Phys. Rev. B 79 121306
[12] utic ' I, Fabian J, Sarma S D 2004 Rev. Mod. Phys. 76 323
[13] Cheng J L, Wu M W, Lü C 2004 Phys. Rev. B 69 115318
[14] Reimann S M, Manninen M 2002 Rev. Mod. Phys. 74 1283
[15] Destefani C F, Ulloa Sergio E, Marques G E 2004 Phys. Rev. B 70 205315
[16] Winkler R 2003 Spin-orbit coupling effects in two-dimensional electron and hole systems (Berlin: Springer) p69
[17] Bulaev D V, Loss D 2005 Phys. Rev. B 71 205324
[18] Olendski O, Shahbazyan T V 2007 Phys. Rev. B 75 041306(4)
[19] Golovach V N, Khaetskii A, Loss D 2004 Phys. Rev. Lett. 93 016601
[1] Datta S, Das B 1990 Appl. Phys. Lett. 56 665
[2] Loss D, DiVincenzo D P 1998 Phys. Rev. A 57 120
[3] Kouwenhoven L P, Elzerman J M, Hanson R, Willems van Beveren L H, Vandersypen L M K 2006 Phys. Status Solidi B 243 3682
[4] Lee S, Dobrowolska M, Furdyna J K 2006 J. App. Phys. 99 08F702
[5] Liao Y Y, Chen Y N, Chuu D S, Brandes T 2006 Phys. Rev. B 73 085310
[6] Li D F, Shi J R 2009 Chin. Phys. B 18 282
[7] Wu Y, Jiao Z X, Lei L, Wen J H, Lai T S, Lin W Z 2006 Acta Phys. Sin. 55 2961 (in Chinese) [吴 羽、 焦中兴、 雷 亮、 文锦辉、 赖天树、 林位株 2006 物理学报 55 2961]
[8] Rugar D, Budakian R, Mamin H J, Chui B W 2004 Nature 430 329
[9] Elzerman J M, Hanson R, Willems van Beveren L H, Witkamp B, Vandersypen L M K, Kouwenhoven L P 2004 Nature 430 431
[10] 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
[11] Pfund A, Shorubalko I, Ensslin K, Leturcq R 2009 Phys. Rev. B 79 121306
[12] utic ' I, Fabian J, Sarma S D 2004 Rev. Mod. Phys. 76 323
[13] Cheng J L, Wu M W, Lü C 2004 Phys. Rev. B 69 115318
[14] Reimann S M, Manninen M 2002 Rev. Mod. Phys. 74 1283
[15] Destefani C F, Ulloa Sergio E, Marques G E 2004 Phys. Rev. B 70 205315
[16] Winkler R 2003 Spin-orbit coupling effects in two-dimensional electron and hole systems (Berlin: Springer) p69
[17] Bulaev D V, Loss D 2005 Phys. Rev. B 71 205324
[18] Olendski O, Shahbazyan T V 2007 Phys. Rev. B 75 041306(4)
[19] Golovach V N, Khaetskii A, Loss D 2004 Phys. Rev. Lett. 93 016601
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