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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及磁场B等参量有不同的依赖关系,其中温度对于电子的自旋弛豫起着主导作用,横向限制势频率次之,磁场和纵向高度的作用再次之.1)在InAs量子点中,ω0的增加对应着有效横向尺寸d的变小,对Γ的值有明显的抑制作用;2)随着T的提高ω0对于电子自旋反转的抑制作用逐渐减弱,T对Γ的影响明显,从1K增加到7K时自旋反转弛豫迅速增加,Γ从103s-1增加到108s-1量级;3)Γ随高度z0的增加而变小,在T=1K时Γ总的量级为100—103s-1,而随着T的增加(T=6K)它将逐渐超过z0的增加对弛豫率Γ的影响;4)Γ随磁场B变化曲线在不同的ω0时均形成一个峰值,而峰值几乎出现在同一B值,这归因于InAs有相当大的g因子使得随磁场增加时塞曼项H^Z对能级产生影响将超过H^SO.
In this paper, the spin-orbit (SO) interaction is taken as the perturbation term for the InAs single electron quantum dot Hamiltonian and the matrix elements of the SO interaction under the Fock-Darwin eigenfunction are calculated. The second order correction of the wave function and considering the effect of the new energy level on the g factor and the effective mass m *, the expression of the electron spin relaxation rate Γ with the phonon assists is calculated. The phonon-assisted electron spin relaxation rate Γ has a different dependence on the parameters of the limiting potential frequency ω0, the temperature T, the vertical height z0 and the magnetic field B. The temperature plays a leading role in the electron spin relaxation and the lateral limit Secondly, the effect of magnetic field and vertical height is secondarily. (1) In InAs quantum dots, the increase of ω0 corresponds to the decrease of the effective transverse dimension d, which obviously inhibits the value of Γ. 2) The effect of ω0 on electron spin inversion is weakened gradually. The effect of T on Γ is obvious. The spin-reverse relaxation increases rapidly from 1K to 7K, and Γ increases from 103s-1 to 108s-1. 3) Γ becomes smaller as the height z0 increases, the total magnitude of Γ is 100-103 s-1 at T = 1K, and as T (T = 6K), it will gradually exceed the effect of the increase of z0 on relaxation rate Γ; 4) The curve of Γ with magnetic field B forms a peak at different ω0 and the peak appears almost at the same value of B Because InAs has a relatively large g factor, the Zeeman HZ affects the energy level more than H ^ SO with increasing magnetic field.