Electric field dependence of spin coherence in (001) $\mathrm{Ga}\mathrm{As}∕{\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ quantum wells

Conduction electron spin lifetimes $\left(T_1\right)$ and spin coherence times $\left(T_2\right)$ are strongly modified in semiconductor quantum wells by electric fields. Quantitative calculations in $\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}$ quantum wells at room temperature show roughly a factor of 4 enhancement in the spin lifetimes at optimal values of the electric fields. The much smaller enhancement compared to previous calculations is due to overestimates of the zero-field spin lifetime and the importance of nonlinear effects.

Figure 1

(Color online) Energy dependence of electron spin precession vector for a $75\mathrm{\AA }$ and a $150\mathrm{\AA }$ $\mathrm{Ga}\mathrm{As}∕100\mathrm{\AA }$ ${\mathrm{Ga}}_{0.6}{\mathrm{Al}}_{0.4}\mathrm{As}$ QW at $300\mathrm{K}$. ${\left[{\Omega }_{x,n}^{\left(D\right)}(1,E)\right]}^2$ as a function of $E$ for a $75\mathrm{\AA }$ QW (a), and a $150\mathrm{\AA }$ QW (b) with $\mathcal{F}=0\mathrm{kV}∕\mathrm{cm}$. ${\left[{\Omega }_{x,n}^{\left(D\right)}(1,E)\right]}^2$ as a function of $E$ for a $75\mathrm{\AA }$ QW (c), and a $150\mathrm{\AA }$ QW (d) with $\mathcal{F}=100\mathrm{kV}∕\mathrm{cm}$. ${\left[{\Omega }_{x,n}^{\left(R\right)}(1,E)\right]}^2$ as a function of $E$ for a $75\mathrm{\AA }$ QW (e), and a $150\mathrm{\AA }$ QW (f) with $\mathcal{F}=100\mathrm{kV}∕\mathrm{cm}$.

Figure 2

(Color online) Electric field dependence of electron spin precession vector for a $75\mathrm{\AA }$ and a $150\mathrm{\AA }$ $\mathrm{Ga}\mathrm{As}∕100\mathrm{\AA }$ ${\mathrm{Ga}}_{0.6}{\mathrm{Al}}_{0.4}\mathrm{As}$ QW at $300\mathrm{K}$. ${\Omega }_{x,1}^{\left(D\right)}(1,E)$ as a function of $\mathcal{F}$ for a $75\mathrm{\AA }$ QW (a), and a $150\mathrm{\AA }$ QW (b). ${\Omega }_{x,1}^{\left(R\right)}(1,E)$ as a function of $\mathcal{F}$ for a $75\mathrm{\AA }$ QW (c), and a $150\mathrm{\AA }$ QW (d). (e) ${\Omega }_{x,3}^{\left(D\right)}$ as a function of $\mathcal{F}$ for a $75\mathrm{\AA }$ QW. (f) ${\Omega }_{x,3}^{\left(R\right)}$ as a function of $\mathcal{F}$ for a $75\mathrm{\AA }$ QW.

Figure 3

(Color online) Electron spin lifetimes, coherence times, and decoherence rates as a function of applied electric field $\mathcal{F}$ for a $50\mathrm{\AA }$, a $75\mathrm{\AA }$, and a $150\mathrm{\AA }$ $\mathrm{Ga}\mathrm{As}∕100\mathrm{\AA }$ ${\mathrm{Ga}}_{0.6}{\mathrm{Al}}_{0.4}\mathrm{As}$ QWs at $300\mathrm{K}$ with $\mu =800{\mathrm{cm}}^2∕\mathrm{V}\mathrm{s}$ assuming neutral impurity scattering. (a) $T_1$ as a function of $\mathcal{F}$ with ${\mathbf{H}}_{\mathrm{o}}\Vert \left[001\right]$. (b) $T_2$ as a function of $\mathcal{F}$ with ${\mathbf{H}}_{\mathrm{o}}\Vert \left[001\right]$. (c) $T_1$ as a function of $\mathcal{F}$ with ${\mathbf{H}}_{\mathrm{o}}\Vert \left[110\right]$, ${\mathbf{H}}_{\mathrm{o}}\Vert \left[1\overline{1}0\right]$, ${\mathbf{H}}_{\mathrm{o}}\Vert \left[100\right]$, and ${\mathbf{H}}_{\mathrm{o}}\Vert \left[010\right]$ for a $50\mathrm{\AA }$ QW. (d) $T_1$ as a function of $\mathcal{F}$ with ${\mathbf{H}}_{\mathrm{o}}\Vert \left[110\right]$, ${\mathbf{H}}_{\mathrm{o}}\Vert \left[1\overline{1}0\right]$, ${\mathbf{H}}_{\mathrm{o}}\Vert \left[100\right]$, and ${\mathbf{H}}_{\mathrm{o}}\Vert \left[010\right]$ for a $75\mathrm{\AA }$ QW. (e) $T_1$ as a function of $\mathcal{F}$ with ${\mathbf{H}}_{\mathrm{o}}\Vert \left[110\right]$, ${\mathbf{H}}_{\mathrm{o}}\Vert \left[1\overline{1}0\right]$, ${\mathbf{H}}_{\mathrm{o}}\Vert \left[1\overline{1}0\right]$, and ${\mathbf{H}}_{\mathrm{o}}\Vert \left[1\overline{1}0\right]$ for a $150\mathrm{\AA }$ QW. (f) $T_2^{-1}$ as a function of $\mathcal{F}$ with ${\mathbf{H}}_{\mathrm{o}}\Vert \left[001\right]$.