Gate-voltage-induced switching of the Rashba spin-orbit interaction in a composition-adjusted quantum well

The coefficient $\alpha$ of the Rashba spin-orbit interaction is calculated in an asymmetric quantum well consisting of ${\mathrm{Ga}}_{0.47}{\mathrm{In}}_{0.53}\mathrm{As}$ (well), ${\mathrm{Al}}_{0.48}{\mathrm{In}}_{0.52}\mathrm{As}$ (left barrier), and ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}{\mathrm{As}}_y{\mathrm{Sb}}_{1-y}$ (right barrier) as a function of the external electric field perpendicular to the well $E_z^{\mathrm{ex}}$ which is controlled by the gate voltage. This coefficient $\alpha$, which depends on the band offset, can be tuned to be zero by adjusting the Al fraction $x$ in the right barrier layer to the optimum value $x_0$ in the case where the wave function vanishes at the left heterointerface. Such a composition-adjusted asymmetric quantum well is proposed as a structure in which the magnitude of $\alpha$ can be switched by changing the polarity of $E_z^{\mathrm{ex}}$. The calculation shows that, when $|x-x_0|<0.01$, the on/off $\left|\alpha \right|$ ratio $>40$ for a large enough $|E_z^{\mathrm{ex}}|$ ($|E_z^{\mathrm{ex}}|>{10}^7$ V/m for a well width of 20 nm), which results in the on/off spin-relaxation-rate ratio exceeding ${10}^3$ in the Dyakonov-Perel mechanism.

Figure 1

A quantum-well structure consisting of three different semiconductors with the zinc-blende structure, ${\mathrm{S}}_{\mathrm{B}}^{\mathrm{L}}, {\mathrm{S}}_{\mathrm{W}}$, and ${\mathrm{S}}_{\mathrm{B}}^{\mathrm{R}}$. $V_{\mathrm{bo}}^{\mathrm{c}}\left(z\right)$ is the potential due to the conduction-band offset.

Figure 2

The factor $b_{\mathrm{off}}^{\mathrm{R}}$ [Eq. (14)] for ${\mathrm{S}}_{\mathrm{W}}={\mathrm{Ga}}_{0.47}{\mathrm{In}}_{0.53}\mathrm{As}$ and ${\mathrm{S}}_{\mathrm{B}}^{\mathrm{R}}={\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}{\mathrm{As}}_y{\mathrm{Sb}}_{1-y}$ as a function of the Al fraction $x$ in ${\mathrm{S}}_{\mathrm{B}}^{\mathrm{R}}$ [16]. We have used band parameters in Ref. [30] and employed the linear interpolation of band offsets between $x=0$ and $x=1$ to obtain $\mathrm{\Delta }{E}_{\mathrm{c}}^{\mathrm{R}}\left[\mathrm{eV}\right]=0.436+1.43x, \mathrm{\Delta }{E}_{\mathrm{v}}^{\mathrm{R}}\left[\mathrm{eV}\right]=0.444-0.354x$, and $\mathrm{\Delta }{E}_{\mathrm{s}}^{\mathrm{R}}\left[\mathrm{eV}\right]=0.373-0.371x$, corresponding to ${\mathrm{Ga}}_{0.47}{\mathrm{In}}_{0.53}\mathrm{As}, E_{\mathrm{g}}\left[\mathrm{eV}\right]=0.816$, and ${\mathrm{\Delta }}_{\mathrm{so}}\left[\mathrm{eV}\right]=0.330$.

Figure 3

Calculated results of (a) $V_{\mathrm{W}}\left(z\right)$ and (b) ${\phi }_0\left(z\right)$ for different values of the external force $F_z=-e{E}_z^{\mathrm{ex}}$ in ${\mathrm{Al}}_{0.48}{\mathrm{In}}_{0.52}\mathrm{As}/{\mathrm{Ga}}_{0.47}{\mathrm{In}}_{0.53}\mathrm{As}/{\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}{\mathrm{As}}_y{\mathrm{Sb}}_{1-y}$ ($x=0.3$). The parameter $W(=z_{\mathrm{I}}^{\mathrm{R}}-z_{\mathrm{I}}^{\mathrm{L}})$ is the well width. The dimensionless quantities are defined by ${\tilde{V}}_{\mathrm{W}}=V_{\mathrm{W}}/{\mathrm{Ry}}^{*}, {\tilde{\phi }}_0={\phi }_0{\left(a_B^{*}\right)}^{1/2}, \tilde{z}=z/a_B^{*}, {\tilde{F}}_z=F_z/({\mathrm{Ry}}^{*}/a_B^{*}), \tilde{W}=W/a_B^{*}$, and ${\tilde{N}}_{\mathrm{s}}=N_{\mathrm{s}}{\left(a_B^{*}\right)}^2$ with $a_B^{*}={\hslash }^2\epsilon /\left(m{e}^2\right)$ and ${\mathrm{Ry}}^{*}={\hslash }^2{\left(a_B^{*}\right)}^{-2}/\left(2m\right)$. For ${\mathrm{Ga}}_{0.47}{\mathrm{In}}_{0.53}\mathrm{As}, a_B^{*}=17.1\mathrm{nm}$ and ${\mathrm{Ry}}^{*}=3.04\mathrm{meV}$. Therefore $\tilde{W}=0.6$ and ${\tilde{N}}_{\mathrm{s}}=6$ correspond to $W=10.3\mathrm{nm}$ and $N_{\mathrm{s}}=2.05\times {10}^{16}{\mathrm{m}}^{-2}$.

Figure 4

Rashba coefficient $\alpha$ as a function of the external force $F_z=-e{E}_z^{\mathrm{ex}}$ for three combinations of interfaces: LL, SS, and LS (see text). (a) The well-width ($W$) dependence for LS. (b) The electron-sheet-density ($N_{\mathrm{s}}$) dependence for LS. The dimensionless Rashba coefficient is defined by $\tilde{\alpha }=(\alpha /\eta )/({\mathrm{Ry}}^{*}/a_B^{*})$. For the definition of other quantities, see the caption of Fig. 3.