Suppression of the D’yakonov-Perel’ spin-relaxation mechanism for all spin components in [111] zincblende quantum wells

We apply the D’yakonov-Perel’ (DP) formalism to [111]-grown zinc blende quantum wells (QW’s) to compute the spin lifetimes of electrons in the two-dimensional electron gas. We account for both bulk and structural inversion asymmetry (Rashba) effects. We see that, under certain conditions, the spin splitting vanishes to first order in $k$, which effectively suppresses the DP spin relaxation mechanism for all three spin components. We predict extended spin lifetimes as a result, giving rise to the possibility of enhanced spin storage. We also study [110]-grown QW’s, where the effect of structural inversion asymmetry is to augment the spin relaxation rate of the component perpendicular to the well. We derive analytical expressions for the spin lifetime tensor and its proper axes, and see that they are dependent on the relative magnitude of the BIA- and SIA-induced splittings.

Figure 1

(a) CB splitting as a function of angle at $k_{\parallel }=0.005{\mathrm{\AA }}^{-1}$ for an 8ML AlSb/GaSb/AlSb quantum well. Shown are results for 0 and −0.38 V of applied bias (note the logarithmic scale). (b) Value of ${\alpha }_{\mathrm{IA}}$ as a function the perpendicular bias.

Figure 2

Spin lifetimes for the three spin components for [001]-, [110]- and [111]-grown QW’s as a function of the ratio of the SIA and the BIA parameters. Note the resonance for all components for in the case of a [111] structure, as opposed to a single component resonance for [001] and [110] structures. The labels ${\tau }_{\xi ,\eta ,\zeta }$ for the [110] orientation refer to the spin relaxation tensor proper axes as defined in Eq. (13).

Figure 3

Spin splitting and directions for the lower conduction subband of a [110]-grown QW. Plot (a) shows the value of the spin splitting from Eq. (12) for states lying on a circle in the $k_x-k_y$ plane with $k=0.01{\mathrm{\AA }}^{-1}$ for various values of the ratio ${\alpha }_R∕{\alpha }_{\mathrm{BIA}}$. Plots (b) and (c) show the spin eigenstates for Eq. (11) for ${\alpha }_R∕{\alpha }_{\mathrm{BIA}}=0$ and ${\alpha }_R∕{\alpha }_{\mathrm{BIA}}=0.35$, respectively. Note that when ${\alpha }_R=0$ all spins are aligned with the $z$ axis. In that case, no spin direction is specified for the $y$ and $-y$ directions because the states are spin degenerate. The value assumed for ${\alpha }_{\mathrm{BIA}}$ is ${10}^{-9}\mathrm{eV}\mathrm{cm}$.