Inhibition of dynamic nuclear polarization by heavy-hole noncollinear hyperfine interactions

We show that the effective hyperfine interaction for heavy-hole states (or any particle described with a $p$-like Bloch function) can induce nontrivial dynamics of nuclear spins. Experimental evidence can be found, e.g., in self-assembled quantum dots by measuring the saturation of nuclear spin polarization with different orientations of an external magnetic field.

Figure 1

Level scheme of the excitonic states in a neutral quantum dot showing optically driven transitions with Rabi frequency $\mathrm{\Omega }$ under the absorption of ${\sigma }_{+}$ polarized light (magenta). The nuclear states are described with the total angular momentum $j$ and magnetization $m$. Hyperfine mediated transitions via the electron are shown in orange and in purple for the hole spin. The excited states relax via spontaneous emission with rates ${\mathrm{\Gamma }}_{\mathrm{sp}}^{\downarrow \Uparrow }\approx {\mathrm{\Gamma }}_{\mathrm{sp}}^{\uparrow \Downarrow }\gg {\mathrm{\Gamma }}_{\mathrm{sp}}^{\uparrow \Uparrow }\approx {\mathrm{\Gamma }}_{\mathrm{sp}}^{\downarrow \Downarrow }$.

Figure 2

(a) Nuclear spin polarization $P$ as a function of pumping time $t_{\mathrm{p}}$ and spontaneous decay rate ${\mathrm{\Gamma }}_{\mathrm{sp}}^{\uparrow \Uparrow }\approx {\mathrm{\Gamma }}_{\mathrm{sp}}^{\downarrow \Downarrow }={\mathrm{\Gamma }}_{\mathrm{sp}}^{\mathrm{d}}$. Values of other parameters are given in the main text. (b) Traces taken along ${\mathrm{\Gamma }}_{\mathrm{sp}}^{\mathrm{d}}=2\times {10}^8,2\times {10}^7,\mathrm{and}2\times {10}^6\mathrm{Hz}$. $P$ saturates at lower values for smaller ${\mathrm{\Gamma }}_{\mathrm{sp}}^{\mathrm{d}}$'s. (c) Trace taken along $t_{\mathrm{p}}=30\mathrm{s}$ showing the dependence on ${\mathrm{\Gamma }}_{\mathrm{sp}}^{\mathrm{d}}$. (d) Comparison of $P$ as a function of $t_{\mathrm{p}}$ between $H_{\mathrm{HF}}^{\mathrm{h}}=H_{\mathrm{HF},z}^{\mathrm{h}}$ (gray), for which saturation corresponds to formation of a nuclear spin dark state, and the full effective Hamiltonian Eq. (7) (red) for ${\mathrm{\Gamma }}_{\mathrm{sp}}^{\mathrm{d}}=2\times {10}^7\mathrm{Hz}$. (e) Same as (d) but compared with $H_{\mathrm{HF}}^{\mathrm{h}}=H_{\mathrm{HF},z}^{\mathrm{h}}+H_{\mathrm{HF},\perp 1}^{\mathrm{h}}$. The result shows that heavy-hole mediated flip-flop processes are negligible. (f) Same as (d) but compared with $H_{\mathrm{HF}}^{\mathrm{h}}=H_{\mathrm{HF},z}^{\mathrm{h}}+H_{\mathrm{HF},\mathrm{nc}}^{\mathrm{h}}$. The heavy-hole hyperfine noncollinear interaction is the origin of the lower values of $P$.

Figure 3

(a) Nuclear spin polarization $P$ as a function of $t_{\mathrm{p}}$ and $\phi$ (angle between the external magnetic field $\mathit{B}$ and the $z$ axis) for ${\mathrm{\Gamma }}_{\mathrm{sp}}^{\mathrm{d}}=2\times {10}^7{\mathrm{s}}^{-1}$. (b) Trace taken along $t_{\mathrm{p}}=30\mathrm{s}$. The effect of the noncollinear interaction can be canceled by orienting the magnetic field opposite to the effective Overhauser field defined by the hyperfine noncollinear Hamiltonian.