Bistability of optically induced nuclear spin orientation in quantum dots

We demonstrate that bistability of the nuclear spin polarization in optically pumped semiconductor quantum dots is a general phenomenon possible in dots with a wide range of parameters. In experiment, this bistability manifests itself via the hysteresis behavior of the electron Zeeman splitting as a function of either pump power or external magnetic field. In addition, our theory predicts that the nuclear polarization can strongly influence the charge dynamics in the dot leading to bistability in the average dot charge.

Figure 1

(Color online) Schematic of the dot showing the absorption of a photon and the radiative escape processes (which can lead to the polarization of nuclei) for the case when the dot is occupied by a $S_z=+\frac{1}{2}$ electron (resulting in spin-flip recombinations taking a nucleus from spin down to spin up). (a) On the left, excitation of the empty dot by ${\sigma }^{-}$ light, exciting a $S_z=+\frac{1}{2}$ electron and $J_z=-\frac{3}{2}$ heavy hole into the wetting layer. They then relax into their lowest confined states on the dot, during which the hole can flip its spin, forming a dark exciton $\left(X_{+}^{+}\right)$. On the right, the spin-flip recombination of the dark exciton, with rate $w_s$, emitting a ${\sigma }^{+}$ photon and flipping a nuclear spin. (b) On the left, excitation by ${\sigma }^{-}$ light of a positively charged dot initially occupied by a $J_z=+\frac{3}{2}$ hole $\left(D^{+}\right)$, forming a positive trion $\left(X_{+}^{+-}\right)$. Most likely, the electron will simply recombine with the $J_z=-\frac{3}{2}$ hole $(X_{+}^{+-}\to D^{+})$, emitting a ${\sigma }^{-}$ photon. However, the electron can also recombine with the $J_z=+\frac{3}{2}$ hole by the flip-flop of its spin with a nucleus $(X_{+}^{+-}\to D^{-})$, emitting a ${\sigma }^{+}$ photon.

Figure 2

(Color online) The function $I\left(S\right)$ for the situation where $w=\tilde{w}$, $\sigma =0.9$, $\tilde{\sigma }=-0.2$, $x=0.6$, and $z=8$ for three different powers: $P=0.0001,0.0003,0.0005$. Stable roots correspond to the solutions of $I\left(S\right)=0$, where $\frac{dI}{dS}<0$.

Figure 3

(Color online) Evolution of nuclear polarization $\left(S\right)$ and the average charging state of the dot $\left(Q\right)$ for $w=\tilde{w}$, $\sigma =0.9$, and $\tilde{\sigma }=-0.2$: (a) as a function of power for $x=0.6$ and various values of $z$, with the arrows indicating a forward or backward sweep; (b) as a function of magnetic field for $z=8$ and three fixed powers $P=0.0001,0.0003,0.1$ corresponding to the low, bistable, and high power regimes, as illustrated in Fig. 2.

Figure 4

(Color online) The dominant line intensities for when $w=\tilde{w}$, $\sigma =0.9$, $\tilde{\sigma }=-0.2$, and $z=8$: (a) As a function of power, taking $x=0.6$; (b) as a function of external magnetic field, for $P=0.0003$.

Figure 5

(Color online) Evolution of $S$ with $P$ in the regime where $w=0.1\tilde{w}$ for $z=0.16,0.4$ and different polarizations of arriving electrons and/or holes. (a) $\sigma =0.9$, $\tilde{\sigma }=-0.2$. The inset shows the evolution of the charging state of the dot for $z=0.4$ (with a very small hysteresis loop). (b) Same for $\sigma =0.45$, $\tilde{\sigma }=-0.1$, with the inset showing the evolution of the dot average charge with power for $z=0.16$.