Optical spin polarization and exchange interaction in doubly charged InAs self-assembled quantum dots

The work is an experimental study of optical spin polarization in $\mathrm{In}\mathrm{As}∕\mathrm{Ga}\mathrm{As}$ quantum dots (QDs) with two resident electrons or holes. A capture of a photogenerated electron-hole pair into such a QD creates a negative or positive tetron (doubly charged exciton). Spin polarization was registered by the circular polarization of the QD photoluminescence (PL). The spin state was found to be radically different in the dots with the opposite sign of the charge. Particularly, under excitation in a GaAs barrier, the polarization of the ground-state PL is negative (relative to the polarization of exciting light) in the negatively charged QDs and positive in the positively charged QDs. With increasing excitation intensity, the negative polarization rises from zero up to a saturation level, while the positive polarization decreases. The negative polarization increases in weak magnetic fields applied in Faraday geometry; however, it is suppressed in strong fields. The positive polarization always increases as a function of magnetic field. We propose a theoretical model that qualitatively explains the experimental results.

Figure 1

PL (solid lines) and PL polarization spectra (엯 and ∎) of doubly positively (a) and negatively (b) charged delta-doped InAs QDs recorded at excitation into the GaAs barrier. $T=10\mathrm{K}$. Excitation energy $h{\nu }_{\mathit{exc}}\left(\mathrm{eV}\right)$: 1.653 (a), 1.59 (b). Excitation power $I_{\mathit{exc}}\left(\mathrm{mW}\right)$: 1 (엯), 5 (∎).

Figure 2

PL and PL polarization excitation spectra of double-charged delta-doped InAs QDs. $T=10\mathrm{K}$. PL spectra of the positively (dotted line) and negatively (solid line) charged dots recorded at $h{\nu }_{\mathit{exc}}=1.653\mathrm{eV}$, $I_{\mathit{exc}}=0.2\mathrm{mW}$, and $h{\nu }_{\mathit{exc}}=1.59\mathrm{eV}$, $I_{\mathit{exc}}=0.05\mathrm{mW}$, respectively. PL circular polarization excitation spectra of the positively (엯) and negatively (∎) charged dots measured in the center of the ground-state PL band. $h{\nu }_{\det }\left(\mathrm{eV}\right)$: 1.109 (엯), 1.117 (∎). $I_{\mathit{exc}}\left(\mathrm{mW}\right)$: 5 (엯), 20 (∎).

Figure 3

Ground-state PL polarization vs excitation power for doubly positively (a) and negatively (b) charged InAs QDs. $T=10\mathrm{K}$. (a) $h{\nu }_{\mathit{exc}}=1.722\mathrm{eV}$, $h{\nu }_{\det }=1.109\mathrm{eV}$. (b) $h{\nu }_{\mathit{exc}}=1.59\mathrm{eV}$, $h{\nu }_{\det }=1.117\mathrm{eV}$.

Figure 4

Longitudinal magnetic field dependence of the ground-state PL polarization of doubly positively (a) and negatively (b) charged InAs QDs. $T=10\mathrm{K}$. Here, the sample with negatively charged dots is a $n\text{−}i\text{−}n$ structure with one layer of InAs QDs. (a) $h{\nu }_{\mathit{exc}}=1.722\mathrm{eV}$, $I_{\mathit{exc}}=5\mathrm{mW}$, $h{\nu }_{\det }=1.109\mathrm{eV}$. (b) $h{\nu }_{\mathit{exc}}=1.55\mathrm{eV}$, $I_{\mathit{exc}}=7\mathrm{mW}$, $h{\nu }_{\det }=1.143\mathrm{eV}$.

Figure 5

Dependences of the PL circular polarization on the excitation intensity and longitudinal magnetic field in the double negatively and positively charged dots, calculated with Eqs. (6, 8). The capture rate $w$ was calculated as $w=W∕h{v}_{\mathit{exc}}{N}_{\text{dot}}$, where $W$ is the pump density and $N_{\text{dot}}$ is the dot density. The following parameters are used: $P_{e0}=0.5$, $\tau =0.5\mathrm{ns}$, $\mid g_b\mid =3$, $\mid g_d\mid =1.4$, ${\delta }_b=100\mu \mathrm{eV}$, ${\delta }_d=2\mu \mathrm{eV}$, $N_{\text{dot}}=5\times {10}^{10}{\mathrm{cm}}^{-2}$, $h{v}_{\mathit{exc}}=1.6\mathrm{eV}$. (a) and (c) $B=0$. (b) and (d) $W=25\mathrm{W}∕{\mathrm{cm}}^2$. See text for details.