Intershell Exchange and Sequential Electrically Injected Spin Populations of InAs Quantum-Dot Shell States

We report sequential spin population of individual shell states of self-assembled InAs quantum dots controlled by a spin-polarized current from an Fe contact, and determine the $s\mathrm{\text{−}}p$ and $p\mathrm{\text{−}}d$ intershell exchange energies. We resolve excitonic features in the electroluminescence (EL) spectra associated with individual quantum levels. In contrast with simple models of shell occupation, the EL circular polarization exhibits maxima shifted with respect to the intensity peaks. Calculations show that this is due to intershell exchange. Exchange energies for the $s\mathrm{\text{−}}p$ and $p\mathrm{\text{−}}d$ shells are $7\pm 2$ and $13.5\pm 1\mathrm{meV}$, respectively.

Figure 1

(a) EL spectra for selected electrical bias conditions, showing sequential occupation of the QD $s$, $p$, $d$, and $f$ shell states. Contour plot at biases (b) 1.7–1.9 V and (c) 1.9–3.0 V show the gradual filling of the QD shell states.

Figure 2

$P_{\mathrm{circ}}$ vs magnetic field at $T=5\mathrm{K}$, $I=30\mathrm{mA}$, $V=3\mathrm{V}$ measured at the (a) EL intensity maxima and (b) polarization maxima (features B, C, D, and E in Fig. 3). The inset shows $P_{\mathrm{circ}}$ vs magnetic field for the $d$ shell at two different bias conditions. A weak background of $+0.3\%/T$ was subtracted from the $f$ shell data in (a) and from all data in (b).

Figure 3

EL spectra and $P_{\mathrm{circ}}$ vs photon energy at $T=5\mathrm{K}$, $B=3\mathrm{T}$ with electrical bias of (a) 0.32 mA, 1.65 V, (b) 2 mA, 1.92 V, and (c) 30 mA, 3 V. The thicker black lines are the EL spectra and the solid red lines are the circular polarization.

Figure 4

Emission spectra calculated in the configuration-interaction approach at magnetic field of 3 T. Emission of the cases of unpolarized (upper panel) and polarized (lower panel) electrons for (a) the biexciton, and (b) the six-exciton system. Black color denotes ${\sigma }^{-}$ polarization while red color denotes ${\sigma }^{+}$ polarization. The ground-state initial configurations of the system are shown schematically on the right of the figure (blue: $s$ shell, brown: $p$ shell, green: $d$ shell). Closed (open) arrows indicate the spin of the electrons (holes).