Probing long-lived dark excitons in self-assembled quantum dots

Long-lived dark exciton states are formed in self-assembled quantum dots due to the combination of the angular momentum of electrons and holes. The lifetime of dark excitons are determined by spin-flip processes that transfer dark excitons into radiative bright excitons. We employ time-resolved spontaneous emission measurements in a modified local density of optical states to unambiguously record the spin-flip rate. Pronounced variations in the spin-flip rate with the quantum dot emission energy are observed demonstrating that the exciton storage time can be extended by controlling the quantum dot size. The energy dependence is compared to a recent model from the literature, in which the spin flip is due to the combined action of short-range exchange interaction and acoustic phonons. We furthermore observe a pronounced enhancement of the spin-flip rate close to semiconductor-air interfaces, which illustrates the important role of interfaces for quantum dot based nanophotonic structures.

Figure 1

(Color online) (a) Three-level exciton scheme consisting of a bright $|b⟩$ and a dark $|d⟩$ state that are coupled through the spin-flip rates ${\gamma }_{bd}$ and ${\gamma }_{db}$. Radiative recombination $\left({\gamma }_{\text{rad}}\right)$ to the ground state $|g⟩$ (no exciton) is only possible for the bright state, while both the bright $\left({\gamma }_{\text{nrad}}^b\right)$ and the dark state $\left({\gamma }_{\text{nrad}}^d\right)$ can decay nonradiatively. (b) Typical decay curve acquired at a detection energy of 1.204 eV (blue squares) at the sample with QDs positioned 170 nm from the interface. The red line is a fit of the biexponential model to the data. Inset: sketch of the sample showing three different distances between the QDs and the GaAs-air interface. (c) The weighted residual obtained from the biexponential fit to the data.

Figure 2

(Color online) (a) The slow decay rate as a function of distance to the interface measured at 1.204 eV. No systematic dependence on distance is observed confirming that the slow rate is due to nonradiative decay of dark excitons. The blue line indicates the averaged rate. (b) Measured ratio of the fast and slow amplitudes versus distance. The dashed blue curve is obtained by multiplying the calculated LDOS with an overall exponential decrease in the spin-flip rate with the distance to the interface. (c) Goodness-of-fit $\left({\chi }_R^2\right)$ for all distances to the interface.

Figure 3

(Color online) The spin-flip rates versus distance $z$ to the interface for six different emission energies. The plotted curves are fits to the experimental data assuming an exponential decay of the spin-flip rate with the distance to the interface. The inset shows the exponential decay length versus emission energy.

Figure 4

(Color online) Measured spin-flip rate at different emission energies for the sample with $\left(z=302\text{nm}\right)$ (solid black circles). The theoretically predicted spin-flip rate using the model of Ref. 10 for parameters that reproduce the energy dependence of the radiative decay rate (dashed blue line) and for optimized parameters (solid red line).