Voltage Control of the Spin Dynamics of an Exciton in a Semiconductor Quantum Dot

We report the observation of a spin-flip process in a quantum dot whereby a dark exciton with total angular momentum $L=2$ becomes a bright exciton with $L=1$. The spin-flip process is revealed in the decay dynamics following nongeminate excitation. We are able to control the spin-flip rate by more than an order of magnitude simply with a dc voltage. The spin-flip mechanism involves a spin exchange with the Fermi sea in the back contact of our device and corresponds to the high temperature Kondo regime. We use the Anderson Hamiltonian to calculate a spin-flip rate, and we find excellent agreement with the experimental results.

Figure 1

(a) Gray-scale plot of the PL from a single quantum dot vs gate voltage $V_g$ at 5 K. White (black) corresponds to 0 (1000) counts. (b) Calculated energy of the initial states vs $V_g$ with parameters chosen to match (a).

Figure 2

PL decay curves measured on the quantum dot in Fig. 1a for various $V_g$. The temperature was 5 K.

Figure 3

(a) Lifetimes and relative intensities of the primary (filled symbols) and secondary (open symbols) components of the PL decay vs $V_g$ for the dot in Figs. 1a, 2. (b) As for (a) but for a dot with $X^0$ emission energy 1.373 eV. The solid lines are the results of the calculations taking ${\gamma }_r=1.8\mathrm{n}{\mathrm{s}}^{-1}$, ${\gamma }_{nr}=0.06{\mathrm{ns}}^{-1}$, ${\delta }_{BD}=0.3\mathrm{meV}$, ${\Gamma }_0=50\mu \mathrm{eV}$ with (a) $\Delta =0.07\mathrm{meV}$ and (b) $\Delta =0.3\mathrm{meV}$. The individual components ${\gamma }_r^{-1}$, ${\gamma }_{nr}^{-1}$, and ${\gamma }_{DB}^{-1}$ are shown by the dashed lines.

Figure 4

Schematic representation of the transition of a dark exciton $d$, state $|i⟩$, to a bright exciton $b$, state $|f⟩$. The splitting between $b$ and $d$ is ${\delta }_{BD}$. Two continuum states are considered, $k$ and $k^{\prime }$, split by ${\delta }_{BD}$. Electrons are labeled with • with arrows $\uparrow$, $\downarrow$ denoting spin. The hole spin is $+\frac{3}{2}$ and remains the same.

Figure 5

Primary and secondary decay times and relative intensities for a single quantum dot with $X^0$ emission energy 1.305 eV (a different dot to Figs. 1, 2, 3) for three different temperatures. As in Fig. 3, the solid lines are the fits to the theory taking $\Delta =0.08\mathrm{meV}$, ${\gamma }_r=1.3{\mathrm{ns}}^{1-}$, ${\gamma }_{nr}=0.06{\mathrm{ns}}^{-1}$, ${\delta }_{BD}=0.6\mathrm{meV}$. ${\Gamma }_0=50$, 100, and $120\mu \mathrm{eV}$ for 5, 12, and 25 K, respectively. Note that $V_1$ and $V_2$ have a small temperature dependence.