Polarized Fine Structure in the Photoluminescence Excitation Spectrum of a Negatively Charged Quantum Dot

We report polarized photoluminescence excitation spectroscopy of the negative trion in single charge-tunable $\mathrm{InAs}/\mathrm{GaAs}$ quantum dots. The spectrum exhibits a $p$-shell resonance with polarized fine structure arising from the direct excitation of the electron spin triplet states. The energy splitting arises from the axially symmetric electron-hole exchange interaction. The magnitude and sign of the polarization are understood from the spin character of the triplet states and a small amount of quantum dot asymmetry, which mixes the wave functions through asymmetric $e\mathrm{\text{−}}e$ and $e\mathrm{\text{−}}h$ exchange interactions.

Figure 1

Bias dependent PL intensity maps. (a) Emission from both the $s$ and $p$ shells of a single dot. (b) Charging structure of the $s$-shell emission from another dot.

Figure 2

Polarized PLE spectra of the $X^{-}$ under ${\sigma }^{+}$ excitation for two dots. The PL emission energies are given in parentheses. The top (bottom) trace for each spectrum is for ${\sigma }^{+}$ (${\sigma }^{-}$) PL detection. The polarized doublet for each dot is expanded in the insets. For dot B, the associated $X^0$ PLE spectrum is also displayed. The left inset shows the energy levels of the ground ($X_{ss}^{-}$) and excited ($X_{sp}^{-}$) state trions with and without $e\mathrm{\text{−}}e$ (${\Delta }_{ee}$) and $e\mathrm{\text{−}}h$ (${\Delta }_{eh}$) exchange splittings.

Figure 3

Energy levels of the negative trion states. The $\Uparrow (\uparrow )$ arrowheads represent the spin projection of the holes (electrons) with $m_s$ the total spin projection of each state. The excited singlet is split from the triplet by ${\Delta }_{ee}$ and the excited triplets are split by ${\Delta }_{eh}$; the symmetric exchange energies. The mixed states are indicated by the dashed arrows, with ${\delta }_{ee}$ and ${\delta }_{eh}$ the asymmetric exchange energies which allow the mixing.

Figure 4

(a) Power dependence of the polarized doublet. (b) PLE half-width. The solid lines are fits to ${\Delta }_{\pm }(P)=\hslash {\Gamma }_{d_{\pm }}\sqrt{1+b_{\pm }P}$. (c) Integrated area of each PLE line with fit to $I_{\mathrm{Area}}(P)=a_{\pm }P/\sqrt{1+b_{\pm }P}$. Parameters $a_{\pm }$ are proportional to the oscillator strengths of the ${\sigma }^{\pm }$-PLE transitions ($a_{-}/a_{\pm }=2$), whereas parameters $b_{\pm }$ also include the relaxation rates to the $s$-shell and recombination rates. The fitted parameters are as follows: $a_{+}=63.5{\mathrm{mW}}^{-1}$, $b_{+}=0.472{\mathrm{mW}}^{-1}$, $\hslash {\Gamma }_{d+}=48.7\mu \mathrm{eV}$, $a_{-}=2a_{+}$, $b_{-}=1.68{\mathrm{mW}}^{-1}$, $\hslash {\Gamma }_{d-}=37.1\mu \mathrm{eV}$.