Optical study of electron-electron exchange interaction in CdTe/ZnTe quantum dots

We present an experimental study of electron-electron exchange interaction in self-assembled CdTe/ZnTe quantum dots based on the photoluminescence measurements. The character and strength of this interaction are obtained by simultaneous observation of various recombination channels of a doubly negatively charged exciton X${}^{2-}$, including previously unrecognized emission lines related to the electron-singlet configuration in the final state. A typical value of the electron singlet-triplet splitting, which corresponds to the exchange integral of electron-electron interaction, has been determined as 20.4 meV with a spread of 1.4 meV across the wide population of quantum dots. We also evidence an unexpected decrease of energy difference between the singlet and triplet states under a magnetic field in Faraday geometry.

Figure 1

(a) Photoluminescence spectrum of a single CdTe/ZnTe QD without polarization resolution. Lines denoted by X${}_{\mathrm{s}}^{2-}$ correspond to recombination of a doubly charged exciton to a state with two electrons in singlet configuration. (b) False-color plot presenting PL spectra of the same QD measured using different linear polarization of detection. The 0${}^{\circ }$ and 90${}^{\circ }$ correspond to cleavage axes of the sample. (c-e) Dependence of the PL intensity of X${}_{\mathrm{s}}^{2-}$, X${}^{2-}$, and X doublets on the orientation of detected polarization for the same QD. In case of X${}^{2-}$, the lower energy line exhibits only partial linear polarization due to the coincidental contribution from unpolarized transition[8]. The intensity of the higher energy component of X${}^{2-}$ was magnified by a factor 4 for better visibility.

Figure 2

A scheme of states and transitions related to the recombination of a doubly charged exciton X${}^{2-}$. Note that the level spacing is not in scale. Colors of the arrows denote polarization of the transition. Red and green (different shades of light grey) denote orthogonal linear polarization, while dark grey denotes unpolarized transition.

Figure 3

Correlation of (a) orientations of polarization and (b) splittings of the doubly charged exciton X${}^{2-}$ for different QDs (red squares). Blue circles represent analog data for the neutral exciton for comparison. Solid line corresponds to the predictions of the spin Hamiltonian model, namely, 90${}^{\circ }$ difference in orientation of polarization and the same splitting of bright and singlet transitions.

Figure 4

Correlation of relative spectral line positions. The relative position of “bright” and “dark” transitions is proportional to the relative position of the other lines of the same QD (e.g., neutral biexciton), while the splitting between singlet and triplet ($2J_{\mathrm{ee}}$) seems to be independent on these relative positions. The inset presents a histogram of the $2J_{\mathrm{ee}}$ constant among studied dots.

Figure 5

(a) Magnetic field dependence of transition energies in Faraday configuration. Empty (full) symbols denote lines with $\sigma +$ ($\sigma -$) helicity. The same data were used to calculate the (b) Zeeman splitting and the (c) diamagnetic shift for each pair of lines.

Figure 6

Energy distances between various pairs of emission lines related to X${}^{2-}$ recombination in a magnetic field in Faraday geometry. The energy of each pair is defined by the average of both components using data from Fig. 5a. Due to the common initial state, the bright-singlet distance is a direct measure of the splitting between singlet and triplet $T_0$ configurations of two electrons.

Figure 7

(a) Photoluminescence spectrum with emission lines related to different recombination channels of X${}^{2-}$ measured in two orthogonal linear polarizations. Arrows point to the transitions originating from the same initial state either to a “singlet” or a triplet configuration. The intensities of these two channels should be equal according to the spin Hamiltonian model. The actual intensity of the “singlet” transition for this dot is only $0.45$ of the intensity of the “bright” transition. (b) Histogram of ratio between intensities of “singlet” and “bright” emission lines for different QDs. The average ratio for the studied population was $0.28$.