Coulomb correlations of charged excitons in semiconductor quantum dots

The emission pattern of charged excitons in a semiconductor quantum dot (QD) is composed of a quadruplet of linearly polarized lines when a magnetic field is applied in a Voigt configuration. The orientation of the linear polarization of exciton emission is controlled by the orientation of the magnetic field in QDs with ${\text{C}}_{3\text{v}}$ symmetry while for QDs with ${\text{C}}_{2\text{v}}$ symmetry it is not. We demonstrate that the $g$ factor of holes is very sensitive to the dot shape asymmetry but that of electrons is not. By comparing the effective $g$ factors obtained for the neutral and charged excitons in the same quantum dot, we uncover the role of Coulomb correlations in these excitonic states. We show that the ${\text{C}}_{3\text{v}}$ symmetry of pyramidal QDs makes them ideal candidates for implementing all-optical many-qubits gates based on electron spin as a quantum bit.

Figure 1

(Color online) Polarized PL spectra of an isolated quantum dot measured (a) without and (b) with a magnetic field of 6.5 T in the Voigt configuration. The linear polarization is oriented in a direction parallel or perpendicular to the magnetic field. Upper inset: Zeeman energy splitting between the bright and dark excitons for each of the linear polarizations. Lines are fits using expressions given in the text. Lower inset: sketch of pyramidal dot showing the photon emission direction $\left(\mathbf{k}\parallel \left[111\right]\right)$ and the orientation of the magnetic field $\left(\mathbf{B}\parallel \left[1–10\right]\right)$.

Figure 2

(Color online) Emission spectra of ${\text{X}}^{-}$ at a magnetic field of 6.5 T displaying a quadruplet of linearly polarized transitions. Lines correspond to fits of the data with Gaussians of identical width. Inset: Zeeman splittings plotted versus magnetic field.

Figure 3

(Color online) Emission spectra of ${\text{X}}^{+}$ at a magnetic field of 6.5 T displaying a quadruplet of linearly polarized transitions. Lines correspond to fits of the data with Gaussians of identical width. Inset: Zeeman splittings plotted versus magnetic field.

Figure 4

(Color online) Effective carrier $g$ factors for the charged excitons measured for a set of ten dots. Inset: hole effective $g$ factor from ${\text{X}}^{-}$ plotted versus anisotropic exchange term $2\left|\delta -{\delta }^{\ast }\right|$.