Fine structure of exciton complexes in high-symmetry quantum dots: Effects of symmetry breaking and symmetry elevation

Quantum dots (QDs) of high symmetry (e.g., $C_{3v}$) have degenerate bright exciton states, unlike QDs of $C_{2v}$ symmetry, making them intrinsically suitable for the generation of entangled photon pairs. Deviations from $C_{3v}$ symmetry are detected in real QDs by polarization-resolved photoluminescence spectroscopy in side-view geometry of InGaAs/AlGaAs dots formed in tetrahedral pyramids. The theoretical analysis reveals both an additional symmetry plane and weak symmetry breaking, as well as the interplay with electron-hole and hole-hole exchange interactions manifested by the excitonic fine structure.

Figure 1

(a) Symmetry hierarchy visualized by three-dimensional objects. (b) and (c) Polarized radiative decay paths of $C_{3v}$ excitons formed with holes of $E_{3/2}$ and $E_{1/2}$ symmetries, and the corresponding decay of $C_s$ excitons. Transitions allowed for $C_{3v}\left(C_s\right)$ but forbidden under $D_{3h}\left(C_{2v}\right)$ are distinguished by thin lines and small arrows. Gray (black) lines indicate $x$-polarized ($y$-polarized) light. Dotted lines indicate $z$-polarized light.

Figure 2

(a) and (c) Polarized PL spectra of two QDs and (b) and (d) the corresponding degree of linear polarization. The PL is recorded for polarization vectors perpendicular (solid lines) and parallel (dotted lines) to the growth direction $z$. The insets illustrate schematic diagrams of (b) single particle energy levels and (d) the QD geometry.

Figure 3

Close-up PL of (a) $X_{\overline{1}0}$ and (b) $X_{0\overline{1}}$. Computed exciton spectra for (c) a symmetric QD, (d)–(e) an asymmetric QD. A Lorentzian broadening parameter $\left(50\mu \text{eV}\right)$ is introduced in (c)–(e). Unbroadened stems are also shown. The insets define polarization directions, and the shape and orientation of the computed QD $\left(a=16\text{nm},b=12.5\text{nm}\right)$.

Figure 4

(a) Polarized radiative decay paths of the positive trion $X_{11}$ for the ideal case $C_{3v}$ (left) and the asymmetric case $C_s$ (right). The numerical model yield dark transitions indicated by thin lines and small arrows. Black solid lines indicate both $x$- and $y$-polarized light. Dotted lines indicate $z$-polarized light. (b) Computed exciton spectra of $X_{1\overline{1}}$ (see caption of Fig. 3). (c) Close-up PL of $X_{1\overline{1}}$.