Geometrical Effects on the Optical Properties of Quantum Dots Doped with a Single Magnetic Atom

The emission spectra of individual self-assembled quantum dots containing a single magnetic Mn atom differ strongly from dot to dot. The differences are explained by the influence of the system geometry, specifically the in-plane asymmetry of the quantum dot and the position of the Mn atom. Depending on both these parameters, one has different characteristic emission features which either reveal or hide the spin state of the magnetic atom. The observed behavior in both zero field and under magnetic field can be explained quantitatively by the interplay between the exciton-manganese exchange interaction (dependent on the Mn position) and the anisotropic part of the electron-hole exchange interaction (related to the asymmetry of the quantum dot).

Figure 1

Low temperature ($T=5\mathrm{K}$) photoluminescence (PL) spectra of three different Mn-doped $\mathrm{CdTe}/\mathrm{ZnTe}$ QDs at $B=0\mathrm{T}$ and $B=11\mathrm{T}$. ${\sigma }_{\pm }$ are circular polarizations and ${\pi }_{x,y}$ are two orthogonal linear polarizations. (a) Exciton strongly coupled with a Mn atom, in a symmetric dot. (b) Exciton less strongly coupled with a Mn atom, in an asymmetric dot. (c) Exciton strongly coupled with a Mn atom, in an asymmetric dot.

Figure 2

Bright state transitions in an asymmetric Mn-doped QD at $B=0\mathrm{T}$ and 11 T. The $e\mathrm{\text{−}}h$ exchange interaction induces anticrossings (energy ${\delta }_2$) of the $\pm 1$ excitons associated with $S_z=-1/2,-3/2,-5/2$ for successive values of $B$; the $S_z=-5/2$ anticrossing is shown to the right.

Figure 3

Measured degree of linear polarization of emission lines $E1–E6$ for QD3 in zero field, as a function of the splitting between the $|J_z=\pm 1,S_z⟩$ states, compared to theoretical behavior (solid curves; dotted curves show the uncertainty range corresponding to the imprecision in ${\delta }_2$). The left inset labels the emission lines. The right inset shows the PL intensity of the lines $E3$ and $E4$ ($S_z=\pm 1/2$), as a function of the linear polarizer orientation.

Figure 4

(a) Intensity map of magnetic field dependence of the emission spectrum of asymmetric Mn-doped dot QD3, for circular polarization $\sigma +$ and $\sigma -$. (b) Optical transitions obtained from the diagonalization of the $\mathrm{\text{spin}}+\mathrm{\text{Zeeman}}+\mathrm{\text{diamagnetism}}$ Hamiltonian in the subspace of the 24 heavy-hole exciton and Mn spin components. Line thickness and color scale for $\sigma +$, $\sigma -$ are proportional to absolute value of the projection of the exciton state on the $J_z=+1$, $-1$ exciton, respectively (green or light gray scale is low intensity, and blue or dark gray scale is high intensity). The two transitions which are forbidden at all magnetic fields ($|J_z=\pm 2,S_z=\mp 5/2⟩$) are not plotted.

Figure 5

Magnetic field dependence of the emission of QD1 and QD2. (a) Exciton strongly coupled with a single manganese atom, in a quasisymmetric dot. Anticrossings discussed in the text are illustrated by the spectra in the left insets. (b) Exciton less strongly coupled with a manganese atom, in a symmetric dot.