Optical and magnetic anisotropies of the hole states in Stranski-Krastanov quantum dots

Using the trion as a monitor we investigate the anisotropy of the single-hole state in epitaxial $\mathrm{Cd}\mathrm{Se}∕\mathrm{Zn}\mathrm{Se}$ quantum dots. Heavy-light hole mixing caused by a symmetry reduction below $D_{2\mathrm{d}}$ results in elliptical polarization of the optical transitions with a specific axis for each dot defined by strain and shape. In a transverse magnetic field, a quartet of strictly linearly polarized lines appears that reveals the off-diagonal coupling of both electron and hole states. Although induced by the field, the linear polarization is not related to the field orientation, but either along or perpendicular to the dot axis seen at zero field. We find an in-plane hole $g$ factor as large as 0.3 with distinct anisotropic behavior.

Figure 1

Zero-field PL feature of a single trion (QD#1) detected in linear polarization along the [110] and $\left[1\overline{1}0\right]$ directions, respectively. Upper left: Definition of the angle $\varphi$ (as well as $\phi$ in an external magnetic field, see Figs. 3, 4). Inset: PL signal of the trion as a function of $\varphi$, circles: QD#1, triangles: QD#2, full rectangles: QD#3. The dashed lines are fits with $A+B\cos \left[2(\varphi -\theta )\right]$. Variation of the excitation polarization (in the figure along $\left[1\overline{1}0\right]$) leaves the data unchanged.

Figure 2

Splitting of the trion PL line (QD#2) in a transverse magnetic field. (a) PL spectra in unpolarized detection mode. (b) Scheme of optical transitions. (c) Separation between inner and outer lines as a function of the field strength. The data points for $B<6\mathrm{T}$ are taken from polarized detection measurements (see Fig. 3) where the splitting is better seen.

Figure 3

(a) and (b) Reconstruction of PL spectra in QD#1 under rotation of the sample around the $z$ axis for $(\vec{B}\perp z)$. The spectra are taken in linear polarizations along $(\vec{e}\Vert \vec{B})$ and perpendicular $(\vec{e}\perp \vec{B})$ to the magnetic-field direction $(B=9\mathrm{T})$. The angle $\phi$ is defined in Fig. 1.

Figure 4

Signal ratio of the outer and inner components for QD#1 as a function of the analyzer position $\varphi$ for various field orientations $\phi$. The data demonstrate that the lines are fully linearly cross polarized. The polarization axes are independent on the magnetic field but specific for the respective QDs. $\theta =38°$ for QD#1 is in accord with the zero-field measurements of Fig. 1.