Anisotropy of in-plane hole $g$ factor in CdTe/ZnTe quantum dots

Optical studies of a bright exciton provide only limited information about the hole anisotropy in a quantum dot. In this work we present a universal method to study heavy-hole anisotropy using a dark exciton in a moderate in-plane magnetic field. By analysis of the linear polarization of the dark exciton photoluminescence we identify two distinct contributions to the hole $g$ factor: the anisotropic one resulting in a fixed orientation of the dark exciton polarization for any direction of the magnetic field and the quasi-isotropic contribution, due to which the polarization orientation rotates with the magnetic field, but in the opposite direction. We employ the proposed method for a number of individual self-assembled CdTe/ZnTe quantum dots, demonstrating a variety of behaviors of in-plane hole $g$ factor: from almost fully anisotropic to almost quasi-isotropic. We conclude that, in general, both contributions play an important role and neither contribution can be neglected.

Figure 1

(a) A typical PL spectrum of a single self-assembled CdTe/ZnTe QD under in-plane magnetic field $B=2$ T (Voigt configuration). (b) False-color map presenting PL spectra of the same QD for different directions of detected linear polarization and (c) corresponding polar plots of $X_{\mathrm{d}}$ and $X$ emission lines intensities vs detection polarization angle $\beta$.

Figure 2

(a) Measured intensity map of brightened dark exciton line for different detection polarization angles and different directions of in-plane magnetic field. The color represents the intensity of the dark exciton line. (b) Simulation of such a map based on the model described in Sec. 2c. The procedure used for determination of light polarization was the same as in Refs. [34, 38]. (c) Brightened dark exciton emission line polarization angle $\gamma$ for different directions of in-plane magnetic field $\phi$. Symbols represent measured data, while the solid line represents the fitted curve described by Eq. (5).

Figure 3

The orientation of linearly polarized light emitted from the recombination of the dark exciton as a function of direction of in-plane magnetic field. Solid lines indicate results of fitting Eq. (5) to obtained data (dots). The almost totally anisotropic nature of the hole wave function corresponds to a low effective hole isotropy parameter $\varepsilon =0.11$. In contrast, the QD characterized by $\varepsilon =0.74$ demonstrates highly isotropic behavior of the hole wave function. Intermediate cases are characterized with moderate effective hole isotropy parameters. (b) and (c) Distribution of the $\varepsilon$ parameter among LT- and HT-type samples.

Figure 4

(a) Correlation of the effective hole isotropy parameter with emission energy of a dark exciton for the HT sample. The ellipsoid in the background is added to guide the eye. Lower-energy QDs tend to have higher $\varepsilon$ values. (b) There is no significant correlation between hole anisotropy and hole-electron exchange anisotropy ${\delta }_1$.