Manipulating the exciton fine structure of single $\mathrm{Cd}\mathrm{Te}∕\mathrm{Zn}\mathrm{Te}$ quantum dots by an in-plane magnetic field

Polarization-resolved photoluminescence (PL) spectroscopy of individual $\mathrm{Cd}\mathrm{Te}∕\mathrm{Zn}\mathrm{Te}$ quantum dots is investigated in the presence of external in-plane magnetic field. We find that the applied field modifies the excitonic fine structure, depending on the quantum dot anisotropy direction (which is randomly oriented in this system). The splitting between “bright” and “dark” states increases with the magnetic field, whereas the anisotropic exchange splitting of the bright excitons can be reduced or enhanced, for the anisotropy orientation, respectively, perpendicular or parallel to the field. For intermediate fields, we observe a rotation of the PL polarization orientation. The results are discussed in terms of an effective spin Hamiltonian derived for the exciton ground state.

Figure 1

(Color online) (a) Linearly polarized excitonic doublet (solid and dashed lines) for magnetic fields $B=0$, 2, and $4\mathrm{T}$ in a dot characterized by $\theta =20°$ at zero field. Inset shows the direction of the magnetic field $B$, parallel here to one of the crystallographic axes ⟨110⟩, with respect to the QD polarization eigenaxis $x$. (b) Mean energy of the “bright” excitonic doublet versus magnetic field. The origin is taken at zero magnetic field. The solid line is a theoretical curve calculated with the model described in the text.

Figure 2

(Color online) Upper panel: $\mu \mathrm{PL}$ spectra at $B=0\mathrm{T}$ for two dots QD1 and QD2 with perpendicular anisotropy orientations, $\theta =20°$ and $\theta =110°$, respectively (open symbols and dashed line, measured at 20°; closed symbols and solid line, measured at 110°). Lower panel: Fine-structure splitting (FSS) vs in-plane magnetic field $B$. Solid lines are theoretical curves according to the model discussed in the last section.

Figure 3

(Color online) (a) Fine-structure splitting (FSS) and (b) PL polarization orientation $\theta +\Delta \theta$ against in-plane magnetic field of four different QDs (different symbols). Lines are guides for the eyes.

Figure 4

(Color online) Schematics of the crystallographic axis configuration with respect to the QD principal axes $x$ and $y$. Thick dashes represent the exciton polarization orientation produced by the field-induced splitting only for different directions of the field. (a) Effect of the cubic term (see text); (b) effect of the linear term, including heavy-hole to light-hole coupling. The shaded area represents a QD elongated along the polarization eigenaxis $x$.

Figure 5

(Color) (a) FSS absolute value vs in-plane field direction $\theta -2\varphi$ and magnitude encoded on a color scale. Cross sections for three directions of the field are displayed on the right-hand side. (b) Rotation angle $\Delta \theta$ of the PL polarization orientation vs in-plane magnetic-field direction and magnitude. Three cross sections for $\theta -2\varphi =0$, $\pi ∕4$, and $\pi ∕2$ are also shown. Calculations are made with an isotropic $g$ factor $(\beta =0)$, ${\delta }_0=0.80\mathrm{meV}$, and a FSS ${\delta }_1=80\mu \mathrm{eV}$ in zero field.

Figure 6

(Color) FSS absolute value on a color scale vs in-plane field direction $\theta -2\varphi$ and magnitude for a strong $g$ factor anisotropy ${\rho }_g$. Depending on its sign with respect to the initial splitting (here ${\delta }_1=80\mu \mathrm{eV}$), it produces very different behaviors: (a) ${\rho }_g=-1.3$ and (b) ${\rho }_g=+1.3$. We used the same average $g$ factor ${\overline{g}}_h=0.78$, $g^e=1.75$, and ${\delta }_0=0.8\mathrm{meV}$ as in Fig. 5.