Dark-bright exciton coupling in asymmetric quantum dots

Symmetry breaking of the confinement in In(Ga)As quantum dots leads to mixing between the bright and dark exciton states and an increase in the oscillator strength of the dark exciton. We demonstrate here that the change in degree of linear polarization of the bright and dark excitons as a function of applied magnetic field, where both parallel and perpendicular magnetic field components are applied, can be used to quantify the dark-bright coupling. Experimental results for a dot where the coupling is weak and the dark exciton is undetectable in zero applied magnetic field are in good agreement with theoretical simulations based on atomistic calculations reported by M. Zieliński et al. [Phys. Rev. B 91, 085403 (2015)].

Figure 1

(a) Schematic QD representations of different point group symmetries, $C_{2v}$ on the left with the twofold symmetry axis and the first mirror plane $\left(xz\right)$ and $C_s$ on the right with the only mirror plane $\left(xz\right)$. (b) Energy level in $C_{2v}$ and $C_s$ symmetries. We used the condition ${\mathrm{\Delta }}_{11}{\mathrm{\Delta }}_{12}<0$, implying a positive energy shift of the level energies in the $C_s$ symmetry compared to $C_{2v}$.

Figure 2

(a) PL spectra recorded without applied magnetic field, showing the BE and XX states emission from the same QD. The linear polarization is analyzed along the two main QD axes $x^{\prime }$ and $y^{\prime }$. The insets show the integrated intensity of the BE and XX components as a function of the excitation power. (b) Polarization diagram of the two BE components. The gray dots correspond to the total intensity. The solid lines are fits using the model developed in Ref. [20].

Figure 3

(a) Sketch of the magnetic field orientation with respect to the sample plane. (b) Schematic of the full biexciton cascade involving the bright and dark excitons. (c) PL spectra for an applied magnetic field of 8 T. The insets represent the power dependence of the dark exciton components and the two transitions from the biexciton to the dark exciton state, labeled $|\text{XX}\rangle \to |{\text{DE}}_H\rangle$ and $|\text{XX}\rangle \to |{\text{DE}}_L\rangle$. (d) Energies of the exciton and biexciton transitions versus magnetic field. The lines are fits using the $C_{2v}$ electron/hole exchange Hamiltonian.

Figure 4

Evolution of the degree of linear polarization as a function of the applied magnetic field for the (a) and (b) dark and (c) and (d) bright exciton branches. The fit residual values do not exceed $4\%$ for the whole range of magnetic field in (a), (c), and (d). This stresses the good quality of the fit, despite unavoidable experimental noise.