Random fine structure and polarized luminescence of triplet excitons in semiconductor nanocrystals

Abstract

We present a theory of polarized photoluminescence of triplet excitons in semiconductor nanocrystal ensembles with the random fine structure contributed by the electron-hole exchange and carrier-nuclear hyperfine interactions. The interaction parameters are assumed to be normally and isotropically distributed. In particular, the exchange interaction is described by the Gaussian orthogonal ensemble of random matrices. The intensity of luminescence as well as the optical orientation and alignment are calculated as functions of the fine structure splitting parameters and the exciton lifetime. We have also analyzed the suppression of optical alignment and enhancement of optical orientation in an external longitudinal magnetic field.

Figures (3)

• Figure 1: Definition of the Euler angles. First, the initial $(xyz)$ system is rotated about the $z$ axis by $\varphi$. The new $y$ axis makes the angle $\varphi$ with the initial $y$ axis. Then the new system is rotated about its $y$ axis (denoted $ON$) by $\theta$. As a result, the new $z$ axis makes the angle $\theta$ with the initial $z$ axis. Finally, the system is rotated about its current $z$ axis by the angle $\psi$. The final coordinate system is denoted $(x'y'z')$.
• Figure 2: Variation of the PL intensity (black solid lines) and degrees of the linear (blue dotted lines) and circular (red dashed lines) polarizations with the exciton lifetime $\tau$. (a) Effect of the exchange interaction calculated after Eqs. \ref{['eq:int_delta']}, \ref{['eq:Pl_delta']}, and \ref{['eq:Pc_delta']}. (b) Effect of the hyperfine interaction calculated after Eqs. \ref{['eq:int_hf']} and \ref{['eq:P_hf']}.
• Figure 3: Dependencies of the optical orientation (red lines) and optical alignment (blue lines) on the external longitudinal magnetic field in cases of the random exchange (a) and hyperfine (b) interaction.