Origin of the Oscillator Strength of the Triplet State of a Trion in a Magnetic Field

The dynamics of the spin-triplet trion state, under high magnetic field in a $\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}$ quantum well, are studied using time resolved spectroscopy. The oscillator strength of the triplet transition is shown to rise with increasing electron density, in good agreement with a theoretical model where the trion interacts with excess electrons in the quantum well. This analysis suggests that the spin-triplet trion state, which is expected to be an optically “dark” state, is experimentally observable due to the interactions with the excess electrons, demonstrating that $X^{-}$ cannot be regarded as an isolated three particle complex.

Figure 1

Transition from $X$ to $X_t^{-}$ and $X_s^{-}$ in time integrated PL at 8 T. Increasing the electron concentration the scattering rate from $X\to X^{-}$ strengthens, resulting in a higher $X_t^{-}$ and $X_s^{-}$ population and stronger PL. The time integrated PL is almost constant all over the $X\to X^{-}$ transition, implying negligible nonradiative decay paths.

Figure 2

Decay times as a function of gate bias (electron concentration) for $X$ (filled rhombus), $X_t^{-}$ (open squares), and $X_s^{-}$ (open circles). $X_t^{-}$ is found to have a decay time longer than any other species as shown in the inset where the decay curves of $X$ and $X^{-}$ are taken at an electron density of $4.3\times {10}^{10}{\mathrm{c}\mathrm{m}}^{-2}$. This shows that the $X_t^{-}$ decay time corresponds to the radiative $X_t^{-}$ lifetime. By contrast, the $X_s^{-}$ decay time coincides with the radiative lifetime of the $X_s^{-}$ state only at high electron densities (solid line). At lower electron concentrations the $X_s^{-}$ decay originates from the $X$ population which feeds the $X^{-}$ state (dashed line).

Figure 3

Schematic diagram of the relaxation and decay dynamics of $X$, $X_t^{-}$, and $X_s^{-}$. See text for specific meaning of the time constants.

Figure 4

The calculated oscillator strength ($f$) of $X_t^{-}+e^{-}$, plotted against the surrounding electron concentration (electron distance from $X_t^{-}$). The model includes the electron-electron exchange interaction. The calculated lines are compared with the experimental $X_t^{-}$ decay rates (symbols, right-hand scale).