Exciton-spin relaxation in quantum dots due to spin-orbit interaction

We present theoretical results for the spin relaxation of exciton-bound electrons and holes in weakly confining quantum dots. The relaxation is driven by the spin-orbit interaction in the conduction band and the linear in the momentum term in the valence band, respectively. The relaxation occurs between the optically active (bright) and inactive (dark) exciton states due to acoustic-phonon-assisted spin flips. The exchange splitting between the bright and dark states acts as a constant external magnetic field. A sequential flip of the (exciton-bound) electron and hole spins results in the spin-flip transition between the bright exciton states (i.e., an exciton-spin relaxation). We find that the spin relaxation time for an exciton-bound electron is several orders of magnitude faster than for a single electron. The resulting exciton spin-relaxation time is also several orders of magnitude faster than the one in small dots which is driven by the electron hole exchange interaction. We obtain the dependence of the exciton-spin relaxation time on dot size and temperature.

Figure 1

The heavy-hole exciton spin states and exciton-bound single-particle spin-flip transitions with rates $W_e$ and $W_h$ for electrons and holes, respectively.

Figure 2

The lateral size variation of the exciton-bound hole-spin relaxation time in flat InGaAs QDs at $4\mathrm{K}$. For the parameters see the text.

Figure 3

The relaxation times in a flat InGaAs quantum dot with a diameter of $50\mathrm{nm}$ as a function of temperature. For the parameters see the text.