Dominant channels of exciton spin relaxation in photoexcited self-assembled (In,Ga)As quantum dots

We present a comprehensive theoretical investigation of spin relaxation processes of excitons in photoexcited self-assembled quantum dots. The exciton spin relaxations are considered between dark- and bright-exciton states via the channels created by various spin-admixture mechanisms, including electron Rashba and Dresselhaus spin-orbital couplings (SOCs), hole linear and hole cubic SOCs, and electron hyperfine interactions, incorporated with single- and double-phonon processes. The hole-Dresselhaus SOC is identified as the dominant spin-admixture mechanism, leading to relaxation rates as fast as $~$${10}^{-2}$ ns${}^{-1}$, consistent with recent observations. Moreover, due to significant electron-hole exchange interactions, single-phonon processes are unusually dominant over two-phonon ones in a photoexcited dot even at temperatures as high as $15\hspace{0.5em}\mathrm{K}$.

Figure 1

Exciton spin relaxation rates in the DX to BX transition and the rates contributed from each spin-flip mechanism, as functions of the QD size. Results with fixed ${\Delta }_{\mathit{eh}}^{\mathit{xc}}=0.4$ meV (dashed line) are also presented for comparison. Inset: Schematic of the DX to BX conversion channels.

Figure 2

Exciton spin relaxation rates due to one- and two-phonon processes as a function of the e-h exchange interaction (a) and the QD size (b) at $T=15$ K. In panel (a), $l_0=5$ nm. In panel (b), size-dependent ${\Delta }_{\mathit{eh}}^{\mathit{xc}}$ is taken. The inset in panel (a) is a schematic of the two-phonon process.

Figure 3

Schematics of the main low-lying exciton configurations coupled by various spin-orbital couplings for the dark-exciton state $|\mathrm{DX}\rangle$ defined by Eq. (10).

Figure 4

Schematics of the main low-lying exciton configurations coupled by various SOCs for the bright-exciton state $|\mathrm{BX}\rangle$ defined by Eq. (12).

Figure 5

Calculated (a) spin-mixture function $P$, (b) product of mean phonon coupling and density of states of involved phonons $\left|\mathrm{M̄}\right|{}^2\rho$, (c) correction factor $F$, and (d) phonon population $N_{q_{{}_{\mathit{TP}0}}}$ as functions of $l_0$ for the dominant $h-D$ SOC and transversal piezoelectric phonon (TP) couplings. The product of the four quantities determine the main exciton spin relaxation rates of QDs as shown by Eq. (20). The results calculated with fixed ${\Delta }_{\mathit{eh}}^{\mathit{xc}}=0.4$ meV are indicated by dashed lines for comparison.