Scaling laws of electron and hole spin relaxation in indirect band gap (In,Al)As/AlAs quantum dots

Abstract

We investigate the electron and heavy hole spin dynamics as a function of magnetic field in ensembles of indirect band gap (In,Al)As/AlAs quantum dots (QDs) with type-I band alignment. Employing a comprehensive model that accounts for both the exciton level quartet and the magnetic-field-driven redistribution of excitons between these states via spin relaxation processes, we extract the electron ($τ_{se}$) and heavy hole ($τ_{sh}$) spin relaxation times as a function of magnetic field for QDs of varying sizes. Our analysis reveals that both $τ_{se}(B)$ and $τ_{sh}(B)$ exhibit power-law scaling behavior, yet the scaling exponents for electrons and heavy holes show markedly different evolution with QD size. For QDs with a diameter of about 9 nm, we find $τ_{se}(B)\propto B^{-5}$ and $τ_{sh}(B)\propto B^{-3}$. Remarkably, increasing the QD diameter to about 16 nm results in a drastic change of the scaling laws, with both $τ_{se}(B)$ and $τ_{sh}(B)$ following a $\propto B^{-9}$ dependence. We discuss the underlying mechanisms responsible for this size-dependent transformation of the magnetic field scaling behavior of carrier spin relaxation.

Figures (5)

• Figure 1: Time-integrated PL spectrum of the (In,Al)As/AlAs QDs. Arrows mark the energies of 1.61, 1.65, 1.70, 1.75, 1.80, and 1.85 eV, where the PL and the PL polarization dynamics shown in Fig. \ref{['Fig2']} were measured. Insets show schematic band diagrams of type-I (In,Al)As/AlAs QDs with direct and indirect band structure. Arrows in the insets indicate the optical transitions associated with the radiative decay of the ground state exciton.
• Figure 2: Dynamics of the magnetic-field-induced circular polarization degree of the PL measured across the emission band (curve colors and corresponding energies are indicated by the arrows in Fig. \ref{['Fig1']}) in the Faraday geometry at magnetic fields of (a) 5 T, (b) 7 T, and (c) 9 T. Panels (d), (e), and (f) show the calculated $P_{c}(t)$ dynamics at the same magnetic fields of 5, 7, and 9 T, respectively. $T = 1.8$ K.
• Figure 3: Electron ($\tau_{se}$, red circles) and heavy-hole ($\tau_{sh}$, blue circles) spin relaxation times obtained from best fits of the experimental data at $T = 1.8$ K. The data are plotted on a double-logarithmic scale to highlight the power-law dependencies. The solid lines indicate power-law scaling with various exponents.
• Figure 4: (Left panels) PL dynamics measured in $\sigma^{+}$ (red) and $\sigma^{-}$ (blue) circular polarization as a function of magnetic field strength; (right panels) corresponding dynamics of the magnetic-field-induced PL circular polarization degree. The measurements were performed in the Faraday geometry at $T = 1.8$ K with detection at 1.85 eV.
• Figure 5: (Left panels) PL dynamics measured in $\sigma^{+}$ (red) and $\sigma^{-}$ (blue) circular polarization as a function of magnetic field strength; (right panels) corresponding dynamics of the magnetic-field-induced PL circular polarization degree. The measurements were performed in the Faraday geometry at $T = 1.8$ K with detection at 1.70 eV.