Figure 1

(Color online) The ${\sigma }^{-}$ polarized PL spectrum of the 2D valence hole gas as a function of the magnetic field. Energy is measured from the exciton line. Arrows mark several peaks identified at high fields: exciton $X$, trions $X^{+}$ (red for spin-singlet and blue for two triplets), and emission spectrum of the acceptor-bound trion $A{X}^{+}$, including a shake-up line $A{X}_{\mathrm{SU}}^{+}$.Reuse & Permissions

Figure 2

(Color online) Top: Comparison of (a) ${\sigma }^{-}$ and (b) ${\sigma }^{+}$ polarized PL spectra at a sequence of magnetic fields between $B=0$ and $23\mathrm{T}$ (same sample as in Fig. 1). Bottom: Magnified spectra at $B=16\mathrm{T}$. Several identified lines include free exciton $X$ and three positive trions $X^{+}$ (spin-singlet and two spin-triplets), acceptor-bound exciton $AX$ and trion $A{X}^{+}$, and a light-hole exciton $X_{\mathrm{lh}}$. Note different spin splittings of the $X$, $A{X}^{+}$, and different $X^{+}$ states. Inset: Schematic of the ${\sigma }^{\pm }$ polarized transitions of a positive spin-singlet trion.Reuse & Permissions

Figure 3

(Color online) Magnetic field dependence of recombination energies identified in polarizations ${\sigma }^{-}$ (a) and ${\sigma }^{+}$ (b) in the PL spectra in Fig. 2. (c) Splitting of the shake-up line.Reuse & Permissions

Figure 4

(Color online) (a) Magnetic field dependence of the trion binding energies determined from the exciton-trion peak splittings, $\Delta =E\left[X\right]-E\left[X^{+}\right]$; lines, numerical calculation of the corresponding Coulomb binding energies (i.e., binding energies ignoring the Zeeman term); (b) Coulomb binding energies of the singlet and dark triplet trions, obtained as ${\sigma }^{\pm }$ averages $\frac{1}{2}({\Delta }^{+}+{\Delta }^{-})$ to remove Zeeman effect; lines, guide for the eye. The crossover occurs at $B\approx 12\mathrm{T}$, and adding the hole Zeeman term to $E\left[X_s^{+}\right]$ shifts it to an even lower field. Note features around $B=14.2\mathrm{T}$, corresponding to $\nu =\frac{1}{3}$.Reuse & Permissions

Figure 5

(Color online) Calculated energy spectra of (a) $3h+e$ and (b) $2h$ systems in the presence of an ionized acceptor $A^{-}$ in the middle of a symmetric quantum well. In (a), $A\text{‐}{X}^{+}$ pair states are connected with the solid lines, and $A{X}_d^{+}$ at angular momentum $M=-1$ is the spin-doublet ground state of an $A$-bound trion. In (c), the $A{X}_d^{+}$ binding energy is compared to the weakly bound ${}^{*}A{X}_d^{+}$ at $M=0$ as a function of the number of included LLs and subbands (lines are a guide for the eye). In (b), four lowest final states for the $A{X}_d^{+}\to A^{+}$ recombination are marked at $M=-1$. In (d), the corresponding four-peak $A{X}_d^{+}$ emission spectrum is overlaid with the experimental data of Fig. 2a. In (e), the hole effective mass $m_h^{*}$ is extracted from the splitting of the experimental shake-up line, equal to the hole cyclotron energy as shown in (b). All data are for a $15\mathrm{nm}$ GaAs quantum well and, except for (e), for magnetic field $B=15\mathrm{T}$.Reuse & Permissions