Figure 1

Scheme (ABSORPTION) of the spin structure and optical transitions for excitons and ${\mathrm{T}}_s^{-}$ and ${\mathrm{T}}_s^{+}$ singlet trions in external magnetic fields. Used parameters: $g_e<0$, $g_h<0$, and $\left|g_e\right|>\left|g_h\right|$. Short black arrows show carrier spins: thin for electrons and thick for holes. They are aligned up and down for $+$ and $-$ spin sign, respectively. The total spin of each state is additionally given by numbers. The thickness of the colored arrows is proportional to the probability of the optical transitions.Reuse & Permissions

Figure 2

Scheme (EMISSION) of the spin structure and optical transitions for excitons and ${\mathrm{T}}_s^{-}$ and ${\mathrm{T}}_s^{+}$ singlet trions in external magnetic fields. Used parameters: $g_e<0$, $g_h<0$, and $\left|g_e\right|>\left|g_h\right|$.Reuse & Permissions

Figure 3

Triplet trion schemes and optical transitions (EMISSION) for the $n$-type and $p$-type regimes. Used parameters: $g_e<0$, $g_h<0$, and $\left|g_e\right|>\left|2g_h\right|$.Reuse & Permissions

Figure 4

Photoluminescence spectra of a 20-nm-thick CdTe/Cd${}_{0.63}$Mg${}_{0.37}$Te QW measured for optical excitation below (1.66 eV) and above (2.33 eV) the band gap of the Cd${}_{0.63}$Mg${}_{0.37}$Te barriers. The peaks are assigned to the exciton (X) and the positively (T${}_s^{+}$) and negatively (T${}_s^{-}$) charged singlet trions.Reuse & Permissions

Figure 5

Pump-probe Kerr rotation signals, measured for resonant excitation of the trion state with and without additional illumination at 2.33 eV, i.e. in the $n$-type and $p$-type regimes, respectively. The dashed line in the lower signal corresponds to a fit of the hole spin beats. The magnetic field is applied perpendicular to the growth axis of the QW structure (Voigt geometry). The inset shows the magnetic field dependence of the Larmor frequency of the electrons, which allows us to evaluate $\left|g_e^{x,y}\right|=1.60$. The $g$-factor component parallel to the growth axis, $\left|g_e^z\right|=1.70$, is evaluated by similar measurements at oblique angles of $3^{°}$.Reuse & Permissions

Figure 6

Reflectivity spectra at $B=14$ T for two circular polarizations. The spectra are shifted vertically for better visibility. The polarization degree of the trion as a function of the magnetic field is shown in the inset by open circles. A fit using Eq. (5) (dashed line) reveals a hole temperature of $T_h=0.6$ K.Reuse & Permissions

Figure 7

Peak positions of the exciton transitions vs magnetic field strength evaluated from the reflectivity measurements. The symbols show resonances observed in ${\sigma }^{+}$ (closed) and ${\sigma }^{-}$ (open) polarizations.Reuse & Permissions

Figure 8

Photoluminescence spectra in the $p$-type and $n$-type regimes, measured under excitation with (a) 1.664 eV and (b) 2.33 eV.Reuse & Permissions

Figure 9

Fan chart of excitons (circles), singlet trions (triangles), and triplet trions (diamonds) extracted from photoluminescence spectra. The circular polarization of the lines is shown by closed (${\sigma }^{+}$) and open (${\sigma }^{-}$) symbols. The symbol size indicates the peak intensity. (a) Below-barrier excitation at a photon energy of 1.66 eV. (b) Above-barrier excitation at a photon energy of 2.33 eV.Reuse & Permissions

Figure 10

Energies of exciton and trion optical transitions (the exciton diamagnetic shift is subtracted), measured in the ${\mathrm{T}}^{-}$ regime under laser excitation with a photon energy of 2.33 eV. (a) $T=0.4$ K. (b) $T=4.2$ K. The circular polarization of the lines is shown by closed (${\sigma }^{+}$) and open (${\sigma }^{-}$) symbols.Reuse & Permissions

Figure 11

Energies of the exciton and trion optical transitions (the exciton diamagnetic shift is subtracted), measured in the ${\mathrm{T}}^{+}$ regime under laser excitation with a photon energy of 1.66 eV. (a) $T=0.4$ K. (b) $T=4.2$ K. The circular polarization of the lines is shown by closed (${\sigma }^{+}$) and open (${\sigma }^{-}$) symbols. The dashed lines show the expected shift of the $+7/2$ to $+3/2$ optical transition.Reuse & Permissions

Figure 12

(a) Energy of the 1$s$ heavy-hole exciton in reflectivity spectra as a function of magnetic field. The dashed line shows the center of gravity of the Zeeman split levels. (b) Exciton Zeeman splitting, taken from the photoluminescence (open circles, excitation 1.66 eV) and reflectivity (solid stars), $T=4.2$ K. (c) Zeeman splitting of electrons and heavy holes as a function of the external magnetic field (Faraday geometry). The electron splitting corresponding to $\left|g_e\right|=1.70$ is shown by the thick gray (red) line. Results for the heavy holes are evaluated from the Zeeman splittings of excitons, ${\mathrm{T}}_s^{-}$, and ${\mathrm{T}}_s^{+}$. As an example, the hole splitting obtained from the exciton PL (excitation 1.66 eV, $T=1.2$ K), is presented by open circles and a polynomial fit (solid line). For the sake of clarity only interpolations are shown for the other data: dashed line from ${\mathrm{T}}_s^{+}$ PL (1.66 eV, $T=0.4$ K) and dash-dot line from ${\mathrm{T}}_s^{-}$ PL (2.33 eV, $T=1.2$ K).Reuse & Permissions

Figure 13

Exciton, electron, and heavy-hole $g$ factors for magnetic fields applied parallel to the structure growth axis (Faraday geometry). For the electron a constant value of $g_e=-1.70$ is shown by the thick gray (red) line. For excitons and heavy holes, for the sake of clarity, we show polynomial regressions of the data. Three dependencies are given for the heavy-hole $g$ factors, evaluated from the Zeeman splittings of excitons (solid line), ${\mathrm{T}}_s^{+}$ (dashed line), and ${\mathrm{T}}_s^{-}$ (dashed-dotted line). For magnetic fields below 6 T the exciton and hole $g$ factors are not shown as the error of their evaluation becomes too large.Reuse & Permissions

Figure 14

Circular polarization degree of the photoluminescence, measured for temperatures of 4.2 K (open symbols) and 0.4 K (solid symbols). The solid and dash-dot lines show ${\mathrm{T}}^{+}$ and ${\mathrm{T}}^{-}$ fittings by Eq. (5), respectively. The dashed lines represent the degree of polarization, extracted from the same formula for $T=0.4$ K.Reuse & Permissions

Figure 15

PL intensities of ${\mathrm{T}}_s^{-}$ and ${\mathrm{T}}_t^{-}$ in the $n$-type regime, plotted in the vicinity of the singlet-triplet crossing. The vertical dashed line corresponds to the magnetic field where the optical transitions of ${\mathrm{T}}_s^{-}$ and ${\mathrm{T}}_t^{-}$ cross each other, see Fig. 10a.Reuse & Permissions

Figure 16

T${}_t^{+}$ energies (diamagnetic shift subtracted) plotted against the magnetic field. Besides the ${\sigma }^{+}$ features (solid symbols) a ${\sigma }^{-}$ contribution is also visible (open symbols). Solid and dashed lines show the calculated $+7/2\to +3/2$ optical transition of ${\mathrm{T}}_t^{+}$, based on X and ${\mathrm{T}}_s^{+}$ Zeeman splittings, respectively.Reuse & Permissions

Figure 17

Photoluminescence spectra for two circular polarizations at a pulsed magnetic field of 51.4 T in the $p$-type regime. In the ${\sigma }^{-}$ polarization X and ${\mathrm{T}}_t^{+}$ are clearly seen as two separate peaks.Reuse & Permissions

Figure 18

Photoluminescence (solid line) and PL excitation (dashed line) spectra at $B=30$ T in the $p$-type regime. The PL is detected in ${\sigma }^{+}$ polarization. The PLE is excited with a ${\sigma }^{+}$ polarized laser and detected at 1.609 eV in ${\sigma }^{-}$ polarization.Reuse & Permissions

Figure 19

Magnetic field dependencies of (a) Coulomb binding energies of positively and negatively charged singlet trions, $T=4.2$ K (open symbols) and 0.4 K (closed symbols). (b) Coulomb binding energy of ${\mathrm{T}}^{-}$ singlet and triplet states.Reuse & Permissions

Figure 20

Coulomb binding energies of ${\mathrm{T}}^{+}$ trion states in the $p$-type regime up to $B=51$ T. Data for the singlet and triplet trions are shown by solid and open symbols, respectively.Reuse & Permissions