Singlet and triplet trion states in high magnetic fields: Photoluminescence and reflectivity spectra of modulation-doped $\mathrm{Cd}\mathrm{Te}∕{\mathrm{Cd}}_{0.7}{\mathrm{Mg}}_{0.3}\mathrm{Te}$ quantum wells

Photoluminescence (PL) and reflectivity spectra from modulation-doped $\mathrm{Cd}\mathrm{Te}∕{\mathrm{Cd}}_x{\mathrm{Mg}}_{1-x}\mathrm{Te}$ quantum well structures containing a two-dimensional electron gas have been studied in magnetic fields up to $45\mathrm{T}$. In high fields, the recombination from the dark triplet trion state was found to be one of the most intense PL lines. A “bright” triplet line is revealed in both reflectivity and PL in magnetic fields above $35\mathrm{T}$. PL spectra were calculated as a function of magnetic field, taking into account exciton, singlet, and triplet trion states. We show that the intense PL from the dark triplet trion is due to the field-induced suppression of singlet trion formation, and a corresponding enhancement of dark trion formation.

Figure 1

Set of PL spectra taken in magnetic fields from $0\text{to}45\mathrm{T}$ from the sample with $n_e=3\times {10}^{10}{\mathrm{cm}}^{-2}$ in ${\sigma }^{-}$ circular polarization. $X$ indicates the exciton line, $T_s$ is the singlet trion line, $T_t^d$ is the dark triplet trion line, and $T_t^b$ is the bright triplet trion line.

Figure 2

Magnetic field dependence of the energy positions for all PL lines. Open circles stand for ${\sigma }^{+}$ polarization; closed circles stand for ${\sigma }^{-}$ polarization. Triangles indicate triplet trion states observed only in ${\sigma }^{-}$ polarization. $X$ indicates the states of optically active exciton in the corresponding polarization ${\sigma }^{+}$ or ${\sigma }^{-}$. $T_s$—indicates the states of the singlet trion in corresponding polarization. $T_t^d$ is optically dark due to the orbital momentum triplet trion state and $T_t^b$ is the bright triplet trion state with $L=0$.

Figure 3

Reflectivity and photoluminescence spectra taken from the sample with electron concentration $n_e=3\times {10}^{10}{\mathrm{cm}}^{-2}$ in the magnetic fields $6\mathrm{T}$, $27\mathrm{T}$, and $45\mathrm{T}$. Heavy solid lines are used for ${\sigma }^{-}$ polarization, dashed-dotted lines − for ${\sigma }^{+}$ polarization. Light solid lines are the result of the deconvolution of the PL spectra by Gaussian fits. Dotted straight lines are comparison of PL and reflectivity spectral features.

Figure 4

The magnetic field dependence of the intensities of all PL lines. The dependence of the triplet line intensity was built by the Gaussian fit of the exciton and triplet trion line. The designations are similar to those in Fig. 1. The intensity of the bright triplet line (not shown in the figure) is nearly equal to the intensity of the exciton line in the range of magnetic fields from $35\text{to}45\mathrm{T}$ where it is observable.

Figure 5

Comparison of energy positions of PL lines in heavily doped $(n_e=3.7\times {10}^{11}{\mathrm{cm}}^{-2})$ and lightly doped $(n_e=3\times {10}^{10}{\mathrm{cm}}^{-2})$ QW structures. Symbols correspond to the heavily doped sample, lines to the lightly doped sample.

Figure 6

Binding energies of the singlet $T_s$ and triplet $T_t^d$, $T_t^b$ trion states as a function of the magnetic field. Symbols, experiment; solid line, calculation (Ref. 29).

Figure 7

The scheme of (a) singlet and (b) triplet trion formation mechanism.

Figure 8

The relative energies of the $X$, $T_s$, $T_t^d$, and $T_t^b$ states after correction by diamagnetic shift and Zeeman splitting of the final state. Circles—exciton and singlet trion in ${\sigma }^{+}$ (open symbols) and ${\sigma }^{-}$ (closed symbols) polarizations. Triangles represent dark and bright triplets in ${\sigma }^{-}$ polarization.

Figure 9

Calculated magnetic field dependence of the intensities of all the PL lines: Exciton $\left(X\right)$ and singlet trion $\left(T_s\right)$ in both ${\sigma }^{+}$ (dashed lines) and ${\sigma }^{-}$ (solid lines) circular polarizations, and also the dark triplet ($T_t^d$, dot-dashed curves).

Figure 10

Modifications of the PL spectra in ${\sigma }^{-}$ polarization with temperature at magnetic fields 28, 35, and $45\mathrm{T}$. Solid line $-1.6\mathrm{K}$, dotted line $-4.2\mathrm{K}$, dashed-dotted line $15\mathrm{K}$.

Figure 11

Calculated PL spectra at temperature $1.6\mathrm{K}$ (solid line), and $15\mathrm{K}$ (dotted line) in a magnetic field of $45\mathrm{T}$.