# Spin Transport in a Quantum Hall Insulator
## 3 Results and Discussion
It has been shown in previous studies [15] that, at low concentrations of magnetoexcitons, the photoluminescence spectrum contains two single-particle lines indicating \(\sigma\)- and \(\sigma\)+ polarizations of light (top left inset in Figure 2). These lines correspond to the radiative recombination of electrons with spin projections of \(+1/2\) and \(-1/2\) and heavy holes with spin projections of \(-3/2\) and \(+3/2\), respectively. As the density of dark magnetoexcitons increases, the luminescence spectrum undergoes significant changes. There appear two additional lines related to recombination originating from three-particle complexes constructed from a dark magnetoexciton and an extra Fermi hole. When spin projections on the axis of the magnetic field of a Fermi hole within the magnetoplasmon and an additional Fermi hole coincide, a spin-triplet is formed. Otherwise, if the spin projections of the two holes are oppositely directed, it leads to the formation of a spin-singlet. The singlet-hole state is called \"plasmaron\" since a photoexcited electron can recombine with one of the Fermi holes, transferring energy and momentum to the new electron-hole pair (plasma oscillations). The plasmaron can be considered as a magneto-plasmon coupled with an extra Fermi hole. The triplet-hole state is known as a \"trion\". An electron incorporated into a trion cannot engage in plasma oscillations. Furthermore, the trion's energy provides no data about the generalized momentum of the magnetoexciton contained therein, as evidenced by the small dispersion of magnetoexcitons compared to the characteristic width of the trion photoluminescence line. For example, increasing the momentum from zero to the inverse magnetic length changes the magnetoexciton energy by 0.1 meV in comparison with the 0.2 meV characteristic linewidth of the trion. Thus, the information acquired from the trion photoluminescence spectra is similar to that retrieved from the resonance reflection spectra. In fact, the trion line's intensity accounts for the total number of magnetoexcitons in the excitation spot. The PL spectrum of a plasmaron, on the contrary, reveals both the total number of magnetoexcitons and their energy distribution function. This energy function, in turn, denotes the distribution function of magnetoexcitons within the plasmaron based on their generalized momenta at the plasma  
Figure 2: Dependence of the PRR signal decay time \(\tau\) on the pumping pulse duration \(\tau_{\text{p}}\), measured at the pump power of 50 \(\upmu\)W for sample 2 (black dots). The insets (left to right) show the shape of the photoluminescence spectra measured for different values of pump pulse duration, \(\tau_{\text{p}}=\) 10 \(\upmu\)s, 30 \(\upmu\)s, 100 \(\upmu\)s, and 1000 \(\upmu\)s.  
The insets in Figure 2 illustrate that at low excitation density, the density of magnetoexcitons with considerable momentum is low, and the plasmaron line (Pln) is absent. As the density of spin excitations grows larger, magnetoexcitons with small momentum begin to scatter into the minimum of the dispersion curve, where the intensity of the plasmaron line with magnetoexciton momenta close to the inverse magnetic length increases relative to that of the trion line (T). As a result, the relaxation time of magnetoexcitons in the ground state measured by the PRR becomes longer (region 2 in Figure 2). This is not surprising since, in the process of relaxation into the ground state, spin excitations have to lose both their energy and momentum about the inverse magnetic length. What is most intriguing is the third region in Figure 2, where the PRR signal decay time decreases drastically. Here, the total number of magnetoexcitons excited in the pumping area, detected from the trion line, varies from that of magnetoexcitons with a generalized momentum about the inverse magnetic length, estimated from the plasmaron line. Indeed, we find the former to be increasing, whereas the latter is decreasing.