# Spin Transport in a Quantum Hall Insulator
## 3 Results and Discussion
Therefore, we conclude that not all excited magnetoexcitons leave the excitation spot, but only those with a generalized momentum about the inverse magnetic length. Optical transitions associated with the three-particle complexes signal the appearance of spin-triplet magnetoexcitons in the probing region. Therefore, by observing the variation in luminescence spectra, it is possible to detect the arrival of the spin-triplet magnetoexcitons that were formed far away from the probing point and yet were able to overcome such a separation distance. The inset in Figure 3 shows another experimental scheme. This time, a single excitation laser beam is split into the pumping and probing components. Long-lived spin-triplet magnetoexcitons are formed in the photoexcitation spot \(\sim\)20 \(\upmu\)m in diameter, where their concentration can be manipulated by varying the pump power. Magnetoexcitons arriving at a probing spot separated from the pumping spot by \(\sim\)200 \(\upmu\)m are registered based on the changes observed in the luminescence spectra. Figure 3 shows the luminescence spectra measured in the probing area for different pumping power levels at the excitation area. Data plots display the lines related to single-particle transitions designated by \(\sigma-\) and \(\sigma+\), as well as the plasmaron (Pln) and trion (T) lines due to the presence of magnetoexcitons in the probing region. We observe that increasing the pumping power at the excitation area leads to a higher intensity of the Pln and T lines, indicating that dark magnetoexcitons from the photoexcitation spot enter the probing area, having overcome the \(\sim\)200 \(\upmu\)m separation distance. In the inset of Figure 3, we plot the dependence of luminescence spectra on the temperature of the helium bath. Here, we can see that as the temperature reaches 0.97 K, the transfer of spin-triplet magnetoexcitons over the distance of 200 \(\upmu\)m comes to a halt. This result agrees with a previous work [16], where it was shown that the transport of magnetoexcitons requires the transition of a non-equilibrium ensemble of magnetoexcitons into a condensed state. However, for the evidence to be fully conclusive, additional measurements are needed at different distances between the pumping and probing spots. As a result of the experiments with the pumping and probing spots spaced apart, we verify the above considerations concerning the type of magnetoexcitons responsible for spin transport. We find that with rising photoexcitation power density, the plasmaron (PIn) line intensity grows until the integral intensity of the plasmaron line approaches that of the trion line (Figure 4). This means that almost all magnetoexcitons from the pumping spot that reach the probing region have the generalized momentum about the inverse magnetic length. Hence, by subtracting a properly weighed PL spectrum of the equilibrium 2 DES from the photoluminescence spectra of the 2 DES measured in the probing spot, we can obtain the generalized momentum distribution function of non-equilibrium magnetoexcitons (inset of Figure 4). These distribution functions clearly indicate that magnetoexciton transport involves namely the magnetoexcitons with momenta about the inverse magnetic length. Figure 3: Photoluminescence spectra for sample 2 measured in the probing spot at a different pump power in the excitation spot. The left-hand inset shows the scheme of photoluminescence spectra measurements with the probing spot separated from the pumping spot by –200 \(\upmu\)m. The right-hand inset shows the photoluminescence spectra measured in the probing spot at Ppump = 25 \(\upmu\)W and different temperatures (0.64 and 0.97 K).