Magneto-optical evidence of the percolation nature of the metal-insulator transition in the two-dimensional electron system

We compare the results of the transport and time-resolved magnetoluminescence measurements in disordered two-dimensional (2D) electron systems in GaAs-${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ heterostructures in the extreme quantum limit, particularly in the vicinity of the metal-insulator transition (MIT). At filling factors $\nu <1\mathrm{}$, the optical signal has two components: the single-rate exponentially decaying part attributed to a uniform liquid and a power-law long-living tail specific to a microscopically inhomogeneous state of electrons. We interpret this result as a separation of the 2D electron system into liquid and localized phases, especially because the MIT occurs strikingly close to those filling factors where the liquid occupies ½ of the sample area (the percolation threshold condition in two-component media)