Resonant photoluminescence of quantum incompressible liquids

We investigate resonant photoluminescence arising from incompressible quantum liquids formed in two-dimensional electron systems. We demonstrate that, for excitons composed of a photoexcited electron occupying the upper spin sublevel of the zeroth Landau level and a valence-band hole, the influence of disorder potential fluctuations on optical recombination is strongly suppressed, indicating complete screening of the disorder. We identify an optical invariant quantity that is insensitive to excitation energy yet strongly dependent on electron temperature, serving as a probe of exciton recombination in quantum liquids. Analysis of this quantity reveals that quantum-liquid formation initiates at $\ensuremath{\nu}=1/3$ as the electron temperature decreases, consistent with the Laughlin state. Upon further cooling, the range of filling factors exhibiting quantum-liquid behavior expands continuously from $\ensuremath{\nu}=1/3$ toward $\ensuremath{\nu}=1/2$. Transitions between distinct incompressible quantum-liquid states occur smoothly, without well-defined phase boundaries separating insulating and conducting regimes. Locally, the system retains quantum-liquid characteristics even as bulk transport measurements indicate finite conductivity. Finally, we present a phase diagram delineating the stability region of incompressible quantum liquids relative to conductive phases.