Extended Data Fig. 3: Exciton compressibility versus average lattice filling.

Fluctuations of the maximum of the PL intensity (\(\sigma ({A}_{\max })/\overline{{A}_{\max }}\)) as a function of the power P of the loading laser, in a different region of our two-dimensional square lattice. As for Fig. 2, experimental results are obtained by statistically analysing a series of 10 measurements for every value of P. The laser excitation profile was set close to the one for the experiments shown in Fig. 2. Remarkably we recover that two insulating phases emerge for P = 7 and 14.4 nW, in good agreement with the findings discussed in the main text. Experiments were realised at T = 330 mK; error bars display statistical confidence while the level of Poissonian fluctuations is given by the grey shaded region.