Abstract
Mesoscopic conductance fluctuations were discovered in a weak localization regime of a strongly disordered two-dimensional HgTe-based semimetal. These fluctuations exist in macroscopic samples with characteristic sizes of 100 μm and exhibit anomalous dependences on the gate voltage, magnetic field, and temperature. They are absent in the regime of electron metal (at positive gate voltages) and strongly depend on the level of disorder in the system. All the experimental facts lead us to the conclusion that the origin of the fluctuations is a special collective state in which the current is conducted through the percolation network of electron resistances. We suppose that the network is formed by fluctuation potential whose amplitude is higher than the Fermi level of electrons due to their very low density.