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The properties of a two-dimensional low density (n<<1) electron system withstrong onsite Hubbard attraction U>W (W is the bandwidth) in the presence of astrong random potential V uniformly distributed in the range from -V to +V areconsidered. Electronic hoppings only at neighboring sites on the square latticeare taken into account, thus W=8t. The calculations were carried out for alattice of 24x24 sites with periodic boundary conditions. In the framework ofthe Bogoliubov - de Gennes approach we observed an appearance of inhomogeneousstates of spatially separated Fermi-Bose mixture of Cooper pairs and unpairedelectrons with the formation of bosonic droplets of different size in thematrix of the unpaired normal states We observed a decrease in the droplet size(from larger droplets to individual bielectronic pairs) when we decrease theelectron density at fixed values of the Hubbard attraction and randompotential. The obtained results are important for the construction of the grossphase diagram and understanding of the nature of the phase transition betweensuperconducting, normal metallic and localized states in quasi-2D (thin) filmof a dirty metal. In a more practical sense it is interesting also for theexperimental implementation of superconducting qubits on quantum circuits withhigh impedances in granular superconductors.

Droplets of the order parameter in a low density attracting electron system in the presence of a strong random potential