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Капли параметра порядка в электронной системе малой плотности с притяжением в присутствии сильного случайного потенциала
The properties of a two-dimensional electron system with a low density (n << 1) with a strong local Hubbard attraction U > W (W is the band width) in the presence of a strong random potential V, uniformly distributed in the range from -V to +V. Electronic jumps only to neighboring nodes of the square lattice at W = 8t were taken into account. The calculations were performed on a 24 х 24 lattice with periodic boundary conditions. Within the framework of the Bogolyubov-de Gennes approach, the appearance of inhomogeneous states of a spatially separated Fermi–Bose mixture of Cooper pairs and unpaired electrons with the formation of boson droplets of different sizes in the matrix of unpaired normal electronic states was observed. The effect of reducing the drop size (from larger drops to individual bielectronic pairs) was observed with a decrease in the electron density at fixed values of the Hubbard attraction and random potential. The results obtained are important for constructing a phase diagram and understanding the nature of the phase transition between superconducting, normal metal, and localized states in a quasi-two-dimensional (thin film) dirty metal. In a more practical sense, the results obtained are also interesting for the experimental implementation of superconducting qubits on high-impedance quantum circuits in granular superconductors.