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

TL;DR

This study investigates how strong disorder and attractive interactions influence the formation of inhomogeneous superconducting states, revealing droplet-like structures and phase transitions relevant for quantum materials and devices.

Contribution

It demonstrates the emergence of inhomogeneous Fermi-Bose mixtures with bosonic droplets in a disordered low-density electron system using Bogoliubov-de Gennes calculations.

Findings

Formation of spatially separated Fermi-Bose mixtures.

Droplet size decreases with electron density reduction.

Insights into phase transitions in disordered superconducting systems.

Abstract

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