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 hops only at neighboring sites on the square lattice are taken into account, thus W = 8t. The calculations were carried out for a lattice of 24 × 24 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.

中文翻译：

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存在强随机势的低密度吸引电子系统中有序参数的液滴

摘要

二维低密度 ( n ≪ 1) 电子系统在强随机势V的存在下具有强现场哈伯德引力U > W（W是带宽）的特性，该电势V均匀分布在 – V到 + V的范围内被考虑。只考虑正方形格子上相邻站点的电子跃点，因此W = 8 t. 计算是针对具有周期性边界条件的 24 × 24 位点的晶格进行的。在 Bogoliubov-de Gennes 方法的框架中，我们观察到了库珀对和不成对电子的空间分离费米-玻色混合物的非均匀状态的出现，在不成对的正常态矩阵中形成了不同大小的玻色液滴。当我们在哈伯德吸引力和随机势的固定值下降低电子密度时，液滴尺寸减小（从较大的液滴到单个双电子对）。获得的结果对于构建总相图和理解超导、正常金属和脏金属准二维（薄膜）局部化状态之间的相变性质非常重要。