Strong Random Potential Research Articles

Droplets of the Order Parameter in a Low Density Attracting Electron System in the Presence of a Strong Random Potential

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.

КАПЛИ ПАРАМЕТРА ПОРЯДКА В ЭЛЕКТРОННОЙ СИСТЕМЕ МАЛОЙ ПЛОТНОСТИ С ПРИТЯЖЕНИЕМ В ПРИСУТСТВИИ СИЛЬНОГО СЛУЧАЙНОГО ПОТЕНЦИАЛА

КАПЛИ ПАРАМЕТРА ПОРЯДКА В ЭЛЕКТРОННОЙ СИСТЕМЕ МАЛОЙ ПЛОТНОСТИ С ПРИТЯЖЕНИЕМ В ПРИСУТСТВИИ СИЛЬНОГО СЛУЧАЙНОГО ПОТЕНЦИАЛА

Energy-level statistics in strongly disordered systems with power-law hopping.

Motivated by neutral excitations in disordered electronic materials and systems of trapped ultracold particles with long-range interactions, we study energy-level statistics of quasiparticles with the power-law hopping Hamiltonian in a strong random potential. In solid-state systems such quasiparticles, which are exemplified by neutral dipolar excitations, lead to long-range correlations of local observables and may dominate energy transport. Focussing on the excitations in disordered electronic systems, we compute the energy-level correlation function in a finite system in the limit of sufficiently strong disorder. At small energy differences the correlations exhibit Wigner-Dyson statistics. In particular, in the limit of very strong disorder the energy-level correlation function is given by for small frequencies and for large frequencies , where is the characteristic matrix element of excitation hopping in a system of volume , and , and are coefficient of order unity which depend on the shape of the system. The energy-level correlation function, which we study, allows for a direct experimental observation, for example, by measuring the correlations of the ac conductance of the system at different frequencies.

Superfluid behavior of a Bose–Einstein condensate in a random potential

We investigate the relation between Bose–Einstein condensation (BEC) and superfluidity in the ground state of a one-dimensional model of interacting bosons in a strong random potential. We prove rigorously that in a certain parameter regime the superfluid fraction can be arbitrarily small while complete BEC prevails. In another regime there is both complete BEC and complete superfluidity, despite the strong disorder.

Temperature dependence of electrical resistivity for Ca-doped perovskite-type Y1−xCaxCoO3 prepared by sol–gel process

Abstract The temperature dependences of DC electrical resistivity for perovskite-type oxides Y1−xCaxCoO3 (0⩽x⩽0.1), prepared by sol–gel process, were investigated in the temperature range from 20 K up to 305 K. The results indicated that with increase of doping content of Ca the resistivity of Y1−xCaxCoO3 decreased remarkably, which was found to be caused mainly by increase of carrier (hole) concentration. In the whole temperature range investigated the temperature dependence of resistivity ρ(T) for the un-doped ( x = 0 ) sample decreased exponentially with decreasing temperature (i.e. ln ρ∝1/T), with a conduction activation energy E a = 0.308 eV ; the resisitivity of lightly doped oxide ( x = 0.01 ) possessed a similar temperature behavior but has a reduced Ea (0.155 eV). Moreover, experiments showed that the relationship ln ρ∝1/T existed only in high-temperature regime for the heavily doped samples (T≳82 and ∼89 K for x = 0.05 and 0.1, respectively); at low temperatures Mott's ln ρ∝T−1/4 law was observed, indicating that heavy doping produced strong random potential, which led to formation of considerable localized states. By fitting of the experimental data to Mott's T−1/4 law, we estimated the density of localized states N(EF) at the Fermi level, which was found to increase with increasing doping content.

Temperature dependence of electrical resistivity for nanocrystalline Mg3+xSb2 prepared by mechanical alloying

The temperature dependence of dc electrical resistivity of nanocrystalline Mg3+xSb2 (nano-Mg3+xSb2) (mean grain sizes d ∼ 30 nm), prepared by mechanical alloying plus hot-pressing (HP), was investigated below room temperature. The results indicate that composition deviation x from stoichiometry has a strong influence on the temperature dependence of the resistivity. For the specimens with smaller absolute composition deviation |x|, their resistivity ρ increased exponentially with decreasing temperature, i.e. lnρ ∝ 1/T in the whole temperature range investigated. However, for the specimens with very large |x| or those with a large |x| after HP for a longer time, the relationship ln ρ ∝ 1/T existed only in the high temperature regime; at low temperatures Mott's ln ρ ∝ T−1/4 law was observed in these specimens, indicating that large compositional deviations produced strong random potential, which led to the formation of considerable localized states. By fitting the experimental data to Mott's T−1/4 law, we estimated the density of localized states N(EF) at the Fermi level, which was found to increase with increasing composition deviation |x| in nano-Mg3+xSb2.