The hopping diffusion model is often used to describe the motion of Brownian ratchets. On the other hand, hopping diffusion is well modeled by Parrondo's paradoxical game method. In this paper, this method is used to simulate the energy characteristics of ratchets. It is known that the most efficient ratchet models are those in which the periodic potential profile can block the backflow of particles and fluctuates for half a period. Therefore, we have considered a one-dimensional hopping diffusion model with two nonequivalent nodes in an elementary cell, the hops of a Brownian particle between which were specified by two sets of transition probabilities. These sets of probabilities corresponded to potential profiles of the desired shape, which periodically shifted relative to each other by half a period. The time dependencies of the work done by the particle against the load force (output energy) and the energy transferred to the particle when switching potentials (input energy) of the system were calculated. The ratchet efficiency (the ratio of output energy to input energy) was calculated as a function of the load force at the moments of potential switching. This value ceased to depend on the time when the process became steady. The simulation results showed that the selected sets of transition probabilities ensure high efficiency of the considered ratchets up to 70%. In this case, the dependence of the efficiency on the load force is a nonmonotonic function, the course of which is in good agreement with the known theoretical data.

The behavior of fine-grained YBa 2 Cu 3 O 6.92 HTSCs during cooling in a weak magnetic field is investigated. The magnetization of samples, the crystallite sizes is which are comparable with the magnetic field penetration depth, is comprehensively analyzed in the range below the superconducting transition temperature. When the crystallite size is smaller than 0.5 μm, vortices are shown not to be fixed to pinning centers, and the temperature dependence of magnetization is completely determined by the screening of crystallites and the temperature of appearance of intercrystallite superconducting currents.

We have studied the effect of sol–gel synthesis conditions on the structural and magnetic properties of the high-Tc superconductor YBa2Cu3Oy (y = 6.92 ± 0.02). Two low-temperature (<800°C) synthesis procedures have been used, differing in the annealing sequence and atmosphere (argon or oxygen). In one procedure, the starting mixture was annealed in an oxygen atmosphere, and the resultant nonsuperconducting tetragonal phase (X-phase) was heat-treated further. In the other procedure, synthesis was carried out in an argon atmosphere, which allowed a superconducting orthorhombic phase to be obtained even after the first anneal. At the same time, it is the former synthesis procedure which has made it possible to obtain nanoparticles and prepare a series of samples with a gradually decreasing degree of structural disorder owing to sequential two-step anneals (argon + oxygen). This approach helps understand general behavior of the structural characteristics, magnetic properties, and superconducting parameters of YBa2Cu3Oy high-Tc materials differing in the degree of structural disorder.

We consider the adiabatic mode of Brownian particle motion in a periodic potential under the action of symmetric dichotomous fluctuations of an external force F with zero mean value (rocking ratchet), in which the fluctuation frequency is much less than the inverse relaxation time of the particle in each of the states of the dichotomous process. Expressions are given for force-dependent fluxes of an adiabatic classical rocking ratchet. In the absence of thermal fluctuations, within the semiclassical approximation, analytical expressions are obtained for the rocking-ratchet tunneling flux in a sawtooth periodic potential of arbitrary asymmetry and in the potential of two sinusoids. It is shown that the tunneling flux has a linear asymptotics in modulus of small F due to (i) the absence of reverse tunneling fluxes with respect to the direction F and (ii) the root dependence of the integrand of the Gamow formula on the potential energy. The main parameters of the model are the energy barrier V0 and the period L of the potentials, as well as the rocking force F and the asymmetry parameter ξ = l / L of the sawtooth potential with the width of one of its teeth equal to l. It is shown that the direction of quantum ratchet motion is opposite to the motion direction of the corresponding classical ratchet in a limited range of values of the rocking force |F| L / V0 < αc , where the parameter αc changes from the value α1 = (√5 − 1) / 2 ≈ 0.618 for the extremely asymmetric sawtooth potential (ξ = 1) to the value α2 = 2 / 3 ≈ 0.667 for the symmetric potential (ξ= 1 / 2). In the range of values α2 < αc < α2, the sign of the tunneling flux changes with the change in the asymmetry parameter ξ. Numerical calculations for the potential of two sinusoids corresponding to the effective value ξ ≈ 0.655 of the asymmetry lead to similar results with αc ≈ 0.81.

The influence of structural inhomogeneity on a superconducting gap near d-wave nodes is co-nsidered for optimally doped YBa2Cu3O6.92 HTSCs. To this aim, specific heat in the temperature range of T = 2‒10 K at magnetic fields H = 0–9 T is analyzed for a series of fine-crystalline samples with different degrees of controlled structural disorder. Information about specific features of the superconducting gap near d-wave nodes in structurally disordered samples is obtained. It is shown that d-wave nodes (typical of an ideal crystal structure) change under the influence of structural disorder with the formation of small Fermi arcs, which are not covered by the superconducting gap, in the vicinity of the nodal point at T $$ \ll $$ Tc. Note that the gap is retained at T ≤ Tc in other directions of the Brillouin zone and coexists with Fermi arcs. This transformation is accompanied by an increase in the nodal slope, a decrease in the Volovik effect, and creation of the metal-type linear term γ(0)T in the temperature dependence of the specific heat, which should not exist for superconductors with an ideal crystal structure; its nature has not yet been established.

The effect of structural inhomogeneity on the superconducting gap near d-wave for optimally doped high-Tc superconductors YBa2Cu3O6.92 sites is considered. For this purpose, the heat capacity was investigated in the temperature range T = 2-10 K and in magnetic fields H = 0-9 T for a series of fine-crystalline samples with different degrees of controlled structural disordering. The information on the features of superconducting gap near d-wave sites in structurally disordered samples is obtained. It is shown that the d-wave sites inherent in an ideal crystal structure under the influence of structural disorder are modified with the formation of small Fermi arcs in the vicinity of nodal points at T << Tc, not covered by a superconducting gap. In this case, the gap itself remains at T ≤ Tc in other directions of the Brillouin zone and coexists with the Fermi arcs. This transformation is accompanied by an increase in the steepness of the nodal slope, a decrease of the Volovik effect, and the generation of a linear term γ (0) T of the metallic type in the temperature dependence of heat capacity, which should not be present in superconductors with an ideal crystal structure and the nature of which has not yet been established.

A technique based on the sol–gel technology is developed for the synthesis of fine-crystalline YBa2Cu3O6.92 (Tc = 91.5 K) high-temperature superconductors (HTSCs), including the step-by-step annealing of the samples in tablet form at the annealing temperature Tann = 750°C in an argon atmosphere. Having the same microstructure with the average crystallite size $$\left\langle D \right\rangle $$ = 200 nm, the sol–gel samples exhibit different magnetic and thermodynamic properties, depending on the number of anneals in argon. Comparison of the characteristics for sol–gel and mechanoactivated fine-crystalline samples of the same composition made it possible to make an assumption about the implementation of incomplete atomic ordering in sol–gel samples at the first stage of annealing with an increase in the degree of structural ordering during the next two stages. This may be the main reason for the change in the physical characteristics of the HTSC sol–gel samples structured at the nanoscale level, depending on the number of annealings in an argon atmosphere.

The evolution of the Schottky anomalies in the temperature dependence of the specific heat (in the temperature range T = 2–10 K and the magnetic field range H = 0–9 T) of polycrystalline YBa 2 Cu 3 O y HTSCs is studied when the oxygen content in coarse-crystalline samples changes and when the degree of structural disordering in optimally doped fine-crystalline samples of the same compound changes. The number of paramagnetic centers with uncompensated spin moments, which generate the Schottky anomalies, and the splitting of the lower energy levels are estimated. A correlation between these parameters and both the number of oxygen vacancies in chain planes and the method of oxygen ordering in chains is found. The experimental data are compared with the results of studying the magnetic susceptibility at T > T c in the same samples. Based on this comparison, we can conclude that the nature of the Schottky centers is related to the formation of paramagnetic centers at breaks in the Cu1–O4 copper–oxygen chains in the basal planes of the crystal structure.

A comparative study of the magnetization and static magnetic susceptibility of high-temperature superconductors (HTSC) YBa 2 Cu 3 O y synthesized by two variants of the sol–gel method with different average sizes of crystallites 〈 D 〉 ranging 0.4–2 μm has been performed in constant magnetic fields ( Н ≤ 6 kOe). It has been shown that the different annealing temperatures and times, at which their crystal structure is formed, change both the average sizes of crystallites 〈 D 〉 and the sizes of the structural homogeneity regions 〈 l 〉 and, at the same time, the magnetic field penetration depth (λ) and the coherence length (ξ). As a result, such parameters as 〈 D 〉 ~ λ and 〈 l 〉 ~ ξ become comparable, leading to a change in the physical characteristics of HTSCs. It has also been shown that the superconducting transition temperature T c determined from the measurements of magnetic characteristics in constant magnetic fields remains within values optimal for superconductivity ( T c ≈ 92 K) in the case of an optimal number ( y ) of oxygen atoms, which determine the levels of charge doping for a given compound.

The low-temperature (2 K ≤ T ≤ 10 K) specific heat of the series of fine-crystalline samples of YBa 2 Cu 3 O y high- T c superconductor optimally doped with oxygen and having different degrees of nanoscale structural inhomogeneity has been studied at the applied magnetic field H = 8 T. The result are compared to those obtained for the equilibrium polycrystalline samples with different oxygen contents y . Information on the quasiparticle excitations in the magnetic field near d -wave nodes of the gap function is obtained. The changes introduced by the structural inhomogeneity to the nodal gap slope (νΔ) in the k -space, which is a key parameter of high- T c superconductors, have also been studied. It is found that νΔ increases with the degree of structural disorder, but the superconducting transition temperature remains nearly the same ( T c = (91.5 ± 0.5) K). It is shown that this is possible if superconductivity is suppressed not only at the nodal point but also near it (owing to the structural disorder). In this case, the density of states in such parts of the Fermi surface is nonzero even at zero temperature, promoting the existence of the linear in temperature contribution to the specific heat (~γ(0) T ), which is characteristic of metals.

A comparative study of the low-temperature specific heat for two types of YBa2Cu3O y high-T c superconductor samples is performed within the temperature range of 2−10 K. The samples of the first type are fine-crystalline optimally doped ones with different degrees of nanoscale structural inhomogeneity. The second type includes coarse-crystalline equilibrium samples with different hole doping levels. A similarity in the behavior of different contributions to the specific heat for structurally inhomogeneous and underdoped samples is revealed. The samples of both types exhibit a metal-like contribution linear in temperature to the specific heat ~γT, which is not characteristic of the superconducting phase. It is found that this contribution moderately grows with the decrease in the oxygen content, whereas with the increase in the structural inhomogeneity, such growth of the linear contribution (γT) becomes anomalously large. This leads to the conclusion about the coexistence of metallic and superconducting states in the bulk of the samples under study. Such common feature of electron systems could be related to the formation of the pseudogap regime. It is demonstrated that this regime suppresses just the superconducting states, leaving intact the metallic ones.

Static magnetic susceptibility χ(T) in the normal state (T c ≤ T ≤ 400 K) and specific heat C(T) near temperature T c of the transition to the superconducting state are experimentally studied for a series of fine crystalline samples of high-temperature YBa2Cu3O y superconductor, having y and T c close to optimal but differing in the degree of nanoscale structural disordering. It is shown that under the influence of structural disordering, there is enhancement of anomalous pseudogap behavior of the studied characteristics and a significant increase in the width of the pseudogap.

Experimental evidence for the existence of chain paramagnetic Curie-type contributions to the temperature dependence of static magnetic susceptibility χ(T) in the normal (nonsuperconducting) state is obtained for a series of pure YBa2Cu3O6 + δ high temperature superconductors with different oxygen contents (0.6 < δ ≤ 1). It is shown that the chain contribution is obvious on χ(T) curves only in the T < 150K range of temperatures, grows along with the number of oxygen vacancies in Cu1–O4 chains, and depends on the ordering of these vacancies.