Self-organization and 1/f noise in granular superconductors

The interplay between the widespread phenomena such as 1/f noise and self-organization of the critical state is studied both theoretically and by computer simulation using a model of multijunction SQUID exposed to an external magnetic field. It is demonstrated that the spectra of the average current in the systems of different size exhibit a broad region of 1/f noise limited only by the system size. However, the coexistence of 1/f noise and self-organization of the critical state was observed only in one two-dimensional system.     

Self-organization of the critical state in a chain of SQUIDs

The critical state of a 1D granular superconductor (modeled as a chain of SQUIDs or, in other words, a 1D Josephson-junction array) is studied on the basis of a system of differential equations for the gauge-invariant phase difference. It is established that the critical state is self-organized. It is shown that the problems of self-organization in the sandpile model and in a granular superconductor belong to the same universality class. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 9, 688–694 (10 November 1998)     

Self-organization of a critical state on complex networks

The critical dynamics of a two-threshold system with the law of conservation of the basic quantity z and in the absence of sink on a scale-free network has been studied. It has been shown that the critical state that is a set of metastable states appears in such a system. The structure of the metastable states is a set of stable clusters of nodes at which the z values are close to the positive and negative threshold values. Avalanches transforming the system from one metastable state to another state appear in the system. The absence of sink is effectively replaced by the annihilation process. The statistics of avalanches in such a system has been analyzed. It has been shown that the self-organized critical state can appear in the system.     

Self-organization in granular slurries

We report the existence of self-organization in wet granular media or slurries, mixtures of particles of different sizes dispersed in a lower density liquid. As in the case of dry granular mixtures, axial banding (alternating bands rich in small and large particles in a long rotating cylinder) and radial segregation (in quasi-2D containers) are observed in slurries. However, when compared with the dry counterpart axial segregation is significantly faster and the spectrum of outcomes is richer. Moreover, experiments with suitable fluids reveal, for the first time, the internal structure of axially segregated systems, something that up to now has been accessible only via magnetic resonance imaging experimentation.     

Direct observation of the critical state in low-κ type-II superconductors

New results on the properties of niobium and vanadium in the mixed state obtained by the neutron depolarization method are presented. Magnetization measurements were taken on several samples differing in their degree of hysteresis to obtain the characteristic fieldsH _c1,H ⁺ andH _c2 (H ⁺ denotes the field where the major hysteresis loop for one sense joins the initial magnetization curve). The depolarization is always observed to begin atH _c1 and to disappear atH ⁺. A theoretical reexamination of the critical state concept for low-κ type-II superconductors leads to the conclusion that the maximum depolarization indicates the entrance of the entire sample into the critical state. The actual value of the depolarization is shown to be a measure of the flux line lattice distortions. Furthermore, evidence for an anisotropic flux density distribution in the mixed state is presented.     

Critical currents and the critical state in superconductors with magnetic ions

The critical state model is used to derive equations that relate the additional magnetic moment (ΔM) produced by the flux pinning to the critical current density (J_c) measured in transport measurements. The equations derived for conventional superconductors can be used for superconductors that contain magnetic ions, if ΔM is replaced by ΔM/(1 + χ′(H)) where χ′(H) is the differential susceptibility. In the critical state, the field gradient has contributions from both the macroscopic supercurrents and the Amperian currents from the magnetic ions. Magnetic measurements are sensitive to both contributions. Transport measurements only characterise the macroscopic supercurrents. For superconductors which contain rare-earth elements, the J_c values calculated using hysteretic magnetisation measurements without including the term χ′(H), can be in error by factors of 7.     

Self-organization of the critical state in a two-dimensional multijunction SQUID under closed boundary conditions

A model of a closed system with self-organization is presented. This is a simplified model of a multijunction SQUID in an ac magnetic field. In our closed system, a self-organized critical state is realized on account of the fact that current dumping, which gives rise to self-organization in open systems, is replaced here by a fundamentally different mechanism — annihilation of the currents. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 2, 119–125 (25 January 1999)     

On the stability of the critical state with inhomogeneous temperature in composite superconductors

The problem of the thermal and magnetic destruction of the critical state in composite superconductors is investigated. The initial distributions of temperature and electromagnetic field are assumed to be essentially inhomogeneous. The limit of the thermomagnetic instability in quasi-stationary approximation is determined. The obtained integral criterion, unlike the analogous criterion for a homogeneous temperature profile, is shown to take into account the influence of any part of the superconductor on the threshold for critical-state instability. Received 11 October 2001 / Received in final form 30 November 2002 Published online 14 February 2003 RID="a" ID="a"e-mail: taylanov@iaph.tkt.uz     

双分散颗粒体系在临界堵塞态的结构特征

堵塞行为是颗粒体系中一种常见的现象,其力学性质与堆积结构的关联非常复杂.本文采用离散元法研究了由两种不同半径颗粒组成的二维双分散无摩擦球形颗粒体系在临界堵塞态所呈现的结构特征,讨论了大小颗粒粒径比与大颗粒百分比对临界堵塞态的影响.数值模拟结果表明,当粒径比小于1.4时,临界平均接触数与大颗粒百分比关系不大,当粒径比大于1.4时随着大颗粒百分比的增大临界平均接触数先减小再增大.而临界体积分数在粒径比小于1.8时随着大颗粒百分比的增加先减小后增大,大于1.8时又基本不随大颗粒百分比而变化.大颗粒百分比在接近0或1时,系统近似为单分散体系,临界平均接触数与体积分数基本不随半径比的增大而变化;在接近0.5时,临界平均接触数随着半径比的增大逐渐减小,而临界体积分数则是先减小后增大.文中对大-小颗粒这一接触类型的百分比也进行了探讨,其值随着大颗粒百分比的增大呈二次函数的变化趋势,粒径比对这一变化趋势只有较小的影响.     

Nonlinear dynamics of the critical state in hard superconductors and composites based on them

The nonlinear dynamics of the magnetic flux within a superconducting plate in response to the continuous rise in temperature over the course of the entire process of applying the magnetic field is investigated within the critical-state model. The results of numerical simulations based on a method developed to solve the system of Fourier and Maxwell equations with an unknown internal magnetic flux penetration boundary are compared with the corresponding analytical expressions of the isothermal theory. It is shown that the difference between the isothermal and nonisothermal models increases as the heat transfer coefficient decreases and as the rate of increase in the magnetic field strength and the transverse dimensions of the superconductor increase. The errors appearing in the isothermal approximation are very significant in the case of a thermally insulated, massive conductor. Consequently, the calculated values of the thermal losses occurring during the time period preceding the flux jump in the isothermal approximation can be significantly lower than the corresponding nonisothermal values. Zh. Tekh. Fiz. 67, 29–33 (September 1997)     

Reentrant phase transition in granular superconductors

The conditions for the appearance of a reentrant superconducting phase in granular materials are studied in mean field approximation applied to periodic models. We assume that the relevant low-lying excitation is the transfer of a Cooper pair from a grain to one of its neighbours, and neglect pair breaking. Both on-grain (U) and nearest neighbour (V) Coulomb interactions are taken into account, and the Coulomb problem is treated in Bethe-Peierls approximation. WhenV/U is not too large, reentrance is predicted ifV/U>(4+3z)^?1/2 wherez is the coordination number. This result is different from a recent criterion suggested by ?imánek, which allows reentrance only in the immediate vicinities of certain discrete values ofV/U. For strong enoughV/U, the models treated here show a transition to an ionic-salt-like charge-ordered state. Reentrant superconductivity is shown to occur also on an ionic background. In actual systems, close-packing effects partially frustrate the ionic ordering and enhance the reentrant feature.     

On the stability of the critical state in hard superconductors with a heterogeneous temperature profile

The problem of the thermal and magnetic destruction of the critical state in hard superconductors is investigated. The initial distributions of temperature and electromagnetic field are assumed to be essentially inhomogeneous. The limit of the thermomagnetic instability in quasi-stationary approximation is determined. The obtained integral criterion, unlike the analogous criterion for a homogeneous temperature profile, is shown to take into account the influence of any part of the superconductor on the threshold for critical-state instability.     

Microwave propagation through granular superconductors

It is shown that, for frequencies less than twice the energy gap, a granular superconductor in the paracoherent state may be highly transparent to electromagnetic radiation. An effective medium theory predicts the limits of concentration and grain size for which this phenomenon may be observed.     

Coherence transition in granular high temperature superconductors

We have studied experimentally the electrical conductivity and specific heat near the superconducting transition of granular samples of YBa₂Cu₃O_7−δ, YBa₂(Cu_2.98Zn_0.02)O_7−δ and GdBa₂Cu₃O_7−δ. The results show that the transition proceeds in two stages. Careful analysis of the conductivity in the regime of approach to the zero resistance state reveals the occurrence of a coherence transition, which is related to the connective nature of the granular samples. This transition occurs when the fluctuating phases of the order parameter in individual grains become long-range ordered. We obtain the exponent for fluctuation conductivity and the relevant critical temperature, T_co, which is close to the point where resistivity vanishes. The specific heat results, when analyzed as dC/dT, show a weak but reproducible cusp-like anomaly at T_co. This finding gives strong support to the interpretation of the coherence transition as a genuine critical phenomenon.     

A minimal size for granular superconductors

We investigate the minimal size of small superconducting grains by means of a Ginzburg–Landau model confined to a sphere of radius R. This model is supposed to describe a material in the form of a ball, whose transition temperature when presented in bulk form, T₀, is known. We obtain an equation for the critical temperature as a function of R and of T₀, allowing us to obtain a minimal radius of the sphere below which no superconducting transition exists. An estimate of values of minimal radii for different materials is done.     

On the critical slowing down in superconductors

The critical dynamics in superconductors without magnetic field is studied by straightforward application of the ?-expansion technique to a generalized Ginzburg-Landau model. It is shown that the dynamic critical exponent and the time dependent correlation function coincide with those obtained by the TDGL approach.