J. Rosenblatt

Macrostructure and Diamagnetic Response of YBa2Cu3O7-x

The experimental low-frequency magnetic response of Y-Ba-Cu-O sintered samples is astonishingly similar to that of model systems made of weakly coupled classical superconducting grains. A quantitative description of this behaviour in the framework of the coherence transition is given. It allows the extraction of important physical information, like the penetration depth λ(T), and provides explanations for the observed low-field sensitivity and temperature dependence of λ.

Coherence in 3D networks: Application to high-Tc superconductors

Three-dimensional networks are interesting in their own right and as model systems for granular superconductors. We develop this idea to discuss the key concept of granularity. It is shown that for not too small grains of size a<l∞ (bulk mean free path) the phenomena of weak localization and paracoherence set in simultaneously. Also, the often-used formula for the resistivity, ρn=Rna, that is ρn∞a, does not describe the dependence of ρn on grain size. Actually ρn∞a−1 in this limit. The diamagnetic behaviour of sintered YBa2Cu3O7 is discussed and shown to be amenable to a quantitative description in terms of critical exponents like a 3D random network. On the other hand, effects due to twin boundaries in single crystals would be expected to result in critical exponents characteristic of the X-Y model.

Current-Voltage Hyperscaling in Arrays of Josephson Junctions

We measure the voltage-supercurrent (V-Is) characteristic of three-dimensional arrays of point contacts and find V ~ Isa with a = 2.1 ± 0.2 at the critical coherence temperature Tc. This behaviour results from the following properties of the coherence transition: i) hyperscaling of critical exponents; ii) general relations satisfied by relevant parameters, in this case the supercurrent, in phase transitions; iii) the crossover exponent is 2β + ν; iv) the paracoherent excess conductivity has the same critical exponent γ as the related X-Y model susceptibility. Previously published data on granular superconductors are compatible with this description.

Scaling in superconducting ceramics

Abstract The formal analogy between the hamiltonian of anX − Y ferromagnet and the pair tunnelling hamiltonian of a granular superconductor allows us to predict a scaling behaviour for the latter. In particular, the voltage-supercurrent characteristic at T = Tc(V ≈ Isa) and the excess conductance above Tc ( σ s ≈ (T − T c ) γ ) are characterized by the critical exponents a and γ. These exponents are measured and similar values are found in both sintered YBaCuO and a granular reference system. The value a ∼- 2 corresponds to three-dimensional (3D) X − Y behaviour and leads us to exclude a possible two-dimensional (2D) Kosterlitz-Thouless transition (for which a = 3) as being responsible for the V − Is characteristic at Tc.

Fractal description of ferromagnetic glasses and random Josephson networks

Abstract The well-known analogies between X-Y ferromagnets and superconducting junction arrays are discussed in the light of data on critical exponents of the latter. The role of disorder is analysed. It is shown that, although the Harris criterion seemingly predicts that disorder is irrelevant, its application to fractal percolating clusters predicts exponent values in very good agreement with experiment.

High Tc superconductors susceptibility: A measurement of their penetration depth

Abstract The diamagnetic response of uncoupled Y-Ba-Cu-O grains imbedded in epoxy resin gives strong indication that intragrain Josephson coupling exists. The temperature dependence of the penetration depth is determined.

Fractal vortices in disordered superconductors

We measure the low-frequency magnetic response χ = χ′ + iχ″ of halogenated ceramics YBa2Cu3O7−δFx as functions of x, AC field amplitude H0 and temperature T. The field of first flux penetration displays scaling behaviour: H1(x, T) = H1(x, 0) (1 − T/Tc)ζ, with Tc the coherence temperature and ζ = 2.7 ± 0.2; in all cases H1 ⪢ Hc1 expected for the ideal material. A model where deviations from stoichiometry are assumed to result in local critical temperatures Tc(r), is described. Superconductivity is due to regions where T< Tc(r) with concentration p(T). The coherence temperature is defined by p(Tc) = pc, the percolation threshold. Critical exponents appear to be related to percolation exponents, in particular ν = 2νp/3βp≅ 1.33, in agreement with the experimental value found in granular superconductors. Expressions are found for the magnetic fields observed in Euclidean space while being due to currents restricted to fractal percolation clusters. The free energy of the resulting fractal vortices accounts for the experimental value of the exponent in the temperature dependence of H1(T).

Disorder and non-linear magnetic response of high Tc superconductors

Abstract We measure the low frequency magnetic response of YBa 2 Cu 3 O 6.7 F x (0≤× −7 T ≤ μ 0 H 0 ≤ 10 −4 T). When changing the amount of disorder (varying x) on the microscopic level we find the same non linear response with field amplitude H 0 as in granular conventional superconductors. The real part of the susceptibility appears as a universal function of H 1 (T)/H 0 where H 1 (T) is the field of first flux penetration. The power law dependence found for H 1 (T) can be understood in the framework of the coherence transition of granular superconductors with random couplings.

Critical and gaussian fluctuations in superconducting oxides

Abstract We discuss the transport properties of high-Tc cuprates as resulting from a two-step transition: a superconducting intragranular transition at T cs and an intergrandular coherence transition at Tc < T cs. The first one can be described by mean-field theory, while the second one displays scaling properties characteristic of critical phenomena. A variety of behaviours are predicted and found for the maximum supercurrent at T < Tc . Critical phase fluctuations typical of granular systems account for the excess conductivity at T ≳ Tc . The rounding of the resistive transition at T ≳ Tcs can be explained by small (gaussian) fluctuations of the order parameter amplitude, once the role of granularity is taken into account. We also propose an explanation for the apparently intrinsic granularity of superconducting oxides.

Phase transitions in granular superconducting matter and the magnetic properties of high Tc ceramics

The paracoherence-coherence transition of weakly coupled superconducting grains is analogous to the paramagnetic-ferromagnetic transition of X-Y ferromagnets. The critical exponents β, γ and ν measured in granular superconductors differ from the X-Y model calculations for translationally invariant systems. We ascribe this discrepancy to disorder. We discuss the magnetic properties of Y Ba Cu O sintered and powdered samples in the framework of the coherence transition. This approach allows us to explain the “incomplete Meissner effect” of superconducting ceramics and to show the existence of several levels of granularity; the latter however do not affect the critical behaviour.