A simple model for the resistive-non-resistive transition in granular superconductors

A simple theory predicts two sharp transitions for a regular granular superconductor. The first is when the grains become superconducting and the second when the resistance vanishes. Recent experiments on NbN and Nb₃Ge are compared with the theory.     

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.     

Spin-size disorder model for granular superconductors with charging effects

A quantum pseudo-spin model with random spin sizes is introduced to study the effects of charging-energy disorder on the superconducting transition in granular superconducting materials. Charging-energy effects result from the small electrical capacitance of the grains when the Coulomb charging energy is comparable to the Josephson-coupling energy. In the pseudo-spin model, randomness in the spin size is argued to arise from the inhomogeneous grain-size distribution. For a particular bimodal spin-size distribution, the model describes percolating granular superconductors. A mean-field theory is developed to obtain the phase diagram as a function of temperature, average charging energy and disorder.     

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.     

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.     

Exact diagonalization studies on two-band minimal model for iron-based superconductors

In order to explore a superconducting mechanism on iron-based superconductors, we numerically study a two-band minimal model considering two degenerate d_xz and d_yz orbitals on Fe atom. We perform exact diagonalization on a two-band and two-leg square ladder totally composed of 10 lattice sites, which is computationally equivalent to 4-leg 20-sites square-Hubbard-ladder. Consequently, we find that a robust pairing occurs in a wide parameter range when the intra-orbital repulsive interaction becomes smaller than the inter-orbital one. Moreover, the obtained binding energy can grow into much larger value than that obtained in the single band Hubbard model depending on the parameter range.     

Self-organization of the critical state in granular superconductors

The critical state in granular superconductors is studied using two mathematical models: systems of differential equations for the gauge-invariant phase difference and a simplified model that is described by a system of coupled mappings and in many cases is equivalent to the standard models used for studying self-organized criticality. It is shown that the critical state of granular superconductors is self-organized in all cases studied. In addition, it is shown that the models employed are essentially equivalent, i.e., they demonstrate not only the same critical behavior, but they also lead to the same noncritical phenomena. The first demonstration of the existence of self-organized criticality in a system of nonlinear differential equations and its equivalence to self-organized criticality in standard models is given in this paper.     

Nodal Cooper-pair stabilized phase dynamics in granular d-wave superconductors

Scanning tunneling microscope measurements on single crystals of Bi2Sr2CaCu2O8+x materials have shown that the d-wave superconductivity in cuprates has nanoscale inhomogeneities and is still robust in spite of their presence. We study the dynamics of Josephson coupling between such granular d-wave superconductors, focusing on the effect of nodal Cooper pairs and disorder. We find that the nodal Cooper pairs give rise to a power-law Josephson coupling which leads to the stabilization of the superconducting phase. Our findings suggest that the d-wave superconductivity in an array of grains is unexpectedly robust against a disordering transition, as observed in the experiments. Furthermore, we predict the existence of a planar Josephson-plasmon mode with characteristic frequency that decreases with temperature.     

Nonlocal effect on the fluctuation conductivity of granular superconductors

The theory of fluctuation conductivity for small impurity concentration is developed. We consider all fluctuation corrections of the first order in the case of dilute impurity concentration including nonlocal electron scattering in the clean superconductor. By using Green’s function technique we first calculate the Cooperon (impurity vertex) and fluctuation propagator K(Ω_k, q) in the presence of impurities. We show that in the clean limit the density-of-states quantum corrections are canceled by the Maki–Thompson (MT) term and it results in the reduction of the total fluctuation correction in clean case to the Aslamazov–Larkin (AL) term only.     

Finite size effects in layered superconductors

We investigate the transition temperature of layered superconductors by considering a stack ofL _z superconducting layers, separated by insulating material. We adopt a pairing Hamiltonian, invoke the variational principle and solve the resulting gap equations numerically. Our results confirm previous weak coupling and Ginzburg-Landau treatments and reveal a rise ofT _c withL _z and saturation at the bulk transition temperature. Thus, the rise ofT _c is traced back to a finite size effect, corresponding to a crossover from 2-d to 3-d superconductivity. The results also reveal a sizeable variation of the gap along the stack with pronounced variation at the ends.     

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.     

Flux trapping in granular superconductors studied by EPR technique

The sensitive and contactless method of microwave absorption has been applied in investigation of the magnetic properties of high-temperature superconductor (HTS). The method allowed the analysis of flux trapping in low magnetic field as a function of texture of the samples.     

Effect of charging energy on transition temperature of granular superconductors

The effect of the zero-point fluctuations of the phase on the transition temperature T_c of a granular superconductor is calculated using a model which takes into account the short-range part of the charging energy. A self-consistent mean field theory predicts a critical value of the ratio of the Josephson coupling constant to the charging energy and the existence of two values of T_c, indicating the possibility of reentrance into normal state at the lower one.