Properties of granular high-Tcsuperconductors in an effective medium theory

Abstract

The authors consider the transport, electromagnetic and thermodynamic properties of a granular high-T_c superconductor by constructing a model of weakly coupled (Josephson junctions) superconducting and normal grains. They start by using an effective medium theory (EMT), for the conductivity and susceptibility, which is supplemented by London electrodynamics for the superconducting grains, in the limit of weak magnetic field and zero transport current. Next the authors assume a Gaussian distribution of junction resistances R, with mean R_o and variance sigma , which determines the Josephson coupling energy between grains. The criterion that this energy must be greater than kT for superconducting clusters enables them to determine the superconducting fraction c_s as a function of temperature. With this they complete the determination of the conductivity and susceptibility of their model. The authors also discuss the specific heat, neglecting fluctuations, which is directly proportional to c_s, in their approximation. Throughout this paper, they adopt the Ginzburg-Landau (GL) expressions for the energy gap Delta (order parameter), which is valid near T_c and for the specific heat C_H, but they allow for possible deviations of numerical coefficients in these expressions from the Bardeen, Cooper and Schrieffer (BCS) microscopic theory, by introducing phenomenological parameters. The authors find, in accord with experiments, differences between the temperatures of zero resistivity, of resistivity drop and for maximum Meissner effect.