Numerical study of resistivity scaling in pi junction granular superconductors

Abstract

Numerical simulations based on Monte Carlo dynamics are used to investigate the resistivity behavior of granular superconductors containing a random distribution of π junctions, as in superconducting materials with d-wave symmetry. The presence of π junctions leads to quenched in circulating currents (chiralities) and to chiral glass behavior at low temperatures, even without an external magnetic field. An XY spin glass model in the phase representation is used to determine the current-voltage characteristics and critical exponents of the resistivity transition. In two dimensions, the linear resistivity is nonzero at finite temperatures and the dynamic scaling analysis of the nonlinear resistivity is consistent with a phase transition at zero temperature. In three dimensions, we find a transition at finite temperatures below which the linear resistivity vanishes and the corresponding critical exponents are determined from the scaling analysis. The results are in good agreement with Langevin simulations in the phase representation. The dynamic exponent z is significantly different from previous results obtained in the vortex representation.Granular superconductors with d-wave symmetry, as some of the unconventional high-T c superconducting materials, can be viewed as a network of Josephson junctions with frustration effects even in zero external magnetic field [1]. Frustration arises from the presence of π junctions which introduce a phase shift of π between superconducting regions, and to half-flux quantum vortices on closed loops with an odd number of these junctions [2,3]. The magnetic properties of granular samples, arising from the orbital currents of theses vortices , have been extensively studied [1,4,5,6,7] and provide an explanation of the paramagnetic Meissner effect [8]. Nevertheless, there are also important consequences for the resistivity behavior of theses systems which also deserve detailed investigations.In a conventional granular superconductor, the phases of neighboring superconducting regions tend to be locked with zero phase shift, and a phase-coherence transition is expected for decreasing temperature into a superconducting state with vanishing linear resistivity. The critical behavior of this resistive transition is reasonable well understood both in the two dimensional limit and in three dimensions. On the other hand, for granular superconductors with a large concentration of π junctions, frustration and disorder effects leads to a vortex glassy phase and the resistive behavior is much less understood. The simplest model of the system is to consider only contributions from the Josephson coupling energy of nearest-neighbor grains,, where θ i is the phase of the local superconducting order parameter, J o > 0 and t ij = 0 or π correspond to the phase shifts of 0 and π junctions. This is equivalent to the interaction of two-component pseudo-spins S = (cos(θ), sin(θ)), coupled by ferro or antiferromagnetic interactions, respectively, which leads to an XY-spin (chiral) glass model for the granul...