Limiting factors of normal-state conductivity in superconducting MgB₂: an application of mean-field theory for a site percolation problem

Abstract

Normal-state conductivity in polycrystalline MgB2 bulk samples having a systematically varied packing factor was studied. The packing factor dependence of phonon term resistivity Δρ(T) = ρ(T)−ρ0 was found to be well explained by the three-dimensional site percolation model. The low packing density of the samples and the wet impurity phases at grain boundaries are suggested to be the main causes of poor electrical connectivity in MgB2. Our model enables quantitative evaluations of the intrinsic resistivity inside the grains, the fraction of the active grains that can carry current and the anisotropy of the grains in polycrystalline samples. The model predicts that the anomaly suppressed connectivity in rather weak-link-free MgB2 can be understood under a scenario of a percolation problem.