Theory of percolative conduction in polycrystalline high-temperature superconductors

Abstract

Conduction in bulk polycrystalline high-${T}_{c}$ superconductors with relatively high critical currents has been shown to be percolative. This phenomenon is due to weak links at grain boundaries. These weak links are the major limiting factor for technological applications that require high-current densities. We formulate a model of these materials that can be reduced to a nonlinear resistor network. The model is solved by analytical approximations and a new numerical technique. The numerical technique is variational, which makes it capable of solving a wide variety of nonlinear problems. The results show that the presence of a distribution of critical currents in the sample does not erase all information about the dissipative electrical properties of individual boundaries. This means that an unambiguous connection can be made between the $I\ensuremath{-}V$ characteristics at the microscopic level and the macroscopic electrical properties.